View the Guide C 2007 document
Reference data
CIBSE Guide C
Corrections and Amendments
Guide C: Reference Data (2007)
Page 4-58: caption to Table 4.125 should read: '90° swept tees, rectangular,
diverging flow: values for ...'
Page 4-63: Table 4.A1.1: units for kinematic viscosity (n) should be 10-6 m2·s-1
The rights of publication or translation are reserved.
No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means
without the prior permission of the Institution.
© April 2007 The Chartered Institution of Building Services
Engineers London
Registered charity number 278104
ISBN: 978-1-903287-80-4
This document is based on the best knowledge available at
the time of publication. However no responsibility of any
kind for any injury, death, loss, damage or delay however
caused resulting from the use of these recommendations can
be accepted by the Chartered Institution of Building Services
Engineers, the authors or others involved in its publication.
In adopting these recommendations for use each adopter by
doing so agrees to accept full responsibility for any personal
injury, death, loss, damage or delay arising out of or in
connection with their use by or on behalf of such adopter
irrespective of the cause or reason therefore and agrees to
defend, indemnify and hold harmless the Chartered
Institution of Building Services Engineers, the authors and
others involved in their publication from any and all liability
arising out of or in connection with such use as aforesaid
and irrespective of any negligence on the part of those
indemnified.
Typeset by CIBSE Publications
Printed in Great Britain by Page Bros. (Norwich) Ltd.,
Norwich, Norfolk NR6 6SA
Note from the publisher
This publication is primarily intended to provide guidance to those responsible for the
design, installation, commissioning, operation and maintenance of building services. It is
not intended to be exhaustive or definitive and it will be necessary for users of the guidance
given to exercise their own professional judgement when deciding whether to abide by or
depart from it.
Foreword
CIBSE Guide C was comprehensively updated for the 2001 edition. Although basic physical
data do not change with time, the refinement of measurement and calculation techniques
and further research make regular review essential. Many of the changes to this edition are
therefore small incremental changes, reflecting such refinement.
It was however recognised that section 4, Flow of fluids in pipes and ducts, while heavily
revised for the 2001 edition, was at that time unable to take account of the latest European
research. The report of this research has now been obtained and its results distilled into
this edition of Guide C. The opportunity has also been taken to rewrite and clarify the text
and to delete many pages of tabular data providing pre-calculated pressure drops through
pipes. It was felt that these tables have outlived their usefulness now that accurate pressure
drops can easily be calculated using spreadsheets or computer programs. Such a spreadsheet
is provided on the CD-ROM that accompanies this Guide.
I would like to express my thanks to all the volunteer authors who agreed to review and
update their work and particularly to Peter Koch for his effort and enthusiasm in revising
section 4. I would also like to thank all contributors, reviewers and CIBSE staff for their
valuable contributions.
Finally I hope that you will continue to find this Guide a useful and authoritative source of
reference and guidance.
Paul Compton
Chairman, CIBSE Guide C
Authors, contributors and acknowledgements
Chapter 1: Properties of humid air
Principal author (2001 and 2007 editions)
W P Jones (consultant)
The tables of psychrometric data are reprinted unchanged from the 1986 edition of Guide
C and were prepared by a task group, see below.
Task group members
W P Jones (Chairman) (consultant)
J F Armour
B G Lawrence
Chapter 2: Properties of water and steam
The tables of data are reprinted unchanged from the 1986 edition of Guide C.
Chapter 3: Heat transfer
This chapter is reprinted from the 2001 edition; the authors and contributors were as
follows.
Principal authors (2001 edition)
D L Loveday (Loughborough University)
A H Taki (De Montford University)
Contributors (2001 edition)
H B Awbi (University of Reading)
P D Compton (Colt International Ltd.)
R M Harris (Centre for Window and Cladding Technology)
M J Holmes (Ove Arup & Partners International Ltd.)
B P Holownia (Loughborough University)
J Moss (Ove Arup & Partners International Ltd.)
T Muneer (Napier University)
H K Versteeg (Loughborough University)
Acknowledgements
American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc.
British Standards Institution
The McGraw-Hill Companies
Pearson Education Ltd.
Chapter 4: Flow of fluids in pipes and ducts
Principal author (2001 and 2007 editions)
P Koch (Université Joseph Fourier, Grenoble; Coventry University)
Contributor (2001 edition)
F Sprenger (Coventry University)
Acknowledgements
American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc.
Centre Technique des Industries Aérauliques et Thermiques
Coventry University, School of Science and the Environment
Sheet Metal and Air Conditioning Contractors’ National Association
Shell Chemicals, Rotterdam
Chapter 5: Fuels and combustion
Principal author (2001 and 2007 editions)
M R I Purvis (Chairman) (University of Portsmouth)
Task group members/Principal authors (2001 edition)
M R I Purvis (Chairman) (University of Portsmouth)
R Dando (Coal Research Establishment)
M Drew (BP Amoco plc)
R J Harris (Advantica Technologies Ltd.)
K Mildren (University of Portsmouth)
Acknowledgement
British Standards Institution
Chapter 6: Units, standard and mathematical data
Principal author (2001 and 2007 editions)
P D Compton (Colt International Ltd.)
Editor
Ken Butcher
CIBSE Publishing Manager
Jacqueline Balian
Contents
1
2
3
Properties of humid air
1-1
1.1
Psychrometric data
1-1
1.2
CIBSE psychrometric chart (–10 to +60 °C)
1-4
1.3
CIBSE psychrometric chart (10 to 120 °C)
1-4
References
1-4
Tables of psychrometric data
1-7
Properties of water and steam
2-1
2.1
2-1
Introduction
References
2-1
Tables of data
2-2
Heat transfer
3-1
3.1
Introduction
3-1
3.2
Heat transfer principles
3-3
3.3
Heat transfer practice
References
4
5
3-14
3-36
Flow of fluids in pipes and ducts
4-1
4.1
Introduction
4-1
4.2
Notation
4-1
4.3
Fluid flow in straight pipes and ducts
4-2
4.4
Components and fittings
4-7
4.5
Flow of water in pipes
4-8
4.6
Flow of steam in pipes
4-10
4.7
Natural gas in pipes
4-10
4.8
Air flow in ducts
4-10
4.9
Pressure loss factors for components and fittings
4-18
4.10
Pressure loss factors for pipework components
4-18
4.11
Pressure loss factors for ductwork components
4-27
References
4-60
Bibliography
4-61
Appendix 4.A1: Properties of various fluids
4-63
Appendix 4.A2: Pipe and duct sizing
4-65
Appendix 4.A3: Capacity K, and complex networks
4-69
Appendix 4.A4: Steam flow in pipes
4-70
Appendix 4.A5: Compressible flow
4-74
Fuels and combustion
5-1
5.1
Introduction
5-1
5.2
Classification of fuels
5-1
5.3
Primary fuels
5-1
5.4
Secondary fuels
5-2
5.5
Specification of fuels
5-2
5.6
Combustion data
5-8
5.7
Stack losses
5-10
References
5-11
Bibliography
5-11
6
Units, standard and mathematical data
6-1
6.1
Introduction
6-1
6.2
The International System of Units (SI)
6-1
6.3
Quantities, units and numbers
6-4
6.4
Metrication in the European Union
6-5
6.5
Conversion factors
Bibliography
Index
6-6
6-14
I-1
1-1
1
Properties of humid air
1.1
Psychrometric data
1.2
CIBSE psychrometric chart (–10 to +60 °C)
1.3
CIBSE psychrometric chart (10 to 120 °C)
Psychrometric tables
1.1
Psychrometric data
1.1.1
Basis of calculation
The relevant specific property of moist, unsaturated air is
determined by adding a proportion of the property of
saturated water vapour to the same property of dry air, on
a mass basis.
The method of formulation suggested by Goff and
Gratch(1,2), based on the ideal gas laws with a modification
to take account of intermolecular forces, has been adopted
for calculating the thermodynamic properties of moist air.
This approach remains in line with current practice(3,4).
The thermodynamic properties of dry air and saturated
water vapour are well established and, although more
recent research work(4–6) has been done, the results are not
significantly different from those obtained in earlier
work(7,8). Hence the thermodynamic properties of dry air
and water vapour, determined by the National Bureau of
Standards(7) and the National Engineering Laboratory(8),
have been retained for the evaluation of the thermodynamic properties of moist air.
Since the properties of dry air and saturated water vapour
are accurately known, the properties of a mixture of the
two can be established for the saturated case. For the
enthalpy and specific volume of moist air, at a condition
other than saturated, the method is exemplified by the
following equations:
h = ha + μ (hs – ha) / 100
(1.1)
v = va + μ (vs – va) / 100
(1.2)
where h is the specific enthalpy of moist air (kJ·kg–1 dry
air), ha is the specific enthalpy of dry air (kJ·kg–1), μ is the
percentage saturation (%), hs is the specific enthalpy of
saturated moist air (kJ·kg–1 dry air), v is the specific
volume of moist air (m3·kg–1 dry air), va is the specific
volume of dry air (m3·kg–1) and vs is the specific volume of
saturated moist air (m3·kg–1 dry air).
A consequence of this is that the humidity of moist air is
expressed as percentage saturation (defined in terms of the
mass of water vapour present), rather than relative
humidity (defined in terms of vapour pressure). The
details of the psychrometric calculations are given in
references 9, 10 and 11.
1.1.2
Standards adopted
All data are tabulated for an internationally agreed
standard atmospheric pressure(12) of 101.325 kPa.
The zero datum adopted by the National Engineering
Laboratory(8) for the expression of the thermodynamic
properties of steam is the triple point of water, +0.01 °C.
The zero datum for the specific enthalpies of both dry air
and liquid water has been taken here as 273.15 K (0 °C).
1.1.3
Formulae used for calculations
Saturated vapour pressure over water(8)
log ps = 30.59051 – 8.2 log (θ + 273.16)
+ 2.4804 × 10–3 (θ + 273.16)
– [3142.31 / (θ + 273.16)]
(1.3)
where ps is the saturated vapour pressure over water at
temperature θ (kPa), θ is the temperature, greater than or
equal to 0 °C (°C).
1-2
Reference data
Saturated vapour pressure over ice(7)
log ps = 9.538 099 7 – [2 663.91 / (θ + 273.15)]
or:
(1.4)
where ps is the saturated vapour pressure over ice at
temperature θ, less than 0 °C (kPa).
pv = psc – 101.325 B (θ – θ s′c)
(1.10)
where psc is the saturated vapour pressure at temperature
θ s′c (kPa), B is a coefficient (K–1) and θ s′c is the screen wet
bulb temperature (°C).
Values of B are as follows:
Moisture content
B = 7.99 × 10–4 K–1 when θ s′c ≥ 0 °C
0.62197 fs ps
gs = ——————
101.325 – fs ps
(1.5)
where gs is the moisture content of saturated moist air
(kg·kg–1 dry air) and fs is a dimensionless enhancement
factor(1–4,11).
Percentage saturation
100 g
μ = ——–
gs
(1.6)
where μ is the percentage saturation (%) and g is the
moisture content of unsaturated moist air (kg·kg–1 dry air).
Vapour pressure of water vapour in unsaturated moist air
pa g
pv = ——————–
fs (0.62197 + g)
(1.7)
where pv is the vapour pressure of superheated water
vapour in unsaturated moist air (kPa) and pa is the
atmospheric (barometric) pressure (kPa).
Relative humidity
100 pv
φ = ———
ps
B = 7.20 × 10–4 K–1 when θ s′c < 0 °C
Adiabatic saturation temperature
hfg (gsa – g)
θ * = θ – —————
(cpa + g cps)
(1.11)
where θ * is the adiabatic saturation temperature (°C), hfg
is the latent heat of evaporation of water at temperature θ *
(kJ·kg–1), gsa is the moisture content of saturated air at
temperature θ * (kg·kg–1 dry air), g is the moisture content
of moist air at the particular psychrometric state (kg·kg–1
dry air), cpa is the mean specific heat capacity of dry air
between temperatures θ and θ * (kJ·kg–1·K–1) and cps is the
mean specific heat capacity of water vapour between
temperatures θ and θ * (kJ·kg–1·K–1).
In the case of the adiabatic saturation temperature above
ice, hfg is replaced by hig , the latent heat of fusion of water
at a temperature θ *.
Dew-point
For a particular psychrometric state, equation 1.7 is used
to calculate the vapour pressure. An iterative technique is
then used with equation 1.3 or 1.4 to determine the
temperature for which the calculated vapour pressure is a
saturated vapour pressure.
(1.8)
Specific volume
where φ is the relative humidity (%).
82.0567 (273.15 + θ )
v = —————————————
28.966 (101.325 – pv) / 101.325
[
Wet bulb temperature
Knowing the value of the vapour pressure, pv , from
equation 1.7 the wet bulb temperature is derived from the
following equations by an iterative technique:
pv = psl – 101.325 A (θ – θ s′l )
]
– [Aaa xa2 + 2 Aaw xa (1 – xa) + Aww (1 – xa)2]
(1.12)
where psl is the saturated vapour pressure at temperature
θ ′s l (kPa), A is a coefficient (K–1), θ is the dry bulb
temperature (°C) and θ ′s l is the sling or mechanically
aspirated wet bulb temperature (°C).
where v is the specific volume (m3·kg–1 dry air), θ is the
dry bulb temperature (°C), Aaa is the second virial
coefficient for dry air(4) (m3·kg–1), Aaw is the interaction
coefficient for moist air(4) (m3·kg–1), Aww is the second
virial coefficient for water vapour (m3·kg–1) and xa is the
mole fraction of dry air.
Values of A are as follows:
The mole fraction of dry air, xa , is given by:
A = 6.66 × 10–4 K–1 when θ s′l ≥ 0 °C
A = 5.94 ×
10–4
K–1
when θ s′l < 0 °C
(1.9)
0.62197
xa = —————–
0.62197 + g
(1.13)
Properties of humid air
1-3
In the original work(1,2) and in later research(4), a third
virial coefficient for water vapour (Awww ) appears in
equation 1.12 but it is complicated to calculate and its
influence is insignificant. It is ignored here, without any
loss of accuracy.
Equation 1.2 yields answers of adequate precision and is
easier to use than equation 1.12.
Specific enthalpy
h = ha + g hg
(1.14)
where h is the specific enthalpy of moist air (kJ·kg–1 dry
air), ha is the specific enthalpy of dry air(7) (kJ·kg–1), g is
the moisture content (kg·kg–1 dry air) and hg is the specific
enthalpy of water vapour at the dry bulb temperature(8)
(kg·kg–1 dry air).
Equation 1.1 gives answers having the same accuracy as
those obtained from equation 1.14 and is simpler to use.
1.1.4
hence are suitable for the whole of the UK. For pressures
outside these limits an application of the ideal gas laws
will give answers of a little less accuracy. Better answers
may be obtained by the use of equations 1.15 and 1.16.
0.624 ps
gs = ——————
(pa – 1.004 ps)
(1.15)
(0.287 + 0.461 g) (273.15 + θ )
v = —————————————
pa
(1.16)
Corrections to specific enthalpy may be taken from Table
1.1.
Figure 1.1, which gives the relationship between height
above sea level and barometric pressure, is drawn from the
equation:
pa = 101.325 exp[(–9.81 ρ z) / (101 325)]
(1.17)
where pa is the particular atmospheric (barometric)
pressure (kPa), ρ is the density of air (kg·m–3) and z is the
altitude above sea level (m).
Psychrometric properties at
non-standard barometric
pressures
The tabulated psychrometric data are accurate within the
range of barometric pressure from 95 kPa to 105 kPa and
Alternatively, the standard relationship(12) for altitude,
atmospheric pressure and temperature may be used. This
is reproduced in Table 1.2.
Table 1.1 Corrections to specific enthalpy at non-standard pressures
Approximate additive corrections to specific enthalpy (/ kJ·kg⫺1 dry air) at stated barometric pressure / kPa
Adiabatic saturation
temperature / °C
82.5
85.0
87.5
90.0
92.5
95.0
97.5
101.325
102.5
30
29
28
27
26
16.90
15.90
14.95
14.00
13.05
14.23
13.40
12.58
11.78
11.02
11.68
11.00
10.30
9.65
9.03
9.29
8.72
8.18
7.67
7.18
6.95
6.55
6.16
5.80
5.44
4.80
4.57
4.30
4.05
3.82
2.86
2.70
2.54
2.40
2.27
0
0
0
0
0
⫺0.82
⫺0.77
⫺0.72
⫺0.68
⫺0.64
25
24
23
22
21
12.20
11.43
10.68
10.00
9.37
10.28
9.64
9.03
8.45
7.92
8.42
7.90
7.40
6.93
6.50
6.70
6.30
5.88
5.51
5.18
5.12
4.80
4.43
4.20
3.92
3.58
3.36
3.15
2.94
2.74
2.14
2.00
1.86
1.73
1.61
0
0
0
0
0
⫺0.60
⫺0.56
⫺0.52
⫺0.48
⫺0.45
20
19
18
17
16
8.77
8.22
7.73
7.25
6.79
7.42
6.95
6.49
6.09
5.68
6.10
5.70
5.35
5.00
4.65
4.84
4.53
4.24
3.97
3.72
3.65
3.43
3.20
3.00
2.80
2.55
2.39
2.23
2.07
1.94
1.50
1.40
1.30
1.21
1.13
0
0
0
0
0
⫺0.42
⫺0.39
⫺0.37
⫺0.35
⫺0.32
15
14
13
12
11
6.33
5.90
5.50
5.13
4.78
5.32
4.95
4.60
4.30
4.04
4.34
4.07
3.80
3.53
3.28
3.48
3.24
3.03
2.82
2.62
2.62
2.44
2.28
2.12
1.97
1.82
1.70
1.60
1.50
1.40
1.07
1.00
0.93
0.86
0.80
0
0
0
0
0
⫺0.30
⫺0.28
⫺0.26
⫺0.24
⫺0.22
10
9
8
7
6
4.44
4.15
3.88
3.62
3.40
3.77
3.51
3.30
3.08
2.88
3.08
2.88
2.68
2.51
2.37
2.46
2.30
2.14
2.00
1.87
1.82
1.70
1.60
1.50
1.40
1.30
1.21
1.12
1.06
1.00
0.74
0.70
0.66
0.62
0.59
0
0
0
0
0
⫺0.20
⫺0.20
⫺0.19
⫺0.19
⫺0.18
5
4
3
2
1
3.20
3.06
2.92
2.78
2.65
2.72
2.60
2.47
2.36
2.25
2.23
2.10
2.02
1.94
1.86
1.74
1.64
1.59
1.54
1.49
1.31
1.24
1.19
1.15
1.10
0.92
0.88
0.84
0.80
0.76
0.56
0.53
0.50
0.48
0.46
0
0
0
0
0
⫺0.17
⫺0.17
⫺0.16
⫺0.16
⫺0.15
0
2.52
2.16
1.79
1.44
1.08
0.72
0.44
0
⫺0.15
1-4
Reference data
1.0
The wet-bulb values shown are those read from a sling or
mechanically aspirated psychrometer and lines of
percentage saturation are plotted instead of relative
humidity. Within the comfort zone, there is no practical
difference between percentage saturation and relative
humidity. In any case, the difference diminishes as
saturated or dry conditions are approached.
Barometric pressure / Pa
0.9
0.8
The psychrometric data used were taken from the tables of
the properties of humid air presented in this chapter of
CIBSE Guide C.
0.7
0.6
1.3
0.5
0
1000
2000
3000
Altitude / m
4000
5000
The psychrometric chart for 10 to 120 °C has been based
on the ideal gas laws. This does not give a significant
difference when compared with a chart constructed using
more accurate data, based on the method of Goff and
Gratch(1,2). The principles of calculation and drawing are
detailed elsewhere(14).
Figure 1.1 Variation of barometric pressure with altitude
Table 1.2 Standard atmospheric data for altitudes to
10 000 m
Altitude / m
Temperature / °C
Pressure / kPa
–500
0
500
1000
18.2
15.0
11.8
8.5
107.478
101.325
95.461
89.875
1500
2000
2500
3000
5.2
2.0
–1.2
–4.5
84.556
79.495
74.682
70.108
4000
5000
6000
7000
–11.0
–17.5
–24.0
–30.5
61.640
54.020
47.181
41.061
8000
9000
10000
–37.0
–43.5
–50.0
35.600
30.742
26.436
References
Atmospheric pressures and temperatures from –5000 m to
+11 000 m may be accurately calculated(3) using the
following equations:
pa = 101.325 (1 – 2.25577 × 10–5 z)5.2559
(1.18)
θ = 15 – 0.0065 z
(1.19)
where pa is the barometric pressure (kPa), θ is the atmospheric temperature (°C) and z is the altitude above sea
level (m).
1.2
CIBSE psychrometric chart
(10 to 120 °C)
CIBSE psychrometric chart
(–10 to +60 °C)
The chart has been designed(13) and constructed using the
two fundamental properties of mass (moisture content)
and energy (specific enthalpy) as linear co-ordinates.
Other physical properties are not then shown as linear
scales(13,14). The 30 °C dry-bulb line has been constructed
at right angles to lines of constant moisture content,
which are horizontal. The scale of specific enthalpy is
obliquely inclined to the vertical scale of moisture
content. In this way, lines of constant dry bulb temperature are approximately vertical, diverging slightly on each
side of the 30 °C line, and the traditional appearance of the
chart is preserved.
1
Goff J A and Gratch S ‘Thermodynamic properties of moist air’
Trans. ASHVE 51 125–164 (1945)
2
Goff J A ‘Standardisation of thermodynamic properties of
moist air’ Trans. ASHVE 55 459–484 (1949)
3
Psychrometrics ch. 6 in ASHRAE Handbook Fundamentals
(Atlanta, GA: American Society of Heating, Refrigerating and
Air-Conditioning Engineers) (2005)
4
Hyland R W and Wexler A ‘Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K and of
saturated moist air from 173.15 K to 372.15 K at pressures to
5 MPa’ Trans. ASHRAE 89(2A) 520–535 (1982)
5
Hyland R W and Wexler A ‘Formulations for the thermodynamic properties of the saturated phases of H2O from
173.15 K to 473.15 K’ Trans. ASHRAE 89(2A) 500–519 (1983)
6
Stimson H F ‘Some precise measurements of the vapour
pressure of water in the range from 25 °C to 100 °C’ J. Res. NBS
73A (1969)
7
Tables of thermal properties of gases NBS Circular 564
(Gaithersburg, MD: National Bureau of Standards) (November
1955)
8
National Engineering Laboratory steam tables (London: Her
Majesty’s Stationery Office) (1964)
9
Jones W P and Lawrence B G New psychrometric data for air
Technical Memorandum No. 11 (London: Polytechnic of the
South Bank)
10
Some fundamental data used by building services engineers
(London: Institution of Heating and Ventilating Engineers)
(1973)
11
Jones W P ‘A review of CIBSE psychrometry’ Building Serv.
Eng. Res. Technol. 15(4) 189–198 (1994)
12
US Standard Atmosphere (Washington DC: U.S. Government
Printing Office) (1976)
13
Jones W P ‘The Psychrometric Chart in SI Units’ J. Inst.
Heating and Ventilating Engineers 38 93 (1970)
14
Bull L C ‘Design and use of the new IHVE psychrometric
chart’ J. Inst. Heating and Ventilating Engineers 32 268 (1964)
0·6
0·4
0·2
0·5
0·6
0·4
0·75
–10
–10
0·3
0·2
–5
–5
0·1
0
25
–10
30
0
0
40
–5
5
th
0·80
5
alp
0·5
5
g –1
)
0
10
55
0·3
15
e
Sp
J .k
y/
(k
50
en
cif
ic
45
0·7
0·8
0·9 Sensible/total heat
1·0 ratio for water
0·9 added at 30 C
0·8
0·7
–5
10
0
20
b
ul
-b
et
W
60
10
t
65
5
15
em
p
e
ra
tu
re
Spec
70
15
80
10
85
90
90
35
80
70
40
60
45
45
50
Percentage saturation / %
50
40
135
50
30
55
140
55
60
0·019
0·020
0·021
0·022
0·023
0·024
0·025
0·026
0·027
0·028
0·029
0·030
0·017
0·018
20
20
20
25
30
Specific enthalpy / (kJ.kg–1)
35
40
0·000
0·001
0·002
0·003
0·004
0·005
0·006
0·007
0·008
0·009
0·010
0·011
0·012
0·013
0·014
0·015
30
Dry-bulb temperature / C
30
0·90
130
20
25
5
10
5
11
0·016
15
–1
3. g
m k
25
95
0
11
0·85
me /
olu
ific v
75
(sl
in
g)
/°
C
Based on a barometric
pressure of 101·325 kPa
0
10
125
60
Moisture content / (kg.kg–1 dry air)
140
135
130
125
120
115
Specific enthalpy / (kJ.kg–1)
0·1
35
Figure 1.2 CIBSE psychrometric chart (–10 to +60 °C)
–1
0
0
85
80
75
70
110
105
100
95
90
120
65
Properties of humid air
1-5
0·3
0·4
20°
2
10
0·
0·5
40
10
°
15
15
20
0
0·9
0·7
80°
Sensible/total heat ratio for
water added at 30°C
60
60
°
0·1
100
20
25
25
30
30
200
10
Spe
cif
ic
e
ntha
160
lpy
1
/ kJ .
70
kg –1
180
190
0·9
210
We
35
35
250
Figure 1.3 CIBSE psychrometric chart (+10 to +120 °C)
10
50
40
30
20
110
150
140
120
130
40
20
40
45
45
50
30
Specific
volume / m3.kg–1
1·0
)
240
220
230
tb
ulb
ur
rat
pe
tem
ng
(sli
e/
°C
260
300
290
270
280
55
50
80
70
60
50
1·1
40
50
60
65
70
75
Dry bulb temperature / °C
90
320
60
80
85
90
30
95
Relative humidity / %
340
70
Specific enthalpy / kJ.kg–1
40
330
80
100
20
350
105
90
110
1·2
115
100
360
110
0·00
120
0·09
0·08
0·07
0·06
0·05
0·04
0·03
0·02
0·01
10
370
tent
310
Mois
90
80
70
/ (kg .
kg –1)
ture
con
250 260 270 280 290
200 210 220 230 240
150 160 170 180 190
120 130 140
1-6
Reference data
300 310 320 330 340
350 360 370
Properties of humid air
1-7
–10 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.03
84.03
80.04
76.05
72.05
70.05
68.06
66.06
64.06
62.06
60.06
58.06
56.06
54.06
52.06
50.06
48.06
46.06
44.06
42.06
40.06
38.06
36.06
34.06
32.06
30.05
28.05
24.05
20.04
16.03
12.03
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
1.607
1.543
1.479
1.414
1.350
1.286
1.221
1.157
1.125
1.093
1.061
1.029
0.996
0.964
0.932
0.900
0.868
0.836
0.804
0.772
0.739
0.707
0.675
0.643
0.611
0.579
0.546
0.514
0.482
0.450
0.386
0.321
0.257
0.193
0.129
0.064
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺6.065
⫺6.224
⫺6.384
⫺6.544
⫺6.703
⫺6.863
⫺7.022
⫺7.182
⫺7.262
⫺7.342
⫺7.421
⫺7.501
⫺7.581
⫺7.661
⫺7.740
⫺7.820
⫺7.900
⫺7.980
⫺8.060
⫺8.139
⫺8.219
⫺8.299
⫺8.379
⫺8.459
⫺8.538
⫺8.618
⫺8.698
⫺8.778
⫺8.858
⫺8.937
⫺9.097
⫺9.256
⫺9.416
⫺9.576
⫺9.735
⫺9.895
⫺10.054
Specific
volume, / (m3·kg⫺1)
0.7468
0.7468
0.7467
0.7466
0.7465
0.7465
0.7464
0.7463
0.7463
0.7462
0.7462
0.7462
0.7461
0.7461
0.7460
0.7460
0.7460
0.7459
0.7459
0.7458
0.7458
0.7458
0.7457
0.7457
0.7457
0.7456
0.7456
0.7455
0.7455
0.7455
0.7454
0.7453
0.7452
0.7452
0.7451
0.7450
0.7449
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.2600
0.2496
0.2392
0.2288
0.2185
0.2081
0.1977
0.1873
0.1821
0.1769
0.1717
0.1665
0.1613
0.1562
0.1510
0.1458
0.1406
0.1354
0.1302
0.1250
0.1198
0.1146
0.1094
0.1042
0.0990
0.0938
0.0885
0.0833
0.0781
0.0729
0.0625
0.0521
0.0417
0.0313
0.0208
0.0104
0.0000
⫺10.0
⫺10.5
⫺10.9
⫺11.4
⫺11.9
⫺12.5
⫺13.1
⫺13.6
⫺14.0
⫺14.3
⫺14.6
⫺14.9
⫺15.3
⫺15.6
⫺16.0
⫺16.4
⫺16.8
⫺17.2
⫺17.6
⫺18.0
⫺18.5
⫺18.9
⫺19.4
⫺19.9
⫺20.5
⫺21.0
⫺21.6
⫺22.2
⫺22.9
⫺23.6
⫺25.2
⫺27.0
⫺29.2
⫺31.9
⫺35.7
⫺41.9
—
⫺10.0
⫺10.1
⫺10.3
⫺10.4
⫺10.5
⫺10.7
⫺10.8
⫺10.9
⫺11.0
⫺11.0
⫺11.1
⫺11.2
⫺11.2
⫺11.3
⫺11.4
⫺11.4
⫺11.5
⫺11.6
⫺11.6
⫺11.7
⫺11.8
⫺11.8
⫺11.9
⫺12.0
⫺12.0
⫺12.1
⫺12.2
⫺12.3
⫺12.3
⫺12.4
⫺12.5
⫺12.7
⫺12.8
⫺12.9
⫺13.1
⫺13.2
⫺13.4
⫺10.0
⫺10.1
⫺10.2
⫺10.3
⫺10.4
⫺10.5
⫺10.7
⫺10.8
⫺10.8
⫺10.9
⫺10.9
⫺11.0
⫺11.0
⫺11.1
⫺11.1
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.4
⫺11.5
⫺11.5
⫺11.6
⫺11.6
⫺11.7
⫺11.8
⫺11.8
⫺11.9
⫺11.9
⫺12.0
⫺12.1
⫺12.2
⫺12.3
⫺12.4
⫺12.6
⫺12.7
⫺12.8
⫺10.0
⫺10.1
⫺10.3
⫺10.4
⫺10.5
⫺10.6
⫺10.8
⫺10.9
⫺10.9
⫺11.0
⫺11.1
⫺11.1
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.5
⫺11.5
⫺11.6
⫺11.7
⫺11.7
⫺11.8
⫺11.8
⫺11.9
⫺12.0
⫺12.0
⫺12.1
⫺12.2
⫺12.2
⫺12.3
⫺12.4
⫺12.6
⫺12.7
⫺12.8
⫺13.0
⫺13.1
⫺13.2
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.2717
0.2609
0.2500
0.2392
0.2284
0.2175
0.2066
0.1958
0.1904
0.1849
0.1795
0.1740
0.1686
0.1632
0.1578
0.1524
0.1469
0.1415
0.1360
0.1306
0.1252
0.1197
0.1143
0.1089
0.1034
0.0980
0.0926
0.0871
0.0817
0.0762
0.0654
0.0545
0.0436
0.0327
0.0218
0.0109
0.0000
⫺9.5
⫺10.0
⫺10.4
⫺10.9
⫺11.5
⫺12.0
⫺12.6
⫺13.2
⫺13.5
⫺13.8
⫺14.1
⫺14.5
⫺14.8
⫺15.2
⫺15.5
⫺15.9
⫺16.3
⫺16.7
⫺17.1
⫺17.5
⫺18.0
⫺18.5
⫺19.0
⫺19.5
⫺20.0
⫺20.6
⫺21.2
⫺21.8
⫺22.5
⫺23.2
⫺24.7
⫺26.5
⫺28.7
⫺31.5
⫺35.3
⫺41.5
—
⫺9.5
⫺9.6
⫺9.8
⫺9.9
⫺10.0
⫺10.2
⫺10.3
⫺10.4
⫺10.5
⫺10.6
⫺10.6
⫺10.7
⫺10.8
⫺10.9
⫺10.9
⫺11.0
⫺11.1
⫺11.1
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.5
⫺11.6
⫺11.6
⫺11.7
⫺11.8
⫺11.8
⫺11.9
⫺12.0
⫺12.1
⫺12.3
⫺12.4
⫺12.5
⫺12.7
⫺12.8
⫺13.0
⫺9.5
⫺9.6
⫺9.7
⫺9.8
⫺9.9
⫺10.1
⫺10.2
⫺10.3
⫺10.3
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.6
⫺10.7
⫺10.7
⫺10.8
⫺10.9
⫺10.9
⫺11.0
⫺11.0
⫺11.1
⫺11.2
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.4
⫺11.5
⫺11.6
⫺11.7
⫺11.8
⫺11.9
⫺12.0
⫺12.1
⫺12.3
⫺12.4
⫺9.5
⫺9.6
⫺9.8
⫺9.9
⫺10.0
⫺10.1
⫺10.3
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.7
⫺10.7
⫺10.8
⫺10.9
⫺10.9
⫺11.0
⫺11.1
⫺11.1
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.5
⫺11.5
⫺11.6
⫺11.7
⫺11.7
⫺11.8
⫺11.9
⫺12.0
⫺12.2
⫺12.3
⫺12.4
⫺12.6
⫺12.7
⫺12.8
–9.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.03
84.04
80.04
76.05
72.05
70.06
68.06
66.06
64.06
62.06
60.06
58.07
56.07
54.07
52.07
50.07
48.07
46.07
44.07
42.07
40.06
38.06
36.06
34.06
32.06
30.06
28.05
24.05
20.04
16.04
12.03
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
1.680
1.613
1.546
1.478
1.411
1.344
1.277
1.210
1.176
1.142
1.109
1.075
1.042
1.008
0.974
0.940
0.907
0.874
0.840
0.806
0.773
0.739
0.706
0.672
0.638
0.605
0.571
0.538
0.504
0.470
0.403
0.336
0.269
0.201
0.134
0.067
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺5.380
⫺5.547
⫺5.713
⫺5.880
⫺6.047
⫺6.214
⫺6.381
⫺6.548
⫺6.631
⫺6.715
⫺6.798
⫺6.882
⫺6.965
⫺7.048
⫺7.132
⫺7.215
⫺7.299
⫺7.382
⫺7.466
⫺7.549
⫺7.633
⫺7.716
⫺7.800
⫺7.883
⫺7.966
⫺8.050
⫺8.133
⫺8.217
⫺8.300
⫺8.384
⫺8.550
⫺8.717
⫺8.884
⫺9.051
⫺9.218
⫺9.385
⫺9.552
Specific
volume, / (m3·kg⫺1)
0.7484
0.7483
0.7482
0.7481
0.7480
0.7480
0.7479
0.7478
0.7478
0.7477
0.7477
0.7476
0.7476
0.7476
0.7475
0.7475
0.7474
0.7474
0.7474
0.7473
0.7473
0.7472
0.7472
0.7472
0.7471
0.7471
0.7470
0.7470
0.7470
0.7469
0.7468
0.7467
0.7467
0.7466
0.7465
0.7464
0.7463
1-8
Reference data
–9 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.03
84.04
80.04
76.05
72.06
70.06
68.06
66.06
64.06
62.07
60.07
58.07
56.07
54.07
52.07
50.07
48.07
46.07
44.07
42.07
40.07
38.07
36.06
34.06
32.06
30.06
28.06
24.05
20.04
16.04
12.03
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
1.755
1.686
1.615
1.545
1.475
1.405
1.334
1.264
1.229
1.194
1.159
1.124
1.089
1.054
1.018
0.983
0.948
0.913
0.878
0.843
0.808
0.773
0.738
0.702
0.667
0.632
0.597
0.562
0.527
0.492
0.421
0.351
0.281
0.211
0.140
0.070
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺4.687
⫺4.862
⫺5.036
⫺5.210
⫺5.385
⫺5.559
⫺5.734
⫺5.908
⫺5.996
⫺6.083
⫺6.170
⫺6.257
⫺6.345
⫺6.432
⫺6.519
⫺6.606
⫺6.694
⫺6.781
⫺6.868
⫺6.955
⫺7.042
⫺7.130
⫺7.217
⫺7.304
⫺7.391
⫺7.479
⫺7.566
⫺7.653
⫺7.740
⫺7.828
⫺8.002
⫺8.177
⫺8.351
⫺8.526
⫺8.700
⫺8.875
⫺9.049
Specific
volume, / (m3·kg⫺1)
0.7499
0.7498
0.7497
0.7496
0.7495
0.7494
0.7494
0.7493
0.7492
0.7492
0.7492
0.7491
0.7491
0.7490
0.7490
0.7489
0.7489
0.7489
0.7488
0.7488
0.7487
0.7487
0.7487
0.7486
0.7486
0.7485
0.7485
0.7484
0.7484
0.7484
0.7483
0.7482
0.7481
0.7480
0.7479
0.7479
0.7478
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.2840
0.2726
0.2613
0.2500
0.2386
0.2273
0.2160
0.2046
0.1989
0.1933
0.1876
0.1819
0.1762
0.1706
0.1649
0.1592
0.1535
0.1479
0.1422
0.1365
0.1308
0.1251
0.1195
0.1138
0.1081
0.1024
0.0967
0.0910
0.0854
0.0797
0.0683
0.0569
0.0455
0.0342
0.0228
0.0114
0.0000
⫺9.0
⫺9.5
⫺9.9
⫺10.4
⫺11.0
⫺11.5
⫺12.1
⫺12.7
⫺13.0
⫺13.3
⫺13.6
⫺14.0
⫺14.3
⫺14.7
⫺15.0
⫺15.4
⫺15.8
⫺16.2
⫺16.6
⫺17.1
⫺17.5
⫺18.0
⫺18.5
⫺19.0
⫺19.5
⫺20.1
⫺20.7
⫺21.3
⫺22.0
⫺22.7
⫺24.3
⫺26.1
⫺28.3
⫺31.1
⫺34.9
⫺41.1
—
⫺9.0
⫺9.1
⫺9.3
⫺9.4
⫺9.6
⫺9.7
⫺9.8
⫺10.0
⫺10.0
⫺10.1
⫺10.2
⫺10.3
⫺10.3
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.7
⫺10.8
⫺10.8
⫺10.9
⫺11.0
⫺11.0
⫺11.1
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.5
⫺11.6
⫺11.7
⫺11.9
⫺12.0
⫺12.1
⫺12.3
⫺12.4
⫺12.6
⫺9.0
⫺9.1
⫺9.2
⫺9.3
⫺9.5
⫺9.6
⫺9.7
⫺9.8
⫺9.9
⫺9.9
⫺10.0
⫺10.1
⫺10.1
⫺10.2
⫺10.2
⫺10.3
⫺10.4
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.6
⫺10.7
⫺10.8
⫺10.8
⫺10.9
⫺10.9
⫺11.0
⫺11.1
⫺11.1
⫺11.3
⫺11.4
⫺11.5
⫺11.6
⫺11.7
⫺11.9
⫺12.0
⫺9.0
⫺9.1
⫺9.3
⫺9.4
⫺9.5
⫺9.7
⫺9.8
⫺9.9
⫺10.0
⫺10.1
⫺10.1
⫺10.2
⫺10.3
⫺10.4
⫺10.4
⫺10.5
⫺10.6
⫺10.6
⫺10.7
⫺10.8
⫺10.8
⫺10.9
⫺11.0
⫺11.0
⫺11.1
⫺11.2
⫺11.3
⫺11.3
⫺11.4
⫺11.5
⫺11.6
⫺11.7
⫺11.9
⫺12.0
⫺12.2
⫺12.3
⫺12.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.2967
0.2849
0.2730
0.2612
0.2493
0.2375
0.2256
0.2138
0.2079
0.2019
0.1960
0.1901
0.1842
0.1782
0.1723
0.1664
0.1604
0.1545
0.1486
0.1426
0.1367
0.1308
0.1248
0.1189
0.1130
0.1070
0.1011
0.0951
0.0892
0.0832
0.0714
0.0595
0.0476
0.0357
0.0238
0.0119
0.0000
⫺8.5
⫺9.0
⫺9.4
⫺9.9
⫺10.5
⫺11.0
⫺11.6
⫺12.2
⫺12.5
⫺12.8
⫺13.2
⫺13.5
⫺13.8
⫺14.2
⫺14.6
⫺14.9
⫺15.3
⫺15.7
⫺16.2
⫺16.6
⫺17.1
⫺17.5
⫺18.0
⫺18.5
⫺19.1
⫺19.7
⫺20.3
⫺20.9
⫺21.5
⫺22.3
⫺23.8
⫺25.7
⫺27.9
⫺30.7
⫺34.5
⫺40.7
—
⫺8.5
⫺8.6
⫺8.8
⫺8.9
⫺9.1
⫺9.2
⫺9.4
⫺9.5
⫺9.6
⫺9.7
⫺9.7
⫺9.8
⫺9.9
⫺9.9
⫺10.0
⫺10.1
⫺10.2
⫺10.2
⫺10.3
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.7
⫺10.8
⫺10.8
⫺10.9
⫺11.0
⫺11.1
⫺11.1
⫺11.3
⫺11.4
⫺11.6
⫺11.8
⫺11.9
⫺12.1
⫺12.2
⫺8.5
⫺8.6
⫺8.7
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.3
⫺9.4
⫺9.5
⫺9.5
⫺9.6
⫺9.7
⫺9.7
⫺9.8
⫺9.8
⫺9.9
⫺10.0
⫺10.0
⫺10.1
⫺10.1
⫺10.2
⫺10.3
⫺10.3
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.6
⫺10.7
⫺10.8
⫺11.0
⫺11.1
⫺11.2
⫺11.3
⫺11.5
⫺11.6
⫺8.5
⫺8.6
⫺8.8
⫺8.9
⫺9.1
⫺9.2
⫺9.3
⫺9.5
⫺9.5
⫺9.6
⫺9.7
⫺9.8
⫺9.8
⫺9.9
⫺10.0
⫺10.0
⫺10.1
⫺10.2
⫺10.3
⫺10.3
⫺10.4
⫺10.5
⫺10.5
⫺10.6
⫺10.7
⫺10.8
⫺10.8
⫺10.9
⫺11.0
⫺11.1
⫺11.2
⫺11.3
⫺11.5
⫺11.6
⫺11.8
⫺11.9
⫺12.1
–8.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.03
84.04
80.05
76.05
72.06
70.06
68.06
66.07
64.07
62.07
60.07
58.07
56.07
54.07
52.07
50.07
48.07
46.07
44.07
42.07
40.07
38.07
36.07
34.07
32.06
30.06
28.06
24.05
20.05
16.04
12.03
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
1.835
1.761
1.688
1.615
1.541
1.468
1.394
1.321
1.284
1.248
1.211
1.174
1.138
1.101
1.064
1.028
0.991
0.954
0.917
0.881
0.844
0.807
0.771
0.734
0.697
0.660
0.624
0.587
0.550
0.514
0.440
0.367
0.294
0.220
0.147
0.073
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺3.986
⫺4.169
⫺4.351
⫺4.534
⫺4.716
⫺4.898
⫺5.081
⫺5.263
⫺5.354
⫺5.446
⫺5.537
⫺5.628
⫺5.719
⫺5.810
⫺5.902
⫺5.993
⫺6.084
⫺6.175
⫺6.266
⫺6.358
⫺6.449
⫺6.540
⫺6.631
⫺6.722
⫺6.814
⫺6.905
⫺6.996
⫺7.087
⫺7.178
⫺7.270
⫺7.452
⫺7.634
⫺7.817
⫺7.999
⫺8.182
⫺8.364
⫺8.546
Specific
volume, / (m3·kg⫺1)
0.7514
0.7513
0.7512
0.7511
0.7510
0.7509
0.7509
0.7508
0.7507
0.7507
0.7506
0.7506
0.7506
0.7505
0.7505
0.7504
0.7504
0.7503
0.7503
0.7502
0.7502
0.7502
0.7501
0.7501
0.7500
0.7500
0.7499
0.7499
0.7498
0.7498
0.7497
0.7496
0.7495
0.7495
0.7494
0.7493
0.7492
Properties of humid air
1-9
–8 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.03
84.04
80.05
76.06
72.06
70.06
68.07
66.07
64.07
62.07
60.07
58.07
56.08
54.08
52.08
50.08
48.08
46.08
44.08
42.07
40.07
38.07
36.07
34.07
32.07
30.06
28.06
24.06
20.05
16.04
12.03
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
1.917
1.840
1.764
1.687
1.610
1.534
1.457
1.380
1.342
1.304
1.265
1.227
1.189
1.150
1.112
1.074
1.035
0.997
0.958
0.920
0.882
0.844
0.805
0.767
0.728
0.690
0.652
0.614
0.575
0.537
0.460
0.383
0.307
0.230
0.153
0.077
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺3.278
⫺3.468
⫺3.659
⫺3.850
⫺4.040
⫺4.231
⫺4.421
⫺4.612
⫺4.707
⫺4.803
⫺4.898
⫺4.993
⫺5.089
⫺5.184
⫺5.279
⫺5.375
⫺5.470
⫺5.565
⫺5.661
⫺5.756
⫺5.851
⫺5.946
⫺6.042
⫺6.137
⫺6.232
⫺6.328
⫺6.423
⫺6.518
⫺6.614
⫺6.709
⫺6.900
⫺7.090
⫺7.281
⫺7.472
⫺7.662
⫺7.853
⫺8.044
Specific
volume, / (m3·kg⫺1)
0.7529
0.7528
0.7527
0.7526
0.7525
0.7524
0.7524
0.7523
0.7522
0.7522
0.7521
0.7521
0.7520
0.7520
0.7519
0.7519
0.7519
0.7518
0.7518
0.7517
0.7517
0.7516
0.7516
0.7515
0.7515
0.7514
0.7514
0.7513
0.7513
0.75113
0.7512
0.7511
0.7510
0.7509
0.7508
0.7507
0.7506
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.3100
0.2976
0.2852
0.2729
0.2605
0.2481
0.2357
0.2334
0.2172
0.2110
0.2048
0.1986
0.1924
0.1862
0.1800
0.1738
0.1676
0.1614
0.1552
0.1490
0.1428
0.1366
0.1304
0.1242
0.1180
0.1118
0.1056
0.0994
0.0932
0.0870
0.0746
0.0621
0.0497
0.0373
0.0249
0.0124
0.0000
⫺8.0
⫺8.5
⫺8.9
⫺9.5
⫺10.0
⫺10.5
⫺11.1
⫺11.7
⫺12.0
⫺12.3
⫺12.7
⫺13.0
⫺13.4
⫺13.7
⫺14.1
⫺14.5
⫺14.9
⫺15.3
⫺15.7
⫺16.1
⫺16.6
⫺17.1
⫺17.6
⫺18.1
⫺18.6
⫺19.2
⫺19.8
⫺20.4
⫺21.1
⫺21.8
⫺23.4
⫺25.2
⫺27.4
⫺30.2
⫺34.1
⫺40.4
—
⫺8.0
⫺8.1
⫺8.3
⫺8.4
⫺8.6
⫺8.7
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.3
⫺9.3
⫺9.4
⫺9.5
⫺9.6
⫺9.6
⫺9.7
⫺9.8
⫺9.9
⫺10.0
⫺10.0
⫺10.1
⫺10.2
⫺10.3
⫺10.3
⫺10.4
⫺10.5
⫺10.6
⫺10.7
⫺10.7
⫺10.9
⫺11.0
⫺11.2
⫺11.4
⫺11.5
⫺11.7
⫺11.8
⫺8.0
⫺8.1
⫺8.2
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.9
⫺8.9
⫺9.0
⫺9.1
⫺9.1
⫺9.2
⫺9.3
⫺9.3
⫺9.4
⫺9.4
⫺9.5
⫺9.6
⫺9.6
⫺9.7
⫺9.8
⫺9.8
⫺9.9
⫺10.0
⫺10.0
⫺10.1
⫺10.2
⫺10.2
⫺10.3
⫺10.4
⫺10.5
⫺10.7
⫺10.8
⫺10.9
⫺11.1
⫺11.2
⫺8.0
⫺8.1
⫺8.3
⫺8.4
⫺8.6
⫺8.7
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.2
⫺9.3
⫺9.4
⫺9.4
⫺9.5
⫺9.6
⫺9.7
⫺9.7
⫺9.8
⫺9.9
⫺10.0
⫺10.0
⫺10.1
⫺10.2
⫺10.3
⫺10.3
⫺10.4
⫺10.5
⫺10.6
⫺10.6
⫺10.8
⫺10.9
⫺11.1
⫺11.2
⫺11.4
⫺11.6
⫺11.7
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.3238
0.3108
0.2979
0.2850
0.2721
0.2592
0.2462
0.2333
0.2268
0.2204
0.2139
0.2074
0.2010
0.1945
0.1880
0.1816
0.1751
0.1686
0.1621
0.1557
0.1492
0.1427
0.1362
0.1298
0.1233
0.1168
0.1103
0.1038
0.0973
0.0909
0.0779
0.0649
0.0519
0.0390
0.0260
0.0130
0.0000
⫺7.5
⫺8.0
⫺8.5
⫺9.0
⫺9.5
⫺10.0
⫺10.6
⫺11.2
⫺11.5
⫺11.9
⫺12.2
⫺12.5
⫺12.9
⫺13.2
⫺13.6
⫺14.0
⫺14.4
⫺14.8
⫺15.2
⫺15.7
⫺16.1
⫺16.6
⫺17.1
⫺17.6
⫺18.2
⫺18.7
⫺19.3
⫺20.0
⫺20.6
⫺21.4
⫺22.9
⫺24.8
⫺27.0
⫺29.8
⫺33.7
⫺40.0
—
⫺7.5
⫺7.7
⫺7.8
⫺8.0
⫺8.1
⫺8.3
⫺8.4
⫺8.6
⫺8.7
⫺8.7
⫺8.8
⫺8.9
⫺9.0
⫺9.0
⫺9.1
⫺9.2
⫺9.3
⫺9.4
⫺9.4
⫺9.5
⫺9.6
⫺9.7
⫺9.8
⫺9.8
⫺9.9
⫺10.0
⫺10.1
⫺10.2
⫺10.2
⫺10.3
⫺10.5
⫺10.6
⫺10.8
⫺11.0
⫺11.1
⫺11.3
⫺11.5
⫺7.5
⫺7.6
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.3
⫺8.4
⫺8.5
⫺8.5
⫺8.6
⫺8.7
⫺8.7
⫺8.8
⫺8.9
⫺8.9
⫺9.0
⫺9.1
⫺9.1
⫺9.2
⫺9.3
⫺9.3
⫺9.4
⫺9.5
⫺9.5
⫺9.6
⫺9.7
⫺9.7
⫺9.8
⫺9.9
⫺10.0
⫺10.1
⫺10.3
⫺10.4
⫺10.5
⫺10.7
⫺10.8
⫺7.5
⫺7.6
⫺7.8
⫺7.9
⫺8.1
⫺8.2
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.8
⫺8.8
⫺8.9
⫺9.0
⫺9.1
⫺9.1
⫺9.2
⫺9.3
⫺9.4
⫺9.4
⫺9.5
⫺9.6
⫺9.7
⫺9.8
⫺9.8
⫺9.9
⫺10.0
⫺10.1
⫺10.1
⫺10.2
⫺10.4
⫺10.5
⫺10.7
⫺10.9
⫺11.0
⫺11.2
⫺11.3
–7.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.03
84.04
80.05
76.06
72.06
70.07
68.07
66.07
64.07
62.08
60.08
58.08
56.08
54.08
52.08
50.08
48.08
46.08
44.08
42.08
40.08
38.08
36.07
34.07
32.07
30.07
28.06
24.06
20.05
16.04
12.03
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.003
1.922
1.842
1.762
1.682
1.602
1.522
1.442
1.402
1.362
1.322
1.282
1.242
1.202
1.162
1.122
1.081
1.041
1.001
0.961
0.921
0.881
0.841
0.801
0.761
0.721
0.681
0.641
0.601
0.561
0.481
0.400
0.320
0.240
0.160
0.080
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺2.560
⫺2.760
⫺2.959
⫺3.158
⫺3.357
⫺3.556
⫺3.756
⫺3.955
⫺4.054
⫺4.154
⫺4.254
⫺4.353
⫺4.453
⫺4.552
⫺4.652
⫺4.752
⫺4.851
⫺4.951
⫺5.051
⫺5.150
⫺5.250
⫺5.349
⫺5.449
⫺5.549
⫺5.648
⫺5.748
⫺5.848
⫺5.947
⫺6.047
⫺6.146
⫺6.346
⫺6.545
⫺6.744
⫺6.943
⫺7.142
⫺7.341
⫺7.541
Specific
volume, / (m3·kg⫺1)
0.7544
0.7543
0.7542
0.7541
0.7541
0.7540
0.7539
0.7538
0.7537
0.7537
0.7536
0.7536
0.7535
0.7535
0.7534
0.7534
0.7533
0.7533
0.7532
0.7532
0.7531
0.7531
0.7530
0.7530
0.7529
0.7529
0.7528
0.7528
0.7528
0.7527
0.7526
0.7525
0.7524
0.7523
0.7522
0.7521
0.7520
1-10
Reference data
–7 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.02
88.04
84.04
80.05
76.06
72.07
70.07
68.07
66.07
64.08
62.08
60.08
58.08
56.08
54.08
52.08
50.08
48.08
46.08
44.08
42.08
40.08
38.08
36.08
34.07
32.07
30.07
28.07
24.06
20.05
16.04
12.04
8.02
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.092
2.008
1.924
1.841
1.757
1.673
1.590
1.506
1.464
1.422
1.380
1.339
1.297
1.255
1.213
1.171
1.130
1.088
1.046
1.004
0.962
0.920
0.878
0.837
0.795
0.753
0.711
0.669
0.628
0.586
0.502
0.418
0.335
0.251
0.167
0.084
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺1.834
⫺2.042
⫺2.250
⫺2.458
⫺2.667
⫺2.875
⫺3.083
⫺3.291
⫺3.395
⫺3.499
⫺3.603
⫺3.708
⫺3.812
⫺3.916
⫺4.020
⫺4.124
⫺4.228
⫺4.332
⫺4.436
⫺4.540
⫺4.644
⫺4.748
⫺4.852
⫺4.956
⫺5.061
⫺5.165
⫺5.269
⫺5.373
⫺5.477
⫺5.581
⫺5.789
⫺5.997
⫺6.206
⫺6.414
⫺6.622
⫺6.830
⫺7.038
Specific
volume, / (m3·kg⫺1)
0.7560
0.7559
0.7558
0.7557
0.7556
0.7555
0.7554
0.7553
0.7552
0.7552
0.7551
0.7551
0.7550
0.7550
0.7549
0.7549
0.7548
0.7548
0.7457
0.7547
0.7546
0.7546
0.7545
0.7545
0.7544
0.7544
0.7543
0.7543
0.7542
0.7542
0.7541
0.7540
0.7539
0.7538
0.7537
0.7536
0.7535
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.3381
0.3246
0.3111
0.2976
0.2842
0.2707
0.2572
0.2437
0.2369
0.2302
0.2234
0.2166
0.2099
0.2031
0.1964
0.1896
0.1828
0.1761
0.1693
0.1626
0.1558
0.1490
0.1423
0.1355
0.1287
0.1220
0.1152
0.1084
0.1017
0.0949
0.0814
0.0678
0.0542
0.0407
0.0271
0.0136
0.0000
⫺7.0
⫺7.5
⫺8.0
⫺8.5
⫺9.0
⫺9.5
⫺10.1
⫺10.7
⫺11.0
⫺11.4
⫺11.7
⫺12.0
⫺12.4
⫺12.8
⫺13.1
⫺13.5
⫺13.9
⫺14.3
⫺14.8
⫺15.2
⫺15.7
⫺16.1
⫺16.6
⫺17.2
⫺17.7
⫺18.3
⫺18.9
⫺19.5
⫺20.2
⫺20.9
⫺22.5
⫺24.3
⫺26.6
⫺29.4
⫺33.3
⫺39.6
—
⫺7.0
⫺7.2
⫺7.3
⫺7.5
⫺7.6
⫺7.8
⫺7.9
⫺8.1
⫺8.2
⫺8.3
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.8
⫺8.8
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.2
⫺9.3
⫺9.4
⫺9.5
⫺9.6
⫺9.7
⫺9.7
⫺9.8
⫺9.9
⫺10.1
⫺10.3
⫺10.4
⫺10.6
⫺10.8
⫺10.9
⫺11.1
⫺7.0
⫺7.1
⫺7.3
⫺7.4
⫺7.5
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.1
⫺8.2
⫺8.3
⫺8.3
⫺8.4
⫺8.5
⫺8.5
⫺8.6
⫺8.7
⫺8.8
⫺8.8
⫺8.9
⫺9.0
⫺9.0
⫺9.1
⫺9.2
⫺9.2
⫺9.3
⫺9.4
⫺9.4
⫺9.6
⫺9.7
⫺9.9
⫺10.0
⫺10.1
⫺10.3
⫺10.4
⫺7.0
⫺7.2
⫺7.3
⫺7.5
⫺7.6
⫺7.8
⫺7.9
⫺8.1
⫺8.1
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.5
⫺8.6
⫺8.7
⫺8.8
⫺8.9
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.3
⫺9.3
⫺9.4
⫺9.5
⫺9.6
⫺9.7
⫺9.7
⫺9.8
⫺10.0
⫺10.1
⫺10.3
⫺10.5
⫺10.6
⫺10.8
⫺11.0
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.3530
0.3390
0.3249
0.3108
0.2967
0.2826
0.2685
0.2544
0.2474
0.2403
0.2333
0.2262
0.2192
0.2121
0.2051
0.1980
0.1909
0.1839
0.1768
0.1698
0.1627
0.1556
0.1486
0.1415
0.1344
0.1274
0.1203
0.1132
0.1062
0.0991
0.0850
0.0708
0.0566
0.0425
0.0283
0.0142
0.0000
⫺6.5
⫺7.0
⫺7.5
⫺8.0
⫺8.5
⫺9.1
⫺9.6
⫺10.2
⫺10.6
⫺10.9
⫺11.2
⫺11.6
⫺11.9
⫺12.3
⫺12.7
⫺13.0
⫺13.4
⫺13.9
⫺14.3
⫺14.7
⫺15.2
⫺15.7
⫺16.2
⫺16.7
⫺17.2
⫺17.8
⫺18.4
⫺19.1
⫺19.7
⫺20.5
⫺22.0
⫺23.9
⫺26.1
⫺29.0
⫺32.9
⫺39.2
—
⫺6.5
⫺6.7
⫺6.8
⫺7.0
⫺7.1
⫺7.3
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.1
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.6
⫺8.7
⫺8.8
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.2
⫺9.3
⫺9.4
⫺9.5
⫺9.7
⫺9.9
⫺10.0
⫺10.2
⫺10.4
⫺10.6
⫺10.7
⫺6.5
⫺6.6
⫺6.8
⫺6.9
⫺7.0
⫺7.2
⫺7.3
⫺7.5
⫺7.5
⫺7.6
⫺7.7
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.0
⫺8.1
⫺8.2
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.5
⫺8.6
⫺8.7
⫺8.7
⫺8.8
⫺8.9
⫺9.0
⫺9.0
⫺9.2
⫺9.3
⫺9.5
⫺9.6
⫺9.8
⫺9.9
⫺10.0
⫺6.5
⫺6.7
⫺6.8
⫺7.0
⫺7.1
⫺7.3
⫺7.4
⫺7.6
⫺7.7
⫺7.8
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.2
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.7
⫺8.8
⫺8.9
⫺9.0
⫺9.1
⫺9.2
⫺9.2
⫺9.3
⫺9.4
⫺9.6
⫺9.7
⫺9.9
⫺10.1
⫺10.3
⫺10.4
⫺10.6
–6.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.03
88.04
84.05
80.06
76.06
72.07
70.07
68.08
66.08
64.08
62.08
60.08
58.08
56.09
54.09
52.09
50.09
48.09
46.09
44.09
42.08
40.08
38.08
36.08
34.08
32.08
30.07
28.07
24.06
20.06
16.05
12.04
8.03
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.184
2.097
2.010
1.922
1.835
1.748
1.660
1.573
1.529
1.485
1.442
1.398
1.354
1.311
1.267
1.223
1.180
1.136
1.092
1.048
1.005
0.961
0.917
0.874
0.830
0.786
0.743
0.699
0.655
0.612
0.524
0.437
0.350
0.262
0.175
0.087
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺1.099
⫺1.316
⫺1.534
⫺1.751
⫺1.969
⫺2.186
⫺2.404
⫺2.621
⫺2.730
⫺2.838
⫺2.947
⫺3.056
⫺3.165
⫺3.273
⫺3.382
⫺3.491
⫺3.600
⫺3.708
⫺3.817
⫺3.926
⫺4.034
⫺4.143
⫺4.252
⫺4.361
⫺4.470
⫺4.578
⫺4.687
⫺4.796
⫺4.904
⫺5.013
⫺5.230
⫺5.448
⫺5.666
⫺5.883
⫺6.100
⫺6.318
⫺6.535
Specific
volume, / (m3·kg⫺1)
0.7575
0.7574
0.7573
0.7572
0.7571
0.7570
0.7569
0.7568
0.7567
0.7567
0.7566
0.7566
0.7565
0.7565
0.7564
0.7563
0.7563
0.7562
0.7562
0.7561
0.7561
0.7560
0.7560
0.7559
0.7559
0.7558
0.7558
0.7557
0.7557
0.7556
0.7555
0.7554
0.7553
0.7552
0.7551
0.7550
0.7549
Properties of humid air
1-11
–6 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.03
88.04
84.05
80.06
76.07
72.07
70.08
68.08
66.08
64.08
62.09
60.09
58.09
56.09
54.09
52.09
50.09
48.09
46.09
44.09
42.09
40.09
38.09
36.08
34.08
32.08
30.08
28.07
24.07
20.06
16.05
12.04
8.03
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.281
2.190
2.098
2.007
1.916
1.825
1.733
1.642
1.597
1.551
1.505
1.460
1.414
1.368
1.323
1.277
1.232
1.186
1.140
1.095
1.049
1.004
0.958
0.912
0.867
0.821
0.776
0.730
0.684
0.639
0.547
0.456
0.365
0.274
0.182
0.091
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
⫺0.354
⫺0.581
⫺0.808
⫺1.035
⫺1.262
⫺1.490
⫺1.717
⫺1.944
⫺2.058
⫺2.171
⫺2.285
⫺2.398
⫺2.512
⫺2.625
⫺2.739
⫺2.852
⫺2.966
⫺3.080
⫺3.193
⫺3.307
⫺3.420
⫺3.534
⫺3.648
⫺3.761
⫺3.875
⫺3.988
⫺4.102
⫺4.216
⫺4.329
⫺4.443
⫺4.670
⫺4.897
⫺5.124
⫺5.351
⫺5.578
⫺5.806
⫺6.033
Specific
volume, / (m3·kg⫺1)
0.7590
0.7589
0.7588
0.7587
0.7586
0.7585
0.7584
0.7583
0.7582
0.7582
0.7581
0.7581
0.7580
0.7579
0.7579
0.7578
0.7578
0.7577
0.7577
0.7576
0.7576
0.7575
0.7575
0.7574
0.7573
0.7573
0.7572
0.7572
0.7571
0.7571
0.7570
0.7568
0.7567
0.7566
0.7565
0.7564
0.7563
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
0.3686
0.3539
0.3392
0.3245
0.3098
0.2950
0.2804
0.2656
0.2583
0.2509
0.2436
0.2362
0.2288
0.2215
0.2141
0.2067
0.1994
0.1920
0.1846
0.1772
0.1699
0.1625
0.1551
0.1478
0.1404
0.1330
0.1256
0.1182
0.1108
0.1035
0.0887
0.0739
0.0592
0.0444
0.0296
0.0148
0.0000
⫺6.0
⫺6.5
⫺7.0
⫺7.5
⫺8.0
⫺8.6
⫺9.1
⫺9.8
⫺10.1
⫺10.4
⫺10.7
⫺11.1
⫺11.4
⫺11.8
⫺12.2
⫺12.6
⫺13.0
⫺13.4
⫺13.8
⫺14.3
⫺14.7
⫺15.2
⫺15.7
⫺16.2
⫺16.8
⫺17.4
⫺18.0
⫺18.6
⫺19.3
⫺20.0
⫺21.6
⫺23.5
⫺25.7
⫺28.6
⫺32.4
⫺38.8
—
⫺6.0
⫺6.2
⫺6.3
⫺6.5
⫺6.7
⫺6.8
⫺7.0
⫺7.2
⫺7.3
⫺7.3
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.0
⫺8.1
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.7
⫺8.8
⫺8.9
⫺9.0
⫺9.1
⫺9.3
⫺9.5
⫺9.6
⫺9.8
⫺10.0
⫺10.2
⫺10.4
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.3847
0.3694
0.3540
0.3387
0.3234
0.3080
0.2926
0.2773
0.2696
0.2619
0.2542
0.2466
0.2389
0.2312
0.2235
0.2158
0.2081
0.2004
0.1927
0.1850
0.1773
0.1696
0.1619
0.1542
0.1465
0.1388
0.1311
0.1234
0.1157
0.1080
0.0926
0.0772
0.0618
0.0463
0.0309
0.0154
0.0000
⫺5.5
⫺6.0
⫺6.5
⫺7.0
⫺7.5
⫺8.1
⫺8.7
⫺9.3
⫺9.6
⫺9.9
⫺10.3
⫺10.6
⫺11.0
⫺11.3
⫺11.7
⫺12.1
⫺12.5
⫺12.9
⫺13.3
⫺13.8
⫺14.2
⫺14.7
⫺15.2
⫺15.8
⫺16.3
⫺16.9
⫺17.5
⫺18.1
⫺18.8
⫺19.6
⫺21.2
⫺23.0
⫺25.3
⫺28.1
⫺32.0
⫺38.4
—
⫺5.5
⫺5.7
⫺5.8
⫺6.0
⫺6.2
⫺6.4
⫺6.5
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.1
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.9
⫺9.1
⫺9.3
⫺9.5
⫺9.6
⫺9.8
⫺10.0
⫺5.5
⫺5.6
⫺5.8
⫺5.9
⫺6.1
⫺6.2
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.0
⫺8.1
⫺8.2
⫺8.4
⫺8.5
⫺8.7
⫺8.8
⫺9.0
⫺9.1
⫺9.3
⫺5.5
⫺5.7
⫺5.8
⫺6.0
⫺6.2
⫺6.3
⫺6.5
⫺6.7
⫺6.8
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.1
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.8
⫺9.0
⫺9.1
⫺9.3
⫺9.5
⫺9.7
⫺9.9
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
⫺6.0
⫺6.1
⫺6.3
⫺6.4
⫺6.6
⫺6.7
⫺6.9
⫺7.0
⫺7.1
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.4
⫺7.5
⫺7.6
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺7.9
⫺8.0
⫺8.1
⫺8.2
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.5
⫺8.6
⫺8.8
⫺8.9
⫺9.1
⫺9.2
⫺9.4
⫺9.5
⫺9.7
⫺6.0
⫺6.2
⫺6.3
⫺6.5
⫺6.6
⫺6.8
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.6
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.1
⫺8.2
⫺8.3
⫺8.4
⫺8.5
⫺8.6
⫺8.7
⫺8.7
⫺8.8
⫺8.9
⫺9.0
⫺9.2
⫺9.3
⫺9.5
⫺9.7
⫺9.9
⫺10.1
⫺10.2
–5.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.01
92.03
88.04
84.05
80.06
76.07
72.08
70.08
68.08
66.08
64.09
62.09
60.09
58.09
56.09
54.09
52.09
50.09
48.09
46.09
44.09
42.09
40.09
38.09
36.09
34.09
32.08
30.08
28.08
24.07
20.06
16.05
12.04
8.03
4.01
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.381
2.286
2.191
2.095
2.000
1.905
1.810
1.714
1.667
1.619
1.572
1.524
1.476
1.429
1.381
1.334
1.286
1.238
1.191
1.143
1.095
1.048
1.000
0.952
0.905
0.857
0.810
0.762
0.714
0.667
0.572
0.476
0.381
0.286
0.190
0.095
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
0.400
0.164
⫺0.074
⫺0.311
⫺0.548
⫺0.785
⫺1.022
⫺1.260
⫺1.378
⫺1.497
⫺1.616
⫺1.734
⫺1.853
⫺1.972
⫺2.090
⫺2.209
⫺2.327
⫺2.446
⫺2.565
⫺2.683
⫺2.802
⫺2.920
⫺3.039
⫺3.158
⫺3.276
⫺3.395
⫺3.514
⫺3.632
⫺3.751
⫺3.869
⫺4.107
⫺4.344
⫺4.581
⫺4.818
⫺5.056
⫺5.293
⫺5.530
Specific
volume, / (m3·kg⫺1)
0.7606
0.7605
0.7604
0.7602
0.7601
0.7600
0.7599
0.7598
0.7597
0.7597
0.7596
0.7596
0.7595
0.7594
0.7594
0.7593
0.7593
0.7592
0.7592
0.7591
0.7590
0.7590
0.7589
0.7589
0.7588
0.7588
0.7587
0.7586
0.7586
0.7585
0.7584
0.7583
0.7582
0.7581
0.7579
0.7578
0.7577
Wet bulb temperature
1-12
Reference data
–5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.03
88.04
84.05
80.06
76.07
72.08
70.08
68.09
66.09
64.09
62.09
60.09
58.10
56.10
54.10
52.10
50.10
48.10
46.10
44.10
42.10
40.09
38.09
36.09
34.09
32.09
30.08
28.08
24.07
20.06
16.05
12.04
8.03
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.486
2.386
2.287
2.187
2.088
1.988
1.889
1.790
1.740
1.690
1.640
1.591
1.541
1.491
1.442
1.392
1.342
1.292
1.243
1.193
1.143
1.094
1.044
0.994
0.944
0.895
0.845
0.795
0.746
0.696
0.597
0.497
0.398
0.298
0.199
0.099
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
1.166
0.918
0.670
0.423
0.175
⫺0.073
⫺0.320
⫺0.568
⫺0.692
⫺0.816
⫺0.940
⫺1.064
⫺1.188
⫺1.311
⫺1.435
⫺1.559
⫺1.683
⫺1.807
⫺1.931
⫺2.055
⫺2.178
⫺2.302
⫺2.426
⫺2.550
⫺2.674
⫺2.798
⫺2.922
⫺3.045
⫺3.169
⫺3.293
⫺3.541
⫺3.789
⫺4.036
⫺4.284
⫺4.532
⫺4.780
⫺5.027
Specific
volume, / (m3·kg⫺1)
0.7621
0.7620
0.7619
0.7618
0.7617
0.7615
0.7614
0.7613
0.7612
0.7612
0.7611
0.7611
0.7610
0.7609
0.7609
0.7608
0.7608
0.7607
0.7606
0.7606
0.7605
0.7605
0.7604
0.7603
0.7603
0.7602
0.7602
0.7601
0.7600
0.7600
0.7599
0.7597
0.7596
0.7595
0.7594
0.7593
0.7591
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.4015
0.3855
0.3695
0.3535
0.3375
0.3215
0.3054
0.2894
0.2814
0.2734
0.2654
0.2573
0.2493
0.2413
0.2333
0.2252
0.2172
0.2092
0.2012
0.1931
0.1851
0.1771
0.1690
0.1610
0.1530
0.1449
0.1369
0.1288
0.1208
0.1127
0.0966
0.0806
0.0645
0.0484
0.0322
0.0161
0.0000
⫺5.0
⫺5.5
⫺6.0
⫺6.5
⫺7.0
⫺7.6
⫺8.2
⫺8.8
⫺9.1
⫺9.4
⫺9.8
⫺10.1
⫺10.5
⫺10.8
⫺11.2
⫺11.6
⫺12.0
⫺12.4
⫺12.9
⫺13.3
⫺13.8
⫺14.3
⫺14.8
⫺15.3
⫺15.9
⫺16.4
⫺17.0
⫺17.7
⫺18.4
⫺19.1
⫺20.7
⫺22.6
⫺24.9
⫺27.7
⫺31.6
⫺38.0
—
⫺5.0
⫺5.2
⫺5.4
⫺5.5
⫺5.7
⫺5.9
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.2
⫺8.3
⫺8.5
⫺8.7
⫺8.9
⫺9.1
⫺9.3
⫺9.5
⫺9.7
⫺5.0
⫺5.1
⫺5.3
⫺5.5
⫺5.6
⫺5.8
⫺5.9
⫺6.1
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.1
⫺8.3
⫺8.4
⫺8.6
⫺8.8
⫺8.9
⫺5.0
⫺5.2
⫺5.3
⫺5.5
⫺5.7
⫺5.9
⫺6.0
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.0
⫺8.1
⫺8.2
⫺8.4
⫺8.6
⫺8.8
⫺8.9
⫺9.1
⫺9.3
⫺9.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.4190
0.4023
0.3856
0.3689
0.3522
0.3355
0.3187
0.3020
0.2936
0.2853
0.2769
0.2685
0.2602
0.2518
0.2434
0.2350
0.2267
0.2183
0.2099
0.2015
0.1932
0.1848
0.1764
0.1680
0.1596
0.1512
0.1428
0.1344
0.1261
0.1177
0.1009
0.0841
0.0673
0.0505
0.0336
0.0168
0.0000
⫺4.5
⫺5.0
⫺5.5
⫺6.0
⫺6.5
⫺7.1
⫺7.7
⫺8.3
⫺8.6
⫺8.9
⫺9.3
⫺9.6
⫺10.0
⫺10.4
⫺10.7
⫺11.1
⫺11.5
⫺12.0
⫺12.4
⫺12.8
⫺13.3
⫺13.8
⫺14.3
⫺14.8
⫺15.4
⫺16.0
⫺16.6
⫺17.2
⫺17.9
⫺18.7
⫺20.3
⫺22.2
⫺24.4
⫺27.3
⫺31.2
⫺37.7
—
⫺4.5
⫺4.7
⫺4.9
⫺5.0
⫺5.2
⫺5.4
⫺5.6
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺7.9
⫺8.1
⫺8.3
⫺8.5
⫺8.7
⫺8.9
⫺9.1
⫺9.3
⫺4.5
⫺4.7
⫺4.8
⫺5.0
⫺5.1
⫺5.3
⫺5.4
⫺5.6
⫺5.7
⫺5.8
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.7
⫺7.9
⫺8.0
⫺8.2
⫺8.4
⫺8.5
⫺4.5
⫺4.7
⫺4.9
⫺5.0
⫺5.2
⫺5.4
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.6
⫺7.7
⫺7.8
⫺8.0
⫺8.2
⫺8.4
⫺8.6
⫺8.8
⫺9.0
⫺9.2
–4.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.03
88.04
84.06
80.07
76.08
72.08
70.09
68.09
66.09
64.10
62.10
60.10
58.10
56.10
54.10
52.10
50.10
48.10
46.10
44.10
42.10
40.10
38.10
36.10
34.09
32.09
30.09
28.08
24.08
20.07
16.06
12.04
8.03
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.594
2.490
2.387
2.283
2.179
2.075
1.972
1.868
1.816
1.764
1.712
1.660
1.608
1.556
1.505
1.453
1.401
1.349
1.297
1.245
1.193
1.141
1.090
1.038
0.986
0.934
0.882
0.830
0.778
0.726
0.623
0.519
0.415
0.311
0.208
0.104
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
1.941
1.683
1.424
1.166
0.907
0.648
0.390
0.131
0.002
⫺0.128
⫺0.257
⫺0.386
⫺0.516
⫺0.645
⫺0.774
⫺0.904
⫺1.033
⫺1.162
⫺1.292
⫺1.421
⫺1.550
⫺1.680
⫺1.809
⫺1.938
⫺2.068
⫺2.197
⫺2.326
⫺2.455
⫺2.585
⫺2.714
⫺2.973
⫺3.231
⫺3.490
⫺3.749
⫺4.007
⫺4.266
⫺4.524
Specific
volume, / (m3·kg⫺1)
0.7637
0.7636
0.7635
0.7633
0.7632
0.7631
0.7629
0.7628
0.7628
0.7627
0.7626
0.7626
0.7625
0.7624
0.7624
0.7623
0.7623
0.7622
0.7621
0.7621
0.7620
0.7619
0.7619
0.7618
0.7618
0.7617
0.7616
0.7616
0.7615
0.7614
0.7613
0.7612
0.7611
0.7609
0.7608
0.7607
0.7606
Properties of humid air
1-13
–4 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.03
88.05
84.06
80.07
76.08
72.09
70.09
68.09
66.10
64.10
62.10
60.10
58.10
56.11
54.11
52.11
50.11
48.11
46.11
44.11
42.10
40.10
38.10
36.10
34.10
32.09
30.09
28.09
24.08
20.07
16.06
12.05
8.03
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.707
2.599
2.490
2.382
2.274
2.166
2.057
1.949
1.895
1.841
1.787
1.732
1.678
1.624
1.570
1.516
1.462
1.408
1.353
1.299
1.245
1.191
1.137
1.083
1.029
0.974
0.920
0.866
0.812
0.758
0.650
0.541
0.433
0.325
0.217
0.108
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
2.729
2.458
2.188
1.918
1.648
1.378
1.108
0.838
0.703
0.568
0.433
0.298
0.163
0.028
⫺0.107
⫺0.242
⫺0.377
⫺0.512
⫺0.647
⫺0.782
⫺0.917
⫺1.052
⫺1.187
⫺1.322
⫺1.457
⫺1.592
⫺1.727
⫺1.862
⫺1.997
⫺2.132
⫺2.402
⫺2.672
⫺2.942
⫺3.212
⫺3.482
⫺3.752
⫺4.022
Specific
volume, / (m3·kg⫺1)
0.7653
0.7651
0.7650
0.7649
0.7647
0.7646
0.7645
0.7643
0.7643
0.7642
0.7641
0.7641
0.7640
0.7640
0.7639
0.7638
0.7638
0.7637
0.7636
0.7636
0.7635
0.7634
0.7634
0.7633
0.7632
0.7632
0.7631
0.7630
0.7630
0.7629
0.7628
0.7626
0.7625
0.7624
0.7622
0.7621
0.7620
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.4371
0.4197
0.4023
0.3849
0.3674
0.3500
0.3326
0.3151
0.3064
0.2977
0.2889
0.2802
0.2715
0.2627
0.2540
0.2452
0.2365
0.2278
0.2190
0.2103
0.2016
0.1928
0.1840
0.1753
0.1666
0.1578
0.1490
0.1403
0.1315
0.1228
0.1052
0.0877
0.0702
0.0526
0.0351
0.0176
0.0000
⫺4.0
⫺4.5
⫺5.0
⫺5.5
⫺6.0
⫺6.6
⫺7.2
⫺7.8
⫺8.1
⫺8.5
⫺8.8
⫺9.2
⫺9.5
⫺9.9
⫺10.3
⫺10.7
⫺11.1
⫺11.5
⫺11.9
⫺12.4
⫺12.8
⫺13.3
⫺13.8
⫺14.4
⫺14.9
⫺15.5
⫺16.1
⫺16.8
⫺17.5
⫺18.2
⫺19.8
⫺21.7
⫺24.0
⫺26.9
⫺30.8
⫺37.3
—
⫺4.0
⫺4.2
⫺4.4
⫺4.6
⫺4.7
⫺4.9
⫺5.1
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.5
⫺7.7
⫺7.9
⫺8.1
⫺8.3
⫺8.5
⫺8.8
⫺9.0
⫺4.0
⫺4.2
⫺4.3
⫺4.5
⫺4.6
⫺4.8
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.3
⫺7.5
⫺7.7
⫺7.8
⫺8.0
⫺8.2
⫺4.0
⫺4.2
⫺4.4
⫺4.5
⫺4.7
⫺4.9
⫺5.1
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.2
⫺7.3
⫺7.4
⫺7.6
⫺7.8
⫺8.0
⫺8.2
⫺8.4
⫺8.6
⫺8.8
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.4560
0.4378
0.4197
0.4015
0.3833
0.3651
0.3469
0.3287
0.3196
0.3105
0.3014
0.2923
0.2832
0.2741
0.2650
0.2559
0.2468
0.2376
0.2285
0.2194
0.2103
0.2011
0.1920
0.1829
0.1738
0.1646
0.1555
0.1464
0.1372
0.1281
0.1098
0.0915
0.0732
0.0549
0.0366
0.0183
0.0000
⫺3.5
⫺4.0
⫺4.5
⫺5.0
⫺5.5
⫺6.1
⫺6.7
⫺7.3
⫺7.6
⫺8.0
⫺8.3
⫺8.7
⫺9.0
⫺9.4
⫺9.8
⫺10.2
⫺10.6
⫺11.0
⫺11.4
⫺11.9
⫺12.4
⫺12.9
⫺13.4
⫺13.9
⫺14.5
⫺15.1
⫺15.7
⫺16.3
⫺17.0
⫺17.8
⫺19.4
⫺21.3
⫺23.6
⫺26.5
⫺30.4
⫺36.9
—
⫺3.5
⫺3.7
⫺3.9
⫺4.1
⫺4.3
⫺4.5
⫺4.7
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.1
⫺7.3
⫺7.5
⫺7.7
⫺8.0
⫺8.2
⫺8.4
⫺8.6
⫺3.5
⫺3.7
⫺3.8
⫺4.0
⫺4.2
⫺4.3
⫺4.5
⫺4.7
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.5
⫺6.5
⫺6.5
⫺6.5
⫺6.5
⫺6.5
⫺6.5
⫺6.5
⫺3.5
⫺3.7
⫺3.9
⫺4.1
⫺4.2
⫺4.4
⫺4.6
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.8
⫺6.9
⫺7.0
⫺7.2
⫺7.4
⫺7.6
⫺7.8
⫺8.0
⫺8.2
⫺8.5
–3.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.03
88.05
84.06
80.07
76.08
72.09
70.09
68.10
66.10
64.10
62.11
60.11
58.11
56.11
54.11
52.11
50.11
48.11
46.11
44.11
42.11
40.11
38.11
36.10
34.10
32.10
30.09
28.09
24.08
20.07
16.06
12.05
8.03
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.824
2.711
2.598
2.485
2.372
2.260
2.146
2.034
1.977
1.920
1.864
1.808
1.751
1.695
1.638
1.582
1.525
1.469
1.412
1.356
1.299
1.243
1.186
1.130
1.073
1.017
0.960
0.904
0.847
0.791
0.678
0.565
0.452
0.339
0.226
0.113
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
3.526
3.244
2.962
2.680
2.399
2.117
1.835
1.553
1.412
1.272
1.131
0.990
0.849
0.708
0.567
0.426
0.285
0.144
0.003
⫺0.138
⫺0.278
⫺0.419
⫺0.560
⫺0.701
⫺0.842
⫺0.983
⫺1.124
⫺1.265
⫺1.406
⫺1.546
⫺1.828
⫺2.110
⫺2.392
⫺2.674
⫺2.956
⫺3.237
⫺3.519
Specific
volume, / (m3·kg⫺1)
0.7668
0.7667
0.7666
0.7664
0.7663
0.7662
0.7660
0.7659
0.7658
0.7657
0.7657
0.7656
0.7655
0.7655
0.7654
0.7653
0.7653
0.7652
0.7651
0.7650
0.7650
0.7649
0.7648
0.7648
0.7647
0.7646
0.7646
0.7645
0.7644
0.7644
0.7642
0.7641
0.7639
0.7638
0.7637
0.7635
0.7634
1-14
Reference data
–3 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.03
88.05
84.06
80.07
76.09
72.09
70.10
68.10
66.11
64.11
62.11
60.11
58.11
56.12
54.12
52.12
50.12
48.12
46.12
44.12
42.11
40.11
38.11
36.11
34.11
32.10
30.10
28.09
24.09
20.08
16.06
12.05
8.03
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
2.946
2.828
2.711
2.593
2.475
2.357
2.239
2.121
2.062
2.004
1.945
1.886
1.827
1.768
1.709
1.650
1.591
1.532
1.473
1.414
1.355
1.296
1.238
1.178
1.120
1.061
1.002
0.943
0.884
0.825
0.707
0.589
0.471
0.354
0.236
0.118
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
4.336
4.042
3.747
3.453
3.159
2.865
2.571
2.277
2.130
1.983
1.836
1.689
1.542
1.395
1.248
1.101
0.954
0.807
0.660
0.513
0.366
0.218
0.072
⫺0.076
⫺0.223
⫺0.370
⫺0.517
⫺0.664
⫺0.811
⫺0.958
⫺1.252
⫺1.546
⫺1.840
⫺2.134
⫺2.428
⫺2.722
⫺3.016
Specific
volume, / (m3·kg⫺1)
0.7684
0.7683
0.7681
0.7680
0.7678
0.7677
0.7676
0.7674
0.7673
0.7673
0.7672
0.7671
0.7670
0.7670
0.7669
0.7668
0.7668
0.7667
0.7666
0.7665
0.7665
0.7664
0.7663
0.7663
0.7662
0.7661
0.7660
0.7660
0.7659
0.7658
0.7657
0.7655
0.7654
0.7652
0.7651
0.7650
0.7648
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.4756
0.4567
0.4377
0.4188
0.3998
0.3808
0.3619
0.3429
0.3334
0.3239
0.3144
0.3049
0.2954
0.2859
0.2764
0.2669
0.2574
0.2479
0.2384
0.2288
0.2193
0.2098
0.2003
0.1908
0.1812
0.1717
0.1622
0.1527
0.1432
0.1336
0.1146
0.0955
0.0764
0.0573
0.0382
0.0191
0.0000
⫺3.0
⫺3.5
⫺4.0
⫺4.5
⫺5.0
⫺5.6
⫺6.2
⫺6.8
⫺7.2
⫺7.5
⫺7.8
⫺8.2
⫺8.6
⫺8.9
⫺9.3
⫺9.7
⫺10.1
⫺10.5
⫺11.0
⫺11.4
⫺11.9
⫺12.4
⫺12.9
⫺13.4
⫺14.0
⫺14.6
⫺15.2
⫺15.9
⫺16.6
⫺17.3
⫺18.9
⫺20.8
⫺23.1
⫺26.0
⫺30.0
⫺36.5
—
⫺3.0
⫺3.2
⫺3.4
⫺3.6
⫺3.8
⫺4.0
⫺4.2
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.7
⫺6.9
⫺7.2
⫺7.4
⫺7.6
⫺7.8
⫺8.1
⫺8.3
⫺3.0
⫺3.2
⫺3.3
⫺3.5
⫺3.7
⫺3.8
⫺4.0
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.0
⫺6.2
⫺6.3
⫺6.5
⫺6.7
⫺6.9
⫺7.1
⫺7.3
⫺7.5
⫺3.0
⫺3.2
⫺3.4
⫺3.6
⫺3.8
⫺4.0
⫺4.2
⫺4.4
⫺4.5
⫺4.6
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.4
⫺6.5
⫺6.6
⫺6.8
⫺7.0
⫺7.2
⫺7.5
⫺7.7
⫺7.9
⫺8.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.4960
0.4762
0.4565
0.4367
0.4170
0.3972
0.3774
0.3576
0.3477
0.3378
0.3279
0.3180
0.3081
0.2982
0.2883
0.2783
0.2684
0.2585
0.2486
0.2387
0.2288
0.2188
0.2089
0.1990
0.1890
0.1791
0.1692
0.1592
0.1493
0.1394
0.1195
0.0996
0.0797
0.0598
0.0399
0.0199
0.0000
⫺2.5
⫺3.0
⫺3.5
⫺4.0
⫺4.6
⫺5.1
⫺5.7
⫺6.4
⫺6.7
⫺7.0
⫺7.4
⫺7.7
⫺8.1
⫺8.4
⫺8.8
⫺9.2
⫺9.6
⫺10.1
⫺10.5
⫺11.0
⫺11.4
⫺11.9
⫺12.4
⫺13.0
⫺13.5
⫺14.1
⫺14.8
⫺15.4
⫺16.1
⫺16.9
⫺18.5
⫺20.4
⫺22.7
⫺25.6
⫺29.6
⫺36.1
—
⫺2.5
⫺2.7
⫺2.9
⫺3.1
⫺3.3
⫺3.5
⫺3.7
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.3
⫺6.5
⫺6.8
⫺7.0
⫺7.2
⫺7.5
⫺7.7
⫺7.9
⫺2.5
⫺2.7
⫺2.8
⫺3.0
⫺3.2
⫺3.4
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.1
⫺6.3
⫺6.5
⫺6.7
⫺6.9
⫺7.1
⫺2.5
⫺2.7
⫺2.9
⫺3.1
⫺3.3
⫺3.5
⫺3.7
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.0
⫺6.1
⫺6.2
⫺6.4
⫺6.6
⫺6.9
⫺7.1
⫺7.3
⫺7.5
⫺7.8
–2.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.04
88.05
84.07
80.08
76.09
72.10
70.10
68.11
66.11
64.11
62.12
60.12
58.12
56.12
54.12
52.12
50.12
48.12
46.12
44.12
42.12
40.12
38.12
36.11
34.11
32.11
30.10
28.10
24.09
20.08
16.07
12.05
8.04
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.073
2.950
2.827
2.704
2.582
2.458
2.336
2.213
2.151
2.090
2.028
1.967
1.905
1.844
1.782
1.721
1.660
1.598
1.537
1.475
1.414
1.352
1.291
1.229
1.168
1.106
1.045
0.983
0.922
0.860
0.738
0.615
0.492
0.369
0.246
0.122
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
5.158
4.851
4.544
4.237
3.930
3.623
3.317
3.010
2.856
2.703
2.550
2.396
2.243
2.089
1.936
1.782
1.629
1.476
1.322
1.169
1.015
0.862
0.708
0.555
0.402
0.248
0.095
⫺0.059
⫺0.212
⫺0.366
⫺0.672
⫺0.979
⫺1.286
⫺1.593
⫺1.900
⫺2.207
⫺2.514
Specific
volume, / (m3·kg⫺1)
0.7700
0.7698
0.7697
0.7695
0.7694
0.7692
0.7691
0.7689
0.7689
0.7688
0.7687
0.7686
0.7686
0.7685
0.7684
0.7683
0.7683
0.7682
0.7681
0.7680
0.7680
0.7679
0.7678
0.7677
0.7677
0.7676
0.7675
0.7674
0.7674
0.7673
0.7671
0.7670
0.7668
0.7667
0.7665
0.7664
0.7662
Properties of humid air
1-15
–2 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.04
88.05
84.07
80.08
76.09
72.10
70.11
68.11
66.11
64.12
62.12
60.12
58.12
56.13
54.13
52.13
50.13
48.13
46.13
44.13
42.12
40.12
38.12
36.12
34.11
32.11
30.11
28.10
24.09
20.08
16.07
12.05
8.04
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.205
3.077
2.949
2.820
2.692
2.564
2.436
2.308
2.244
2.179
2.115
2.051
1.987
1.923
1.859
1.795
1.731
1.667
1.602
1.538
1.474
1.410
1.346
1.282
1.218
1.154
1.090
1.026
0.962
0.897
0.769
0.641
0.513
0.385
0.256
0.128
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
5.992
5.672
5.352
5.032
4.712
4.392
4.072
3.752
3.591
3.431
3.271
3.111
2.951
2.791
2.631
2.471
2.311
2.151
1.991
1.831
1.671
1.511
1.350
1.190
1.030
0.870
0.710
0.550
0.390
0.230
⫺0.090
⫺0.410
⫺0.730
⫺1.050
⫺1.371
⫺1.691
⫺2.011
Specific
volume, / (m3·kg⫺1)
0.7716
0.7714
0.7713
0.7711
0.7710
0.7708
0.7706
0.7705
0.7704
0.7703
0.7703
0.7702
0.7701
0.7700
0.7699
0.7699
0.7698
0.7697
0.7696
0.7695
0.7695
0.7694
0.7693
0.7692
0.7692
0.7691
0.7690
0.7689
0.7688
0.7688
0.7686
0.7684
0.7683
0.7681
0.7680
0.7678
0.7677
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.5171
0.4966
0.4760
0.4554
0.4348
0.4141
0.3935
0.3729
0.3626
0.3522
0.3419
0.3316
0.3212
0.3109
0.3006
0.2902
0.2799
0.2696
0.2592
0.2489
0.2385
0.2282
0.2178
0.2075
0.1971
0.1868
0.1764
0.1661
0.1557
0.1453
0.1246
0.1038
0.0831
0.0623
0.0416
0.0208
0.0000
⫺2.0
⫺2.5
⫺3.0
⫺3.5
⫺4.1
⫺4.6
⫺5.2
⫺5.9
⫺6.2
⫺6.5
⫺6.9
⫺7.2
⫺7.6
⫺8.0
⫺8.4
⫺8.8
⫺9.2
⫺9.6
⫺10.0
⫺10.5
⫺11.0
⫺11.5
⫺12.0
⫺12.5
⫺13.1
⫺13.7
⫺14.3
⫺15.0
⫺15.7
⫺16.4
⫺18.0
⫺20.0
⫺22.3
⫺25.2
⫺29.2
⫺35.7
—
⫺2.0
⫺2.2
⫺2.4
⫺2.6
⫺2.8
⫺3.0
⫺3.3
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.2
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺5.9
⫺6.2
⫺6.4
⫺6.6
⫺6.9
⫺7.1
⫺7.4
⫺7.6
⫺2.0
⫺2.2
⫺2.4
⫺2.5
⫺2.7
⫺2.9
⫺3.1
⫺3.3
⫺3.4
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.0
⫺5.1
⫺5.2
⫺5.4
⫺5.5
⫺5.8
⫺6.0
⫺6.1
⫺6.4
⫺6.6
⫺6.7
⫺2.0
⫺2.2
⫺2.4
⫺2.6
⫺2.8
⫺3.0
⫺3.2
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.1
⫺5.3
⫺5.4
⫺5.5
⫺5.6
⫺5.7
⫺5.8
⫺6.0
⫺6.3
⫺6.5
⫺6.7
⫺7.0
⫺7.2
⫺7.4
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.5391
0.5177
0.4962
0.4747
0.4533
0.4318
0.4103
0.3888
0.3780
0.3672
0.3565
0.3457
0.3349
0.3242
0.3134
0.3026
0.2918
0.2810
0.2703
0.2595
0.2487
0.2379
0.2271
0.2163
0.2056
0.1948
0.1840
0.1732
0.1623
0.1515
0.1299
0.1083
0.0866
0.0650
0.0433
0.0217
0.0000
⫺1.5
⫺2.0
⫺2.5
⫺3.0
⫺3.6
⫺4.1
⫺4.7
⫺5.4
⫺5.7
⫺6.0
⫺6.4
⫺6.7
⫺7.1
⫺7.5
⫺7.9
⫺8.3
⫺8.7
⫺9.1
⫺9.6
⫺10.0
⫺10.5
⫺11.0
⫺11.5
⫺12.1
⫺12.6
⫺13.2
⫺13.8
⫺14.5
⫺15.2
⫺16.0
⫺17.6
⫺19.5
⫺21.8
⫺24.8
⫺28.8
⫺35.3
—
⫺1.5
⫺1.7
⫺1.9
⫺2.1
⫺2.4
⫺2.6
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.5
⫺5.8
⫺6.0
⫺6.3
⫺6.5
⫺6.8
⫺7.0
⫺7.3
⫺1.5
⫺1.7
⫺1.9
⫺2.1
⫺2.2
⫺2.4
⫺2.6
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺5.0
⫺5.2
⫺5.4
⫺5.6
⫺5.8
⫺6.0
⫺6.2
⫺6.4
⫺1.5
⫺1.7
⫺1.9
⫺2.1
⫺2.3
⫺2.5
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.7
⫺4.8
⫺5.0
⫺5.1
⫺5.2
⫺5.3
⫺5.4
⫺5.7
⫺5.9
⫺6.1
⫺6.4
⫺6.6
⫺6.8
⫺7.1
–1.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.04
88.06
84.07
80.09
76.10
72.11
70.11
68.12
66.12
64.12
62.13
60.13
58.13
56.13
54.13
52.13
50.13
48.13
46.13
44.13
42.13
40.13
38.13
36.12
34.12
32.12
30.11
28.11
24.10
20.09
16.07
12.06
8.04
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.342
3.208
3.075
2.941
2.807
2.674
2.540
2.406
2.339
2.272
2.206
2.139
2.072
2.005
1.938
1.872
1.805
1.738
1.671
1.604
1.537
1.470
1.404
1.337
1.270
1.203
1.136
1.069
1.003
0.936
0.802
0.668
0.535
0.401
0.267
0.134
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
6.840
6.506
6.172
5.838
5.504
5.171
4.837
4.503
4.336
4.169
4.002
3.835
3.668
3.501
3.334
3.167
3.000
2.833
2.666
2.499
2.332
2.165
1.998
1.831
1.664
1.497
1.330
1.163
0.996
0.829
0.496
0.162
⫺0.172
⫺0.506
⫺0.840
⫺1.174
⫺1.508
Specific
volume, / (m3·kg⫺1)
0.7732
0.7730
0.7729
0.7727
0.7725
0.7724
0.7722
0.7720
0.7720
0.7719
0.7718
0.7717
0.7716
0.7715
0.7715
0.7714
0.7713
0.7712
0.7711
0.7710
0.7710
0.7709
0.7708
0.7707
0.7706
0.7706
0.7705
0.7704
0.7703
0.7702
0.7701
0.7699
0.7697
0.7696
0.7694
0.7692
0.7691
1-16
Reference data
–1 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.04
88.06
84.07
80.09
76.10
72.11
70.12
68.12
66.12
64.13
62.13
60.13
58.14
56.14
54.14
52.14
50.14
48.14
46.14
44.14
42.14
40.13
38.13
36.13
34.12
32.12
30.12
28.11
24.10
20.09
16.07
12.06
8.04
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.484
3.345
3.206
3.066
2.927
2.787
2.648
2.509
2.439
2.369
2.300
2.230
2.160
2.091
2.021
1.951
1.882
1.812
1.742
1.672
1.603
1.533
1.463
1.394
1.324
1.254
1.185
1.115
1.045
0.976
0.836
0.697
0.558
0.418
0.279
0.139
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
7.702
7.354
7.005
6.657
6.309
5.960
5.612
5.264
5.090
4.916
4.741
4.567
4.393
4.219
4.045
3.871
3.696
3.522
3.348
3.174
3.000
2.826
2.652
2.477
2.303
2.129
1.955
1.781
1.607
1.433
1.084
0.736
0.388
0.039
⫺0.309
⫺0.657
⫺1.006
Specific
volume, / (m3·kg⫺1)
0.7748
0.7746
0.7744
0.7743
0.7741
0.7739
0.7738
0.7736
0.7735
0.7734
0.7733
0.7732
0.7732
0.7731
0.7730
0.7729
0.7728
0.7727
0.7726
0.7726
0.7725
0.7724
0.7723
0.7722
0.7721
0.7720
0.7720
0.7719
0.7718
0.7717
0.7715
0.7714
0.7712
0.7710
0.7708
0.7707
0.7705
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.5620
0.5396
0.5172
0.4949
0.4725
0.4501
0.4277
0.4052
0.3940
0.3828
0.3716
0.3604
0.3492
0.3379
0.3267
0.3155
0.3042
0.2930
0.2818
0.2705
0.2593
0.2480
0.2368
0.2255
0.2143
0.2030
0.1918
0.1805
0.1692
0.1580
0.1354
0.1129
0.0903
0.0678
0.0452
0.0226
0.0000
⫺1.0
⫺1.5
⫺2.0
⫺2.5
⫺3.1
⫺3.7
⫺4.3
⫺4.9
⫺5.2
⫺5.6
⫺5.9
⫺6.3
⫺6.6
⫺7.0
⫺7.4
⫺7.8
⫺8.2
⫺8.6
⫺9.1
⫺9.6
⫺10.0
⫺10.5
⫺11.1
⫺11.6
⫺12.2
⫺12.8
⫺13.4
⫺14.1
⫺14.8
⫺15.5
⫺17.2
⫺19.1
⫺21.4
⫺24.4
⫺28.4
⫺35.0
—
⫺1.0
⫺1.2
⫺1.4
⫺1.7
⫺1.9
⫺2.1
⫺2.3
⫺2.5
⫺2.7
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.2
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.2
⫺5.4
⫺5.7
⫺5.9
⫺6.2
⫺6.4
⫺6.7
⫺6.9
⫺1.0
⫺1.2
⫺1.4
⫺1.6
⫺1.8
⫺1.9
⫺2.1
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.6
⫺4.8
⫺5.0
⫺5.2
⫺5.4
⫺5.6
⫺5.8
⫺6.0
⫺1.0
⫺1.2
⫺1.4
⫺1.6
⫺1.9
⫺2.1
⫺2.3
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺2.9
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.9
⫺4.0
⫺4.1
⫺4.2
⫺4.3
⫺4.4
⫺4.6
⫺4.7
⫺4.8
⫺4.9
⫺5.0
⫺5.3
⫺5.5
⫺5.8
⫺6.0
⫺6.2
⫺6.5
⫺6.7
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.5857
0.5624
0.5391
0.5158
0.4924
0.4691
0.4457
0.4224
0.4107
0.3990
0.3873
0.3756
0.3639
0.3522
0.3405
0.3288
0.3171
0.3054
0.2937
0.2820
0.2702
0.2585
0.2468
0.2351
0.2234
0.2116
0.1999
0.1882
0.1764
0.1647
0.1412
0.1177
0.0942
0.0706
0.0471
0.0236
0.0000
⫺0.5
⫺1.0
⫺1.5
⫺2.0
⫺2.6
⫺3.2
⫺3.8
⫺4.4
⫺4.7
⫺5.1
⫺5.4
⫺5.8
⫺6.1
⫺6.5
⫺6.9
⫺7.3
⫺7.7
⫺8.2
⫺8.6
⫺9.1
⫺9.6
⫺10.1
⫺10.6
⫺11.1
⫺11.7
⫺12.3
⫺12.9
⫺13.6
⫺14.3
⫺15.1
⫺16.7
⫺18.7
⫺21.0
⫺23.9
⫺28.0
⫺34.6
—
⫺0.5
⫺0.7
⫺0.9
⫺1.2
⫺1.4
⫺1.6
⫺1.9
⫺2.1
⫺2.2
⫺2.3
⫺2.4
⫺2.6
⫺2.7
⫺2.8
⫺2.9
⫺3.0
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.8
⫺5.0
⫺5.3
⫺5.5
⫺5.8
⫺6.1
⫺6.3
⫺6.6
⫺0.5
⫺0.7
⫺0.9
⫺1.1
⫺1.3
⫺1.5
⫺1.7
⫺1.9
⫺2.0
⫺2.1
⫺2.2
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.2
⫺4.4
⫺4.6
⫺4.8
⫺5.0
⫺5.2
⫺5.5
⫺5.7
⫺0.5
⫺0.7
⫺0.9
⫺1.2
⫺1.4
⫺1.6
⫺1.8
⫺2.0
⫺2.2
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.6
⫺3.7
⫺3.8
⫺3.9
⫺4.0
⫺4.2
⫺4.3
⫺4.4
⫺4.5
⫺4.6
⫺4.9
⫺5.1
⫺5.4
⫺5.6
⫺5.9
⫺6.2
⫺6.4
–0.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.04
88.06
84.08
80.09
76.11
72.12
70.12
68.13
66.13
64.13
62.14
60.14
58.14
56.14
54.14
52.14
50.14
48.14
46.14
44.14
42.14
40.14
38.14
36.13
34.13
32.13
30.12
28.12
24.11
20.09
16.08
12.06
8.04
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.632
3.487
3.342
3.196
3.051
2.906
2.760
2.615
2.542
2.470
2.397
2.325
2.252
2.179
2.107
2.034
1.961
1.889
1.816
1.744
1.671
1.598
1.526
1.453
1.380
1.308
1.235
1.162
1.090
1.017
0.872
0.726
0.581
0.436
0.291
0.145
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
8.577
8.214
7.851
7.485
7.124
6.761
6.398
6.035
5.853
5.672
5.490
5.309
5.127
4.945
4.764
4.582
4.400
4.219
4.037
3.856
3.674
3.492
3.311
3.129
2.948
2.766
2.584
2.403
2.221
2.040
1.676
1.313
0.950
0.587
0.224
⫺0.140
⫺0.503
Specific
volume, / (m3·kg⫺1)
0.7764
0.7762
0.7760
0.7759
0.7757
0.7755
0.7753
0.7751
0.7751
0.7750
0.7749
0.7748
0.7747
0.7746
0.7745
0.7744
0.7743
0.7742
0.7742
0.7741
0.7740
0.7739
0.7738
0.7737
0.7736
0.7735
0.7734
0.7734
0.7733
0.7732
0.7730
0.7728
0.7726
0.7725
0.7723
0.7721
0.7719
Properties of humid air
1-17
0 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.04
88.06
84.08
80.10
76.11
72.12
70.13
68.13
66.14
64.14
62.14
60.14
58.15
56.15
54.15
52.15
50.15
48.15
46.15
44.15
42.15
40.14
38.14
36.14
34.14
32.13
30.13
28.12
24.11
20.10
16.08
12.06
8.04
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.789
3.637
3.486
3.334
3.183
3.031
2.880
2.728
2.652
2.576
2.501
2.425
2.349
2.273
2.198
2.122
2.046
1.970
1.894
1.819
1.743
1.667
1.591
1.516
1.440
1.364
1.288
1.212
1.137
1.061
0.909
0.758
0.606
0.455
0.303
0.152
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
9.475
9.096
8.717
8.338
7.959
7.580
7.201
6.822
6.633
6.443
6.254
6.064
5.875
5.685
5.496
5.306
5.117
4.927
4.738
4.548
4.359
4.169
3.980
3.790
3.601
3.411
3.222
3.032
2.843
2.653
2.274
1.895
1.516
1.137
0.758
0.379
0.000
Specific
volume, / (m3·kg⫺1)
0.7780
0.7778
0.7776
0.7775
0.7773
0.7771
0.7769
0.7767
0.7766
0.7765
0.7764
0.7763
0.7762
0.7761
0.7761
0.7760
0.7759
0.7758
0.7757
0.7756
0.7755
0.7754
0.7753
0.7752
0.7751
0.7750
0.7749
0.7748
0.7747
0.7747
0.7745
0.7743
0.7741
0.7739
0.7737
0.7735
0.7733
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.6108
0.5865
0.5622
0.5379
0.5136
0.4892
0.4649
0.4405
0.4283
0.4161
0.4039
0.3918
0.3796
0.3674
0.3552
0.3429
0.3307
0.3185
0.3063
0.2941
0.2819
0.2696
0.2574
0.2452
0.2330
0.2207
0.2085
0.1962
0.1840
0.1718
0.1473
0.1228
0.0982
0.0737
0.0491
0.0246
0.0000
0.0
⫺0.5
⫺1.0
⫺1.5
⫺2.1
⫺2.7
⫺3.3
⫺3.9
⫺4.2
⫺4.6
⫺4.9
⫺5.3
⫺5.7
⫺6.0
⫺6.4
⫺6.8
⫺7.3
⫺7.7
⫺8.1
⫺8.6
⫺9.1
⫺9.6
⫺10.1
⫺10.7
⫺11.2
⫺11.8
⫺12.5
⫺13.1
⫺13.8
⫺14.6
⫺16.3
⫺18.2
⫺20.5
⫺23.5
⫺27.6
⫺34.2
—
0.0
⫺0.2
⫺0.5
⫺0.7
⫺0.9
⫺1.1
⫺1.4
⫺1.6
⫺1.7
⫺1.9
⫺2.0
⫺2.1
⫺2.2
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.9
⫺4.0
⫺4.1
⫺4.3
⫺4.4
⫺4.7
⫺4.9
⫺5.2
⫺5.5
⫺5.7
⫺6.0
⫺6.3
0.0
⫺0.2
⫺0.4
⫺0.6
⫺0.8
⫺1.0
⫺1.2
⫺1.4
⫺1.5
⫺1.6
⫺1.7
⫺1.8
⫺1.9
⫺2.0
⫺2.1
⫺2.2
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.8
⫺4.0
⫺4.2
⫺4.4
⫺4.7
⫺4.9
⫺5.1
⫺5.3
0.0
⫺0.2
⫺0.4
⫺0.7
⫺0.9
⫺1.1
⫺1.3
⫺1.6
⫺1.7
⫺1.8
⫺1.9
⫺2.0
⫺2.2
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.3
⫺3.4
⫺3.5
⫺3.6
⫺3.8
⫺3.9
⫺4.0
⫺4.1
⫺4.3
⫺4.5
⫺4.8
⫺5.0
⫺5.3
⫺5.5
⫺5.8
⫺6.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.6333
0.6082
0.5830
0.5578
0.5325
0.5073
0.4821
0.3468
0.4442
0.4315
0.4189
0.4062
0.3936
0.3810
0.3683
0.3556
0.3430
0.3303
0.3177
0.3050
0.2923
0.2796
0.2670
0.2543
0.2416
0.2289
0.2162
0.2035
0.1908
0.1781
0.1527
0.1273
0.1019
0.0764
0.0510
0.0255
0.0000
0.5
0.0
⫺0.6
⫺1.1
⫺1.6
⫺2.2
⫺2.8
⫺3.5
⫺3.8
⫺4.2
⫺4.5
⫺4.9
⫺5.2
⫺5.6
⫺6.0
⫺6.4
⫺6.8
⫺7.3
⫺7.7
⫺8.2
⫺8.7
⫺9.2
⫺9.7
⫺10.2
⫺10.8
⫺11.4
⫺12.1
⫺12.7
⫺13.4
⫺14.2
⫺15.9
⫺17.8
⫺20.2
⫺23.1
⫺27.2
⫺33.8
—
0.5
0.3
0.0
⫺0.2
⫺0.5
⫺0.7
⫺0.9
⫺1.2
⫺1.3
⫺1.4
⫺1.6
⫺1.7
⫺1.8
⫺1.9
⫺2.1
⫺2.2
⫺2.3
⫺2.4
⫺2.6
⫺2.7
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.3
⫺3.5
⫺3.6
⫺3.7
⫺3.9
⫺4.0
⫺4.3
⫺4.6
⫺4.8
⫺5.1
⫺5.4
⫺5.7
⫺6.0
0.5
0.3
0.1
⫺0.1
⫺0.3
⫺0.5
⫺0.8
⫺1.0
⫺1.1
⫺1.2
⫺1.3
⫺1.4
⫺1.5
⫺1.6
⫺1.7
⫺1.8
⫺1.9
⫺2.0
⫺2.1
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺2.9
⫺3.0
⫺3.1
⫺3.3
⫺3.4
⫺3.6
⫺3.8
⫺4.1
⫺4.3
⫺4.5
⫺4.8
⫺5.0
0.5
0.3
0.1
⫺0.2
⫺0.4
⫺0.7
⫺0.9
⫺1.1
⫺1.3
⫺1.4
⫺1.5
⫺1.6
⫺1.7
⫺1.9
⫺2.0
⫺2.1
⫺2.2
⫺2.4
⫺2.5
⫺2.6
⫺2.7
⫺2.9
⫺3.0
⫺3.1
⫺3.2
⫺3.4
⫺3.5
⫺3.6
⫺3.7
⫺3.9
⫺4.1
⫺4.4
⫺4.7
⫺4.9
⫺5.2
⫺5.5
⫺5.8
0.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.02
92.05
88.07
84.08
80.10
76.11
72.13
70.13
68.14
66.14
64.14
62.15
60.15
58.15
56.15
54.16
52.16
50.16
48.16
46.16
44.15
42.15
40.15
38.15
36.14
34.14
32.14
30.13
28.13
24.11
20.10
16.08
12.07
8.05
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
3.930
3.772
3.615
3.458
3.301
3.144
2.986
2.829
2.751
2.672
2.594
2.515
2.436
2.358
2.279
2.200
2.122
2.043
1.965
1.886
1.808
1.729
1.650
1.572
1.493
1.415
1.336
1.258
1.179
1.100
0.943
0.786
0.629
0.471
0.314
0.157
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
10.334
9.941
9.548
9.154
8.761
8.368
7.975
7.581
7.385
7.188
6.992
6.795
6.598
6.402
6.205
6.008
5.812
5.615
5.418
5.222
5.025
4.829
4.632
4.435
4.239
4.042
3.846
3.649
3.452
3.256
2.862
2.469
2.076
1.683
1.290
0.896
0.503
Specific
volume, / (m3·kg⫺1)
0.7796
0.7794
0.7792
0.7790
0.7788
0.7787
0.7785
0.7783
0.7782
0.7781
0.7780
0.7779
0.7778
0.7777
0.7776
0.7775
0.7774
0.7773
0.7772
0.7771
0.7770
0.7769
0.7768
0.7767
0.7766
0.7765
0.7764
0.7763
0.7762
0.7761
0.7759
0.7757
0.7755
0.7753
0.7752
0.7750
0.7748
1-18
Reference data
1 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.05
88.07
84.09
80.10
76.12
72.13
70.14
68.14
66.15
64.15
62.15
60.16
58.16
56.16
54.16
52.16
50.16
48.16
46.16
44.16
42.16
40.16
38.15
36.15
34.15
32.14
30.14
28.13
24.12
20.10
16.09
12.07
8.05
4.02
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
4.075
3.912
3.749
3.586
3.423
3.260
3.097
2.934
2.852
2.771
2.690
2.608
2.526
2.445
2.364
2.282
2.200
2.119
2.038
1.956
1.874
1.793
1.712
1.630
1.548
1.467
1.386
1.304
1.222
1.141
0.978
0.815
0.652
0.489
0.326
0.163
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
11.20
10.80
10.39
9.98
9.573
9.165
8.757
8.349
8.145
7.941
7.737
7.533
7.329
7.125
6.921
6.717
6.513
6.309
6.105
5.901
5.697
5.493
5.289
5.085
4.881
4.678
4.474
4.270
4.066
3.862
3.454
3.046
2.638
2.230
1.822
1.414
1.006
Specific
volume, / (m3·kg⫺1)
0.7812
0.7810
0.7808
0.7806
0.7804
0.7802
0.7800
0.7798
0.7797
0.7796
0.7795
0.7794
0.7793
0.7792
0.7791
0.7790
0.7789
0.7788
0.7787
0.7786
0.7785
0.7784
0.7783
0.7782
0.7781
0.7780
0.7779
0.7778
0.7777
0.7776
0.7774
0.7772
0.7770
0.7768
0.7766
0.7764
0.7762
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.6566
0.6305
0.6044
0.5783
0.5521
0.5260
0.4998
0.4736
0.4605
0.4474
0.4343
0.4212
0.4081
0.3950
0.3819
0.3688
0.3556
0.3425
0.3294
0.3162
0.3031
0.2900
0.2768
0.2637
0.2505
0.2374
0.2242
0.2110
0.1979
0.1847
0.1584
0.1320
0.1056
0.0792
0.0528
0.0264
0.0000
1.0
0.4
⫺0.1
⫺0.7
⫺1.2
⫺1.8
⫺2.4
⫺3.0
⫺3.4
⫺3.7
⫺4.1
⫺4.4
⫺4.8
⫺5.2
⫺5.6
⫺6.0
⫺6.4
⫺6.9
⫺7.3
⫺7.8
⫺8.3
⫺8.8
⫺9.3
⫺9.8
⫺10.4
⫺11.0
⫺11.7
⫺12.3
⫺13.0
⫺13.8
⫺15.5
⫺17.4
⫺19.8
⫺22.8
⫺26.8
⫺33.5
—
1.0
0.8
0.5
0.3
0.1
⫺0.3
⫺0.5
⫺0.7
⫺0.9
⫺1.0
⫺1.1
⫺1.3
⫺1.4
⫺1.5
⫺1.6
⫺1.8
⫺1.9
⫺2.0
⫺2.2
⫺2.3
⫺2.4
⫺2.6
⫺2.7
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.4
⫺3.5
⫺3.6
⫺3.9
⫺4.2
⫺4.5
⫺4.8
⫺5.1
⫺5.3
⫺5.6
1.0
0.8
0.6
0.4
0.2
⫺0.1
⫺0.3
⫺0.5
⫺0.6
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.2
⫺1.3
⫺1.4
⫺1.5
⫺1.6
⫺1.7
⫺1.8
⫺2.0
⫺2.1
⫺2.2
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.8
⫺2.9
⫺3.0
⫺3.2
⫺3.5
⫺3.7
⫺3.9
⫺4.2
⫺4.4
⫺4.7
1.0
0.8
0.5
0.3
0.1
⫺0.2
⫺0.5
⫺0.7
⫺0.8
⫺0.9
⫺1.1
⫺1.2
⫺1.3
⫺1.4
⫺1.6
⫺1.7
⫺1.8
⫺1.9
⫺2.1
⫺2.2
⫺2.3
⫺2.5
⫺2.6
⫺2.7
⫺2.8
⫺3.0
⫺3.1
⫺3.2
⫺3.4
⫺3.5
⫺3.8
⫺4.0
⫺4.3
⫺4.6
⫺4.9
⫺5.1
⫺5.4
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.6807
0.6536
0.6265
0.5995
0.5724
0.5453
0.5181
0.4910
0.4774
0.4638
0.4503
0.4367
0.4231
0.4095
0.3959
0.3823
0.3687
0.3551
0.3415
0.3279
0.3142
0.3006
0.2870
0.2734
0.2597
0.2461
0.2324
0.2188
0.2052
0.1915
0.1642
0.1369
0.1095
0.0822
0.0548
0.0274
0.0000
1.5
0.9
0.4
⫺0.2
⫺0.8
⫺1.4
⫺2.0
⫺2.6
⫺3.0
⫺3.3
⫺3.7
⫺4.0
⫺4.4
⫺4.8
⫺5.2
⫺5.6
⫺6.0
⫺6.4
⫺6.9
⫺7.4
⫺7.8
⫺8.4
⫺8.9
⫺9.4
⫺10.0
⫺10.6
⫺11.3
⫺11.9
⫺12.6
⫺13.4
⫺15.1
⫺17.0
⫺19.4
⫺22.4
⫺26.5
⫺33.2
—
1.5
1.3
1.0
0.8
0.5
0.3
⫺1.0
⫺0.3
⫺0.4
⫺0.6
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.2
⫺1.4
⫺1.5
⫺1.6
⫺1.8
⫺1.9
⫺2.0
⫺2.2
⫺2.3
⫺2.4
⫺2.6
⫺2.7
⫺2.9
⫺3.0
⫺3.1
⫺3.3
⫺3.6
⫺3.8
⫺4.1
⫺4.4
⫺4.7
⫺5.0
⫺5.3
1.5
1.3
1.1
0.9
0.7
0.4
0.2
⫺0.1
⫺0.2
⫺0.3
⫺0.4
⫺0.5
⫺0.6
⫺0.8
⫺0.9
⫺1.0
⫺1.1
⫺1.2
⫺1.3
⫺1.4
⫺1.6
⫺1.7
⫺1.8
⫺1.9
⫺2.0
⫺2.1
⫺2.3
⫺2.4
⫺2.5
⫺2.6
⫺2.9
⫺3.1
⫺3.3
⫺3.6
⫺3.8
⫺4.1
⫺4.3
1.5
1.3
1.0
0.8
0.6
0.3
0.1
⫺0.3
⫺0.4
⫺0.5
⫺0.6
⫺0.8
⫺0.9
⫺1.0
⫺1.1
⫺1.3
⫺1.4
⫺1.5
⫺1.7
⫺1.8
⫺1.9
⫺2.1
⫺2.2
⫺2.3
⫺2.5
⫺2.6
⫺2.7
⫺2.9
⫺3.0
⫺3.1
⫺3.4
⫺3.7
⫺4.0
⫺4.2
⫺4.5
⫺4.6
⫺5.1
1.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.05
88.07
84.09
80.11
76.12
72.14
70.14
68.15
66.15
64.15
62.16
60.16
58.16
56.17
54.17
52.17
50.17
48.17
46.17
44.17
42.16
40.16
38.16
36.16
34.15
32.15
30.14
28.14
24.12
20.11
16.09
12.07
8.05
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
4.225
4.056
3.887
3.718
3.549
3.380
3.211
3.042
2.958
2.873
2.789
2.704
2.620
2.535
2.451
2.366
2.282
2.197
2.113
2.028
1.944
1.859
1.775
1.690
1.606
1.521
1.436
1.352
1.268
1.183
1.014
0.845
0.676
0.507
0.338
0.169
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
12.09
11.66
11.24
10.82
10.40
9.972
9.548
8.125
8.914
8.702
8.491
8.279
8.068
7.856
7.644
7.438
7.221
7.010
6.798
6.587
6.375
6.163
5.952
5.740
5.529
5.317
5.106
4.894
4.682
4.471
4.048
3.625
3.202
2.778
2.355
1.932
1.509
Specific
volume, / (m3·kg⫺1)
0.7828
0.7826
0.7824
0.7822
0.7820
0.7818
0.7816
0.7814
0.7813
0.7812
0.7811
0.7810
0.7809
0.7808
0.7806
0.7805
0.7804
0.7803
0.7802
0.7801
0.7800
0.7799
0.7798
0.7797
0.7796
0.7795
0.7794
0.7793
0.7792
0.7791
0.7789
0.7787
0.7784
0.7782
0.7780
0.7778
0.7776
Properties of humid air
1-19
2 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.05
88.07
84.09
80.11
76.13
72.14
70.15
68.15
66.16
64.16
62.16
60.17
58.17
56.17
54.17
52.17
50.17
48.17
46.17
44.17
42.17
40.17
38.16
36.16
34.16
32.15
30.15
28.14
24.13
20.11
16.09
12.07
8.05
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
4.380
4.205
4.030
3.855
3.679
3.504
3.329
3.154
3.066
2.979
2.891
2.803
2.716
2.628
2.540
2.453
2.365
2.278
2.190
2.102
2.015
1.927
1.840
1.752
1.664
1.577
1.489
1.402
1.314
1.226
1.051
0.876
0.701
0.526
0.350
0.175
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
12.98
12.54
12.10
11.67
11.23
10.79
10.35
9.911
9.692
9.472
9.253
9.033
8.814
8.594
8.375
8.156
7.936
7.717
7.497
7.278
7.058
6.839
6.620
6.400
6.181
5.961
5.742
5.523
5.303
5.084
4.645
4.206
3.767
3.328
2.890
2.451
2.012
Specific
volume, / (m3·kg⫺1)
0.7845
0.7843
0.7840
0.7838
0.7836
0.7834
0.7832
0.7829
0.7828
0.7827
0.7826
0.7825
0.7824
0.7823
0.7822
0.7821
0.7820
0.7819
0.7817
0.7816
0.7815
0.7814
0.7813
0.7812
0.7811
0.7810
0.7809
0.7808
0.7807
0.7805
0.7803
0.7801
0.7799
0.7797
0.7795
0.7792
0.7790
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.7055
0.6774
0.6494
0.6213
0.5933
0.5652
0.5371
0.5089
0.4949
0.4808
0.4667
0.4526
0.4386
0.4245
0.4104
0.3963
0.3822
0.3681
0.3540
0.3399
0.3257
0.3116
0.2975
0.2834
0.2692
0.2551
0.2410
0.2268
0.2127
0.1985
0.1702
0.1419
0.1135
0.0852
0.0568
0.0284
0.0000
2.0
1.4
0.8
0.2
⫺0.3
⫺0.9
⫺1.5
⫺2.2
⫺2.5
⫺2.9
⫺3.2
⫺3.6
⫺4.0
⫺4.3
⫺4.7
⫺5.2
⫺5.6
⫺6.0
⫺6.5
⫺6.9
⫺7.4
⫺7.9
⫺8.5
⫺9.0
⫺9.6
⫺10.2
⫺10.9
⫺11.5
⫺12.2
⫺13.0
⫺14.7
⫺16.7
⫺19.0
⫺22.0
⫺26.1
⫺32.8
—
2.0
1.8
1.5
1.3
1.0
0.8
0.5
0.3
0.1
⫺0.1
⫺0.3
⫺0.4
⫺0.5
⫺0.7
⫺0.8
⫺0.9
⫺1.1
⫺1.2
⫺1.4
⫺1.5
⫺1.6
⫺1.8
⫺1.9
⫺2.0
⫺2.2
⫺2.3
⫺2.5
⫺2.6
⫺2.8
⫺2.9
⫺3.2
⫺3.5
⫺3.8
⫺4.1
⫺4.4
⫺4.7
⫺5.0
2.0
1.8
1.6
1.4
1.1
0.9
0.7
0.5
0.4
0.3
0.1
⫺0.1
⫺0.2
⫺0.3
⫺0.4
⫺0.6
⫺0.7
⫺0.8
⫺0.9
⫺1.0
⫺1.1
⫺1.3
⫺1.4
⫺1.5
⫺1.6
⫺1.7
⫺1.9
⫺2.0
⫺2.1
⫺2.2
⫺2.5
⫺2.7
⫺3.0
⫺3.2
⫺3.5
⫺3.7
⫺4.0
2.0
1.8
1.5
1.3
1.0
0.8
0.5
0.3
0.2
⫺0.1
⫺0.2
⫺0.3
⫺0.5
⫺0.6
⫺0.7
⫺0.9
⫺1.0
⫺1.1
⫺1.3
⫺1.4
⫺1.5
⫺1.7
⫺1.8
⫺1.9
⫺2.1
⫺2.2
⫺2.3
⫺2.5
⫺2.6
⫺2.8
⫺3.0
⫺3.3
⫺3.6
⫺3.9
⫺4.2
⫺4.5
⫺4.8
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.7311
0.7020
0.6730
0.6439
0.6148
0.5857
0.5566
0.5274
0.5129
0.4983
0.4837
0.4691
0.4545
0.4399
0.4253
0.4107
0.3961
0.3815
0.3669
0.3522
0.3376
0.3230
0.3083
0.2937
0.2791
0.2644
0.2498
0.2351
0.2204
0.2058
0.1764
0.1471
0.1177
0.0883
0.0589
0.0294
0.0000
2.5
1.9
1.3
0.7
0.1
⫺0.5
⫺1.1
⫺1.8
⫺2.1
⫺2.4
⫺2.8
⫺3.2
⫺3.5
⫺3.9
⫺4.3
⫺4.7
⫺5.2
⫺5.6
⫺6.1
⫺6.5
⫺7.0
⫺7.5
⫺8.1
⫺8.6
⫺9.2
⫺9.8
⫺10.5
⫺11.1
⫺11.8
⫺12.6
⫺14.3
⫺16.3
⫺18.7
⫺21.7
⫺25.8
⫺32.5
—
2.5
2.3
2.0
1.7
1.5
1.2
1.0
0.7
0.6
0.5
0.3
0.2
0.1
⫺0.3
⫺0.4
⫺0.5
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.2
⫺1.4
⫺1.5
⫺1.7
⫺1.8
⫺2.0
⫺2.1
⫺2.2
⫺2.4
⫺2.5
⫺2.8
⫺3.1
⫺3.4
⫺3.8
⫺4.1
⫺4.4
⫺4.7
2.5
2.3
2.1
1.8
1.6
1.4
1.2
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.1
⫺0.1
⫺0.3
⫺0.4
⫺0.5
⫺0.6
⫺0.7
⫺0.9
⫺1.0
⫺1.1
⫺1.2
⫺1.4
⫺1.5
⫺1.6
⫺1.7
⫺1.9
⫺2.1
⫺2.4
⫺2.6
⫺2.9
⫺3.1
⫺3.4
⫺3.7
2.5
2.3
2.0
1.8
1.5
1.3
1.0
0.8
0.6
0.5
0.4
0.2
0.1
⫺0.2
⫺0.3
⫺0.4
⫺0.6
⫺0.7
⫺0.9
⫺1.0
⫺1.1
⫺1.3
⫺1.4
⫺1.5
⫺1.7
⫺1.8
⫺2.0
⫺2.1
⫺2.3
⫺2.4
⫺2.7
⫺3.0
⫺3.3
⫺3.6
⫺3.9
⫺4.2
⫺4.5
2.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.05
88.08
84.10
80.12
76.13
72.15
70.15
68.16
66.16
64.17
62.17
60.17
58.18
56.18
54.18
52.18
50.18
48.18
46.18
44.18
42.18
40.17
38.17
36.17
34.16
32.16
30.15
28.15
24.13
20.12
16.10
12.08
8.05
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
4.540
4.359
4.177
3.996
3.814
3.632
3.451
3.269
3.178
3.088
2.997
2.906
2.815
2.724
2.633
2.543
2.452
2.361
2.270
2.179
2.089
1.998
1.907
1.816
1.725
1.635
1.544
1.453
1.362
1.271
1.090
0.908
0.727
0.545
0.363
0.182
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
13.89
13.44
12.98
12.53
12.07
11.62
11.16
10.71
10.48
10.25
10.02
9.796
9.568
9.341
9.113
8.886
8.658
8.430
8.203
7.976
7.748
7.520
7.293
7.065
6.838
6.610
6.383
6.155
5.928
5.700
5.245
4.790
4.335
3.880
3.425
2.970
2.515
Specific
volume, / (m3·kg⫺1)
0.7861
0.7859
0.7856
0.7854
0.7852
0.7850
0.7847
0.7845
0.7844
0.7843
0.7842
0.7841
0.7840
0.7838
0.7837
0.7836
0.7835
0.7834
0.7833
0.7832
0.7830
0.7829
0.7829
0.7827
0.7826
0.7825
0.7824
0.7823
0.7821
0.7820
0.7818
0.7816
0.7813
0.7811
0.7809
0.7807
0.7804
1-20
Reference data
3 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.06
88.08
84.10
80.12
76.14
72.15
70.16
68.16
66.17
64.17
62.18
60.18
58.18
56.18
54.19
52.19
50.19
48.19
46.19
44.18
42.18
40.18
38.18
36.17
34.17
32.16
30.16
28.15
24.14
20.12
16.10
12.08
8.06
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
4.706
4.518
4.329
4.141
3.953
3.765
3.576
3.388
3.294
3.200
3.106
3.012
2.918
2.824
2.729
2.635
2.541
2.447
2.353
2.259
2.166
2.071
1.976
1.882
1.788
1.694
1.600
1.506
1.412
1.318
1.129
0.941
0.753
0.565
0.376
0.188
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
14.81
14.34
13.87
13.40
12.93
12.45
11.98
11.51
11.27
11.04
10.80
10.57
10.33
10.09
9.859
9.623
9.387
9.151
8.915
8.679
8.444
8.208
7.972
7.736
7.500
7.264
7.028
6.792
6.556
6.320
5.849
5.377
4.905
4.433
3.962
3.490
3.018
Specific
volume, / (m3·kg⫺1)
0.7877
0.7875
0.7873
0.7870
0.7868
0.7866
0.7863
0.7861
0.7860
0.7859
0.7857
0.7856
0.7855
0.7854
0.7853
0.7852
0.7850
0.7849
0.7848
0.7847
0.7846
0.7844
0.7843
0.7842
0.7841
0.7840
0.7839
0.7837
0.7836
0.7835
0.7833
0.7830
0.7828
0.7826
0.7823
0.7821
0.7819
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.7575
0.7274
0.6973
0.6672
0.6371
0.6069
0.5768
0.5466
0.5314
0.5164
0.5012
0.4861
0.4710
0.4559
0.4407
0.4256
0.4105
0.3953
0.3802
0.3650
0.3499
0.3347
0.3195
0.3044
0.2892
0.2740
0.2588
0.2436
0.2284
0.2132
0.1828
0.1524
0.1220
0.0915
0.0610
0.0305
0.0000
3.0
2.4
1.8
1.2
0.6
⫺0.1
⫺0.7
⫺1.3
⫺1.7
⫺2.0
⫺2.4
⫺2.7
⫺3.1
⫺3.5
⫺3.9
⫺4.3
⫺4.7
⫺5.2
⫺5.6
⫺6.1
⫺6.6
⫺7.1
⫺7.7
⫺8.2
⫺8.8
⫺9.4
⫺10.1
⫺10.7
⫺11.5
⫺12.2
⫺13.9
⫺15.9
⫺18.3
⫺21.3
⫺25.4
⫺32.1
—
3.0
2.7
2.5
2.2
2.0
1.7
1.4
1.2
1.0
0.9
0.8
0.6
0.5
0.4
0.2
0.1
⫺0.3
⫺0.4
⫺0.5
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.3
⫺1.4
⫺1.6
⫺1.7
⫺1.9
⫺2.0
⫺2.2
⫺2.5
⫺2.8
⫺3.1
⫺3.4
⫺3.7
⫺4.1
⫺4.4
3.0
2.8
2.6
2.3
2.1
1.9
1.6
1.4
1.3
1.2
1.1
0.9
0.8
0.7
0.6
0.5
0.3
0.2
0.1
⫺0.2
⫺0.3
⫺0.5
⫺0.6
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.2
⫺1.4
⫺1.5
⫺1.7
⫺2.0
⫺2.3
⫺2.5
⫺2.8
⫺3.1
⫺3.3
3.0
2.8
2.5
2.2
2.0
1.7
1.5
1.2
1.1
1.0
0.8
0.7
0.6
0.4
0.3
0.2
⫺0.2
⫺0.3
⫺0.5
⫺0.6
⫺0.7
⫺0.9
⫺1.0
⫺1.2
⫺1.3
⫺1.4
⫺1.6
⫺1.7
⫺1.9
⫺2.0
⫺2.3
⫺2.6
⫺2.9
⫺3.2
⫺3.5
⫺3.8
⫺4.2
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.7848
0.7536
0.7225
0.6913
0.6600
0.6288
0.5976
0.5663
0.5506
0.5350
0.5193
0.5037
0.4880
0.4723
0.4567
0.4410
0.4253
0.4096
0.3939
0.3782
0.3625
0.3468
0.3311
0.3154
0.2997
0.2839
0.2682
0.2525
0.2367
0.2210
0.1895
0.1579
0.1264
0.0948
0.0632
0.0316
0.0000
3.5
2.9
2.3
1.7
1.1
0.4
⫺0.3
⫺0.9
⫺1.2
⫺1.6
⫺1.9
⫺2.3
⫺2.7
⫺3.1
⫺3.5
⫺3.9
⫺4.3
⫺4.8
⫺5.2
⫺5.7
⫺6.2
⫺6.7
⫺7.2
⫺7.8
⫺8.4
⫺9.0
⫺9.6
⫺10.3
⫺11.1
⫺11.8
⫺13.5
⫺15.5
⫺17.9
⫺20.9
⫺25.0
⫺31.8
—
3.5
3.2
3.0
2.7
2.4
2.2
1.9
1.6
1.5
1.4
1.2
1.1
0.9
0.8
0.7
0.5
0.4
0.2
0.1
⫺0.3
⫺0.4
⫺0.6
⫺0.7
⫺0.9
⫺1.0
⫺1.2
⫺1.4
⫺1.5
⫺1.7
⫺1.8
⫺2.1
⫺2.4
⫺2.8
⫺3.1
⫺3.4
⫺3.7
⫺4.1
3.5
3.3
3.0
2.8
2.6
2.3
2.1
1.9
1.7
1.6
1.5
1.4
1.3
1.1
1.0
0.9
0.8
0.7
0.5
0.4
0.3
0.2
⫺0.2
⫺0.3
⫺0.5
⫺0.6
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.4
⫺1.6
⫺1.9
⫺2.2
⫺2.5
⫺2.7
⫺3.0
3.5
3.2
3.0
2.7
2.5
2.2
1.9
1.7
1.5
1.4
1.3
1.1
1.0
0.9
0.7
0.6
0.5
0.3
0.2
⫺0.2
⫺0.3
⫺0.5
⫺0.6
⫺0.8
⫺0.9
⫺1.1
⫺1.2
⫺1.4
⫺1.5
⫺1.7
⫺2.0
⫺2.3
⫺2.6
⫺2.9
⫺3.2
⫺3.5
⫺3.9
3.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.06
88.08
84.10
80.12
76.14
72.16
70.16
68.17
66.17
64.18
62.18
60.19
58.19
56.19
54.19
52.19
50.19
48.19
46.19
44.19
42.19
40.19
38.18
36.18
34.17
32.17
30.16
28.16
24.14
20.12
16.10
12.08
8.06
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
4.877
4.682
4.486
4.291
4.096
3.901
3.706
3.511
3.414
3.316
3.218
3.121
3.024
2.926
2.828
2.731
2.633
2.536
2.438
2.341
2.243
2.146
2.048
1.951
1.853
1.756
1.658
1.560
1.463
1.365
1.170
0.975
0.780
0.585
0.390
0.195
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
15.75
15.26
14.77
14.28
13.79
13.30
12.81
12.32
12.08
11.84
11.59
11.35
11.10
10.86
10.61
10.37
10.12
9.879
9.634
9.390
9.146
8.901
8.656
8.412
8.167
7.923
7.678
7.434
7.189
6.944
6.455
5.966
5.477
4.988
4.499
4.010
3.520
Specific
volume, / (m3·kg⫺1)
0.7894
0.7891
0.7889
0.7887
0.7884
0.7882
0.7879
0.7877
0.7876
0.7874
0.7873
0.7872
0.7871
0.7869
0.7868
0.7867
0.7866
0.7865
0.7663
0.7862
0.7861
0.7860
0.7858
0.7857
0.7856
0.7855
0.7854
0.7852
0.7851
0.7850
0.7847
0.7845
0.7843
0.7840
0.7838
0.7835
0.7833
Properties of humid air
1-21
4 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.06
88.08
84.11
80.13
76.15
72.16
70.17
68.17
66.18
64.19
62.19
60.19
58.20
56.20
54.20
52.20
50.20
48.20
46.20
44.20
42.20
40.19
38.19
36.19
34.18
32.18
30.17
28.16
24.15
20.13
16.11
12.09
8.06
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
5.053
4.851
4.649
4.446
4.244
4.042
3.840
3.638
3.537
3.436
3.335
3.234
3.133
3.032
2.931
2.830
2.728
2.628
2.526
2.425
2.324
2.223
2.122
2.021
1.920
1.819
1.718
1.617
1.516
1.415
1.213
1.011
0.808
0.606
0.404
0.202
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
16.70
16.19
15.68
15.18
14.67
14.16
13.66
13.15
12.90
12.64
12.39
12.14
11.88
11.63
11.38
11.12
10.87
10.61
10.36
10.11
9.854
9.600
9.347
9.093
8.840
8.586
8.333
8.080
7.826
7.573
7.066
6.559
6.052
5.545
5.038
4.531
4.024
Specific
volume, / (m3·kg⫺1)
0.7910
0.7908
0.7905
0.7903
0.7900
0.7898
0.7895
0.7893
0.7891
0.7890
0.7889
0.7888
0.7886
0.7885
0.7884
0.7883
0.7881
0.7880
0.7879
0.7877
0.7876
0.7875
0.7874
0.7872
0.7871
0.7870
0.7869
0.7867
0.7866
0.7865
0.7862
0.7860
0.7857
0.7855
0.7852
0.7850
0.7847
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.8129
0.7807
0.7484
0.7161
0.6937
0.6514
0.6190
0.5866
0.5704
0.5542
0.5380
0.5218
0.5056
0.4893
0.4731
0.4568
0.4406
0.4244
0.4081
0.3918
0.3756
0.3593
0.3430
0.3267
0.3105
0.2942
0.2779
0.2616
0.2453
0.2289
0.1963
0.1636
0.1310
0.0982
0.0655
0.0328
0.0000
4.0
3.4
2.8
2.2
1.6
0.9
0.2
⫺0.5
⫺0.8
⫺1.2
⫺1.5
⫺1.9
⫺2.3
⫺2.7
⫺3.1
⫺3.5
⫺3.9
⫺4.3
⫺4.8
⫺5.3
⫺5.8
⫺6.3
⫺6.8
⫺7.4
⫺8.0
⫺8.6
⫺9.2
⫺9.9
⫺10.7
⫺11.4
⫺13.1
⫺15.1
⫺17.5
⫺20.5
⫺24.7
⫺31.5
—
4.0
3.7
3.5
3.2
2.9
2.7
2.4
2.1
2.0
1.8
1.7
1.5
1.4
1.2
1.1
1.0
0.8
0.7
0.5
0.4
0.2
0.1
⫺0.4
⫺0.5
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.3
⫺1.5
⫺1.8
⫺2.1
⫺2.4
⫺2.8
⫺3.1
⫺3.4
⫺3.8
4.0
3.8
3.5
3.3
3.1
2.8
2.6
2.3
2.2
2.1
2.0
1.8
1.7
1.6
1.5
1.3
1.2
1.1
1.0
0.8
0.7
0.6
0.4
0.3
0.2
0.1
⫺0.3
⫺0.5
⫺0.6
⫺0.7
⫺1.0
⫺1.3
⫺1.6
⫺1.8
⫺2.1
⫺2.4
⫺2.7
4.0
3.7
3.5
3.2
2.9
2.7
2.4
2.1
2.0
1.9
1.7
1.6
1.4
1.3
1.2
1.0
0.9
0.7
0.6
0.5
0.3
0.2
⫺0.2
⫺0.4
⫺0.5
⫺0.7
⫺0.8
⫺1.0
⫺1.1
⫺1.3
⫺1.6
⫺1.9
⫺2.2
⫺2.6
⫺2.9
⫺3.2
⫺3.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.8420
0.8086
0.7751
0.7417
0.7082
0.6747
0.6412
0.6076
0.5908
0.5741
0.5573
0.5405
0.5237
0.5069
0.4900
0.4732
0.4564
0.4396
0.4227
0.4059
0.3890
0.3722
0.3553
0.3385
0.3216
0.3047
0.2878
0.2710
0.2541
0.2372
0.2034
0.1695
0.1357
0.1018
0.0679
0.0340
0.0000
4.5
3.9
3.3
2.7
2.1
1.4
0.7
⫺0.1
⫺0.4
⫺0.7
⫺1.1
⫺1.5
⫺1.8
⫺2.2
⫺2.6
⫺3.1
⫺3.5
⫺3.9
⫺4.4
⫺4.9
⫺5.4
⫺5.9
⫺6.4
⫺7.0
⫺7.6
⫺8.2
⫺8.8
⫺9.5
⫺10.3
⫺11.0
⫺12.7
⫺14.7
⫺17.1
⫺20.2
⫺24.3
⫺31.1
—
4.5
4.2
4.0
3.7
3.4
3.1
2.8
2.6
2.4
2.3
2.1
2.0
1.8
1.7
1.5
1.4
1.2
1.1
0.9
0.8
0.6
0.5
0.3
0.2
⫺0.3
⫺0.5
⫺0.6
⫺0.8
⫺0.9
⫺1.1
⫺1.4
⫺1.8
⫺2.1
⫺2.4
⫺2.8
⫺3.1
⫺3.5
4.5
4.3
4.0
3.8
3.5
3.3
3.0
2.8
2.7
2.5
2.4
2.3
2.2
2.0
1.9
1.8
1.6
1.5
1.4
1.3
1.1
1.0
0.9
0.7
0.6
0.5
0.3
0.2
0.1
⫺0.4
⫺0.6
⫺0.9
⫺1.2
⫺1.5
⫺1.8
⫺2.1
⫺2.4
4.5
4.2
4.0
3.7
3.4
3.2
2.9
2.6
2.5
2.3
2.2
2.0
1.9
1.7
1.6
1.5
1.3
1.2
1.0
0.9
0.7
0.6
0.4
0.3
0.1
⫺0.3
⫺0.5
⫺0.6
⫺0.8
⫺0.9
⫺1.3
⫺1.6
⫺1.9
⫺2.2
⫺2.6
⫺2.9
⫺3.2
4.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.06
88.09
84.11
80.13
76.15
72.17
70.17
68.18
66.19
64.19
62.20
60.20
58.20
56.21
54.21
52.21
50.21
48.21
46.21
44.21
42.20
40.20
38.20
36.19
34.19
32.18
30.18
28.17
24.15
20.13
16.11
12.09
8.06
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
5.235
5.025
4.816
4.607
4.397
4.188
3.978
3.769
3.664
3.560
3.455
3.350
3.246
3.141
3.036
2.932
2.827
2.722
2.617
2.513
2.408
2.303
2.199
2.094
1.989
1.884
1.780
1.675
1.570
1.466
1.256
1.047
0.838
0.628
0.419
0.209
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
17.66
17.14
16.61
16.09
15.56
15.04
14.51
13.98
13.72
13.46
13.20
12.93
12.67
12.41
12.15
11.88
11.62
11.36
11.09
10.83
10.57
10.31
10.04
9.781
9.518
9.256
8.993
8.730
8.467
8.205
7.679
7.154
6.628
6.103
5.578
5.052
4.527
Specific
volume, / (m3·kg⫺1)
0.7927
0.7924
0.7922
0.7919
0.7916
0.7914
0.7911
0.7909
0.7907
0.7906
0.7905
0.7903
0.7902
0.7901
0.7899
0.7898
0.7897
0.7895
0.7894
0.7893
0.7891
0.7890
0.7889
0.7888
0.7886
0.7885
0.7884
0.7882
0.7881
0.7880
0.7877
0.7874
0.7872
0.7869
0.7867
0.7864
0.7861
1-22
Reference data
5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.06
88.09
84.12
80.14
76.16
72.17
70.18
68.19
66.19
64.20
62.20
60.21
58.21
56.21
54.21
52.22
50.22
48.22
46.21
44.21
42.21
40.21
38.20
36.20
34.19
32.19
30.18
28.17
24.16
20.14
16.12
12.09
8.06
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
5.422
5.206
4.989
4.772
4.555
4.338
4.121
3.904
3.796
3.687
3.579
3.470
3.362
3.254
3.145
3.037
2.928
2.820
2.711
2.603
2.494
2.386
2.278
2.169
2.061
1.952
1.884
1.735
1.627
1.518
1.301
1.084
0.868
0.651
0.434
0.217
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
18.64
18.10
17.55
17.01
16.46
15.92
15.37
14.83
14.56
14.29
14.01
13.74
13.47
13.20
12.92
12.65
12.38
12.11
11.84
11.56
11.29
11.02
10.75
10.47
10.20
9.930
9.658
9.385
9.113
8.841
8.296
7.752
7.208
6.663
6.119
5.574
5.030
Specific
volume, / (m3·kg⫺1)
0.7944
0.7941
0.7938
0.7935
0.7933
0.7930
0.7927
0.7925
0.7923
0.7922
0.7920
0.7919
0.7918
0.7916
0.7915
0.7914
0.7912
0.7911
0.7910
0.7908
0.7907
0.7905
0.7904
0.7903
0.7901
0.7900
0.7899
0.7897
0.7896
0.7895
0.7892
0.7889
0.7886
0.7884
0.7881
0.7878
0.7875
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.8719
0.8373
0.8027
0.7681
0.7334
0.6987
0.6640
0.6293
0.6119
0.5945
0.5771
0.5598
0.5424
0.5250
0.5075
0.4901
0.4727
0.4553
0.4378
0.4204
0.4030
0.3855
0.3680
0.3506
0.3331
0.3156
0.2981
0.2806
0.2632
0.2456
0.2106
0.1756
0.1405
0.1054
0.0703
0.0352
0.0000
5.0
4.4
3.8
3.2
2.5
1.9
1.2
0.4
0.0
⫺0.3
⫺0.7
⫺1.0
⫺1.4
⫺1.8
⫺2.2
⫺2.6
⫺3.1
⫺3.5
⫺4.0
⫺4.5
⫺5.0
⫺5.5
⫺6.0
⫺6.6
⫺7.2
⫺7.8
⫺8.4
⫺9.1
⫺9.9
⫺10.6
⫺12.4
⫺14.4
⫺16.8
⫺19.8
⫺24.0
⫺30.8
—
5.0
4.7
4.4
4.2
3.9
3.6
3.3
3.0
2.9
2.7
2.6
2.4
2.3
2.1
2.0
1.8
1.7
1.5
1.4
1.2
1.1
0.9
0.7
0.6
0.4
0.3
0.1
⫺0.4
⫺0.6
⫺0.7
⫺1.1
⫺1.4
⫺1.8
⫺2.1
⫺2.5
⫺2.8
⫺3.2
5.0
4.8
4.5
4.3
4.0
3.8
3.5
3.2
3.1
3.0
2.9
2.7
2.6
2.5
2.3
2.2
2.1
1.9
1.8
1.7
1.5
1.4
1.3
1.1
1.0
0.9
0.7
0.6
0.5
0.3
⫺0.3
⫺0.6
⫺0.9
⫺1.2
⫺1.5
⫺1.8
⫺2.1
5.0
4.7
4.5
4.2
3.9
3.6
3.3
3.1
2.9
2.8
2.6
2.5
2.3
2.2
2.0
1.9
1.7
1.6
1.4
1.3
1.1
1.0
0.8
0.7
0.5
0.4
0.2
0.1
⫺0.4
⫺0.6
⫺0.9
⫺1.2
⫺1.6
⫺1.9
⫺2.2
⫺2.6
⫺2.9
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.9028
0.8670
0.8312
0.7953
0.7594
0.7235
0.6876
0.6516
0.6336
0.6156
0.5976
0.5796
0.5616
0.5436
0.5256
0.5076
0.4895
0.4715
0.4534
0.4354
0.4173
0.3992
0.3811
0.3630
0.3450
0.3269
0.3088
0.2906
0.2725
0.2544
0.2181
0.1818
0.1455
0.1092
0.0728
0.0364
0.0000
5.5
4.9
4.3
3.7
3.0
2.4
1.6
0.9
0.5
0.1
⫺0.3
⫺0.6
⫺0.1
⫺1.4
⫺1.8
⫺2.2
⫺2.7
⫺3.1
⫺3.6
⫺4.0
⫺4.5
⫺5.1
⫺5.6
⫺6.2
⫺6.8
⫺7.4
⫺8.0
⫺8.7
⫺9.5
⫺10.2
⫺12.0
⫺14.0
⫺16.4
⫺19.4
⫺23.6
⫺30.5
—
5.5
5.2
4.9
4.6
4.4
4.1
3.8
3.5
3.3
3.2
3.0
2.9
2.7
2.6
2.4
2.3
2.1
1.9
1.8
1.6
1.5
1.3
1.1
1.0
0.8
0.7
0.5
0.3
0.2
⫺0.4
⫺0.7
⫺1.1
⫺1.4
⫺1.8
⫺2.1
⫺2.5
⫺2.9
5.5
5.2
5.0
4.7
4.5
4.2
4.0
3.7
3.6
3.4
3.3
3.2
3.0
2.9
2.8
2.6
2.5
2.4
2.2
2.1
2.0
1.8
1.7
1.5
1.4
1.3
1.1
1.0
0.8
0.7
0.4
0.1
⫺0.5
⫺0.8
⫺1.2
⫺1.4
⫺1.8
5.5
5.2
4.9
4.7
4.4
4.1
3.8
3.5
3.4
3.2
3.1
2.9
2.8
2.6
2.5
2.3
2.2
2.0
1.9
1.7
1.6
1.4
1.2
1.1
0.9
0.8
0.6
0.5
0.3
0.1
⫺0.4
⫺0.9
⫺1.2
⫺1.6
⫺1.9
⫺2.3
⫺2.6
5.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.03
92.07
88.09
84.12
80.14
76.16
72.18
70.19
68.19
66.20
64.21
62.21
60.21
58.22
56.22
54.22
52.22
50.22
48.22
46.22
44.22
42.22
40.21
38.21
36.21
34.20
32.19
30.19
28.18
24.16
20.14
16.12
12.09
8.07
4.03
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
5.618
5.393
5.167
4.942
4.718
4.493
4.268
4.044
3.931
3.819
3.707
3.594
3.482
3.370
3.257
3.145
3.033
2.920
2.808
2.696
2.584
2.471
2.359
2.246
2.134
2.022
1.910
1.797
1.685
1.573
1.348
1.123
0.899
0.674
0.449
0.225
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
19.64
19.07
18.51
17.94
17.38
16.82
16.25
15.69
15.40
15.12
14.84
14.56
14.28
13.99
13.71
13.43
13.15
12.87
12.58
12.30
12.02
11.74
11.46
11.17
10.89
10.61
10.33
10.05
9.764
9.482
8.918
8.353
7.789
7.225
6.661
6.097
5.533
Specific
volume, / (m3·kg⫺1)
0.7960
0.7958
0.7955
0.7952
0.7949
0.7916
0.7943
0.7941
0.7939
0.7938
0.7936
0.7935
0.7934
0.7932
0.7931
0.7929
0.7928
0.7926
0.7925
0.7924
0.7922
0.7921
0.7919
0.7918
0.7917
0.7915
0.7914
0.7912
0.7911
0.7909
0.7907
0.7904
0.7901
0.7898
0.7895
0.7892
0.7890
Properties of humid air
1-23
6 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.07
88.10
84.12
80.15
76.17
72.19
70.19
68.20
66.21
64.21
62.22
60.22
58.23
56.23
54.23
52.23
50.23
48.23
46.23
44.23
42.23
40.22
38.22
36.21
34.21
32.20
30.19
28.19
24.17
20.15
16.12
12.10
8.07
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
5.816
5.584
5.351
5.118
4.886
4.653
4.420
4.188
4.071
3.955
3.839
3.722
3.606
3.490
3.373
3.257
3.141
3.024
2.907
2.792
2.675
2.559
2.443
2.326
2.210
2.094
1.978
1.861
30.19
1.628
1.396
1.163
0.931
0.698
0.465
0.233
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
20.65
20.06
19.48
18.89
18.31
17.72
17.14
16.56
16.26
15.97
15.68
15.39
15.09
14.80
14.51
14.22
13.93
13.63
13.34
13.05
12.76
12.46
12.17
11.88
11.59
11.30
11.00
10.71
10.42
10.13
9.542
8.958
8.373
7.789
7.205
6.620
6.036
Specific
volume, / (m3·kg⫺1)
0.7977
0.7974
0.7971
0.7968
0.7966
0.7963
0.7960
0.7957
0.7955
0.7954
0.7952
0.7951
0.7949
0.7948
0.7946
0.7945
0.7944
0.7942
0.7941
0.7939
0.7938
0.7936
0.7935
0.7933
0.7932
0.7930
0.7929
0.7927
0.7926
0.7924
0.7921
0.7919
0.7916
0.7913
0.7910
0.7907
0.7904
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.9346
0.8976
0.8605
0.8234
0.7862
0.7491
0.7119
0.6747
0.6560
0.6374
0.6188
0.6002
0.5815
0.5628
0.5442
0.5255
0.5068
0.4882
0.4695
0.4508
0.4321
0.4134
0.3946
0.3759
0.3572
0.3385
0.3197
0.3010
0.2822
0.2634
0.2259
0.1883
0.1507
0.1131
0.0754
0.0377
0.0000
6.0
5.4
4.8
4.2
3.5
2.8
2.1
1.4
1.0
0.6
0.2
⫺0.2
⫺0.6
⫺1.0
⫺1.4
⫺1.8
⫺2.2
⫺2.7
⫺3.2
⫺3.6
⫺4.1
⫺4.7
⫺5.2
⫺5.8
⫺6.4
⫺7.0
⫺7.6
⫺8.3
⫺9.1
⫺9.9
⫺11.6
⫺13.6
⫺16.0
⫺19.1
⫺23.3
⫺30.1
—
6.0
5.7
5.4
5.1
4.8
4.5
4.2
3.9
3.8
3.6
3.5
3.3
3.2
3.0
2.8
2.7
2.5
2.4
2.2
2.0
1.9
1.7
1.6
1.4
1.2
1.1
0.9
0.7
0.6
0.4
⫺0.4
⫺0.7
⫺1.1
⫺1.5
⫺1.8
⫺2.2
⫺2.6
6.0
5.7
5.5
5.2
5.0
4.7
4.4
4.2
4.0
3.9
3.8
3.6
3.5
3.4
3.2
3.1
2.9
2.8
2.7
2.5
2.4
2.2
2.1
2.0
1.8
1.7
1.5
1.4
1.2
1.1
0.8
0.5
0.2
⫺0.5
⫺0.8
⫺1.1
⫺1.4
6.0
5.7
5.4
5.1
4.9
4.6
4.3
4.0
3.8
3.7
3.5
3.4
3.2
3.1
2.9
2.8
2.6
2.4
2.3
2.1
2.0
1.8
1.7
1.5
1.3
1.2
1.0
0.8
0.7
0.5
0.2
⫺0.6
⫺0.9
⫺1.3
⫺1.6
⫺2.0
⫺2.3
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
0.9674
0.9291
0.8907
0.8523
0.8139
0.7754
0.7370
0.6984
0.6792
0.6599
0.6406
0.6213
0.6020
0.5827
0.5634
0.5441
0.5247
0.5054
0.4860
0.4667
0.4473
0.4280
0.4086
0.3892
0.3698
0.3504
0.3310
0.3116
0.2922
0.2728
0.2339
0.1950
0.1560
0.1171
0.0781
0.0391
0.0000
6.5
5.9
5.3
4.7
4.0
3.3
2.6
1.9
1.5
1.1
0.7
0.2
⫺0.2
⫺0.6
⫺1.0
⫺1.4
⫺1.8
⫺2.3
⫺2.7
⫺3.2
⫺3.7
⫺4.3
⫺4.8
⫺5.4
⫺6.0
⫺6.6
⫺7.2
⫺7.9
⫺8.7
⫺9.5
⫺11.2
⫺13.2
⫺15.6
⫺18.7
⫺22.9
⫺29.8
—
6.5
6.2
5.9
5.6
5.3
5.0
4.7
4.4
4.2
4.1
3.9
3.8
3.6
3.4
3.3
3.1
3.0
2.8
2.6
2.5
2.3
2.1
2.0
1.8
1.6
1.4
1.3
1.1
0.9
0.8
0.4
0.1
⫺0.8
⫺1.2
⫺1.5
⫺1.9
⫺2.3
6.5
6.2
6.0
5.7
5.4
5.2
4.9
4.6
4.5
4.4
4.2
4.1
3.9
3.8
3.7
3.5
3.4
3.2
3.1
2.9
2.8
2.7
2.5
2.4
2.2
2.1
1.9
1.8
1.6
1.5
1.2
0.9
0.6
0.3
⫺0.5
⫺0.8
⫺1.1
6.5
6.2
5.9
5.6
5.3
5.0
4.7
4.4
4.3
4.1
4.0
3.8
3.7
3.5
3.3
3.2
3.0
2.9
2.7
2.5
2.4
2.2
2.1
1.9
1.7
1.6
1.4
1.2
1.1
0.9
0.5
0.2
⫺0.6
⫺0.9
⫺1.3
⫺1.7
⫺2.1
6.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.07
88.10
84.13
80.15
76.17
72.19
70.20
68.21
66.21
64.22
62.23
60.23
58.23
56.24
54.24
52.24
50.24
48.24
46.24
44.24
42.23
40.23
38.23
36.22
34.22
32.21
30.20
28.19
24.18
20.15
16.13
12.10
8.07
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
6.022
5.782
5.541
5.300
5.059
4.818
4.577
4.336
4.216
4.095
3.975
3.854
3.734
3.614
3.493
3.373
3.252
3.132
3.011
2.891
2.770
2.650
2.529
2.409
2.289
2.168
2.048
1.927
1.807
1.686
1.445
1.204
0.964
0.723
0.482
0.241
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
21.67
21.08
20.46
19.86
19.25
18.65
18.04
17.44
17.13
16.83
16.53
16.22
15.92
15.62
15.32
15.01
14.71
14.41
14.11
13.80
13.50
13.20
12.90
12.59
12.29
11.99
11.68
11.38
11.08
10.78
10.17
9.566
8.960
8.355
7.750
7.144
6.539
Specific
volume, / (m3·kg⫺1)
0.7994
0.7991
0.7988
0.7985
0.7982
0.7979
0.7976
0.7973
0.7971
0.7970
0.7968
0.7967
0.7965
0.7964
0.7962
0.7961
0.7959
0.7958
0.7956
0.7955
0.7953
0.7952
0.7950
0.7949
0.7947
0.7945
0.7944
0.7942
0.7941
0.7939
0.7936
0.7933
0.7930
0.7927
0.7924
0.7921
0.7918
1-24
Reference data
7 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.07
88.10
84.13
80.16
76.18
72.20
70.21
68.22
66.22
64.23
62.23
60.24
58.24
56.24
54.25
52.25
50.25
48.25
46.25
44.24
42.24
40.24
38.23
36.23
34.22
32.22
30.21
28.20
24.18
20.16
16.13
12.11
8.07
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
6.235
5.986
5.736
5.487
5.238
4.988
4.739
4.489
4.365
4.240
4.115
3.990
3.866
3.741
3.616
3.492
3.367
3.242
3.118
2.993
2.868
2.744
2.619
2.494
2.369
2.245
2.120
1.995
1.871
1.746
1.496
1.247
0.998
0.748
0.499
0.249
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
22.72
22.09
21.46
20.84
20.21
19.58
18.95
18.33
18.01
17.70
17.39
17.07
16.76
16.45
16.13
15.82
15.51
15.19
14.88
14.57
14.25
13.94
13.62
13.31
13.00
12.68
12.37
12.06
11.74
11.43
10.80
10.18
9.550
8.923
8.296
7.669
7.042
Specific
volume, / (m3·kg⫺1)
0.8011
0.8008
0.8005
0.8002
0.7999
0.7995
0.7992
0.7989
0.7988
0.7986
0.7984
0.7983
0.7981
0.7980
0.7978
0.7977
0.7975
0.7973
0.7972
0.7970
0.7969
0.7967
0.7965
0.7964
0.7962
0.7961
0.7959
0.7958
0.7956
0.7954
0.7951
0.7948
0.7945
0.7942
0.7939
0.7935
0.7932
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.001
0.9616
0.9219
0.8822
0.8424
0.8026
0.7628
0.7229
0.7030
0.6830
0.6631
0.6431
0.6231
0.6032
0.5832
0.5632
0.5432
0.5232
0.5031
0.4831
0.4631
0.4430
0.4230
0.4029
0.3828
0.3628
0.3427
0.3226
0.3025
0.2824
0.2421
0.2018
0.1616
0.1212
0.0808
0.0404
0.0000
7.0
6.4
5.8
5.2
4.5
3.8
3.1
2.3
2.0
1.5
1.1
0.7
0.3
⫺0.1
⫺0.6
⫺1.0
⫺1.4
⫺1.9
⫺2.3
⫺2.8
⫺3.3
⫺3.8
⫺4.4
⫺5.0
⫺5.6
⫺6.2
⫺6.8
⫺7.5
⫺8.3
⫺9.1
⫺10.8
⫺12.8
⫺15.3
⫺18.3
⫺22.6
⫺29.5
—
7.0
6.7
6.4
6.1
5.8
5.5
5.2
4.8
4.7
4.5
4.4
4.2
4.0
3.9
3.7
3.5
3.4
3.2
3.0
2.9
2.7
2.5
2.4
2.2
2.0
1.8
1.7
1.5
1.3
1.1
0.8
0.4
⫺0.5
⫺0.8
⫺1.2
⫺1.6
⫺2.0
7.0
6.7
6.5
6.2
5.9
5.6
5.4
5.1
5.0
4.8
4.7
4.5
4.4
4.2
4.1
4.0
3.8
3.7
3.5
3.4
3.2
3.1
2.9
2.8
2.6
2.5
2.3
2.2
2.0
1.9
1.6
1.2
0.9
0.6
0.3
⫺0.5
⫺0.8
7.0
6.7
6.4
6.1
5.8
5.5
5.2
4.9
4.7
4.6
4.4
4.3
4.1
3.9
3.8
3.6
3.5
3.3
3.1
3.0
2.8
2.6
2.5
2.3
2.1
2.0
1.8
1.6
1.4
1.3
0.9
0.6
0.2
⫺0.6
⫺1.0
⫺1.4
⫺1.8
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.036
0.9951
0.9541
0.9130
0.8718
0.8306
0.7894
0.7482
0.7276
0.7069
0.6863
0.6656
0.6449
0.6243
0.6036
0.5829
0.5622
0.5415
0.5208
0.5000
0.4793
0.4585
0.4378
0.4170
0.3963
0.3755
0.3547
0.3339
0.3131
0.2923
0.2506
0.2089
0.1672
0.1255
0.0837
0.0419
0.0000
7.5
6.9
6.3
5.7
5.0
4.3
3.6
2.8
2.4
2.0
1.6
1.2
0.8
0.3
⫺0.1
⫺0.6
⫺1.0
⫺1.4
⫺1.9
⫺2.4
⫺2.9
⫺3.4
⫺4.0
⫺4.6
⫺5.2
⫺5.8
⫺6.4
⫺7.1
⫺7.9
⫺8.7
⫺10.4
⫺12.4
⫺14.9
⫺18.0
⫺22.2
⫺29.1
—
7.5
7.2
6.9
6.6
6.3
6.0
5.6
5.3
5.1
5.0
4.8
4.7
4.5
4.3
4.1
4.0
3.8
3.6
3.5
3.3
3.1
2.9
2.8
3.6
2.4
2.2
2.1
1.9
1.7
1.5
1.1
0.8
0.4
⫺0.5
⫺0.9
⫺1.3
⫺1.7
7.5
7.2
7.0
6.7
6.4
6.1
5.8
5.6
5.4
5.3
5.1
5.0
4.8
4.7
4.5
4.4
4.2
4.1
3.9
3.8
3.6
3.5
3.3
3.2
3.0
2.9
2.7
2.6
2.4
2.2
1.9
1.6
1.3
1.0
0.6
0.3
⫺0.5
7.5
7.2
6.9
6.6
6.3
6.0
5.7
5.3
5.2
5.0
4.9
4.7
4.5
4.4
4.2
4.0
3.9
3.7
3.5
3.4
3.2
3.0
2.9
2.7
2.5
2.3
2.2
2.0
1.8
1.6
1.3
0.9
0.6
0.2
⫺0.7
⫺1.1
⫺1.5
7.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.08
88.11
84.14
80.16
76.19
72.21
70.22
68.22
66.23
64.24
62.24
60.25
58.25
56.25
54.25
52.26
50.26
48.26
46.26
44.25
42.25
40.25
38.24
36.24
34.23
32.22
30.22
28.21
24.19
20.16
16.14
12.11
8.08
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
6.455
6.196
5.938
5.680
5.422
5.164
4.906
4.647
4.518
4.389
4.260
4.131
4.002
3.873
3.744
3.615
3.486
3.356
3.227
3.098
2.969
2.840
2.711
2.582
2.453
2.324
2.195
2.066
1.936
1.807
1.549
1.291
1.033
0.775
0.516
0.258
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
23.78
23.13
22.48
21.83
21.18
20.53
19.88
19.23
18.91
18.58
18.26
17.93
17.61
17.28
16.96
16.63
16.31
15.99
15.66
15.34
15.01
14.69
14.36
14.04
13.71
13.39
13.06
12.74
12.41
12.09
11.44
10.79
10.14
9.493
8.843
8.194
7.545
Specific
volume, / (m3·kg⫺1)
0.8028
0.8025
0.8022
0.8019
0.8015
0.8012
0.8009
0.8005
0.8004
0.8002
0.8001
0.7999
0.7997
0.7996
0.7994
0.7992
0.7991
0.7989
0.7987
0.7986
0.7984
0.7983
0.7981
0.7979
0.7978
0.7976
0.7974
0.7973
0.7971
0.7969
0.7966
0.7963
0.7960
0.7956
0.7953
0.7950
0.7946
Properties of humid air
1-25
8 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.08
88.11
84.14
80.17
76.19
72.21
70.22
68.23
66.24
64.24
62.25
60.25
58.26
56.26
54.26
52.27
50.27
48.27
46.26
44.26
42.26
40.26
38.25
36.25
34.24
32.23
30.22
28.21
24.19
20.17
16.14
12.11
8.08
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
6.681
6.414
6.146
5.879
5.612
5.345
5.078
4.810
4.677
4.543
4.909
4.276
4.142
4.009
3.875
3.741
3.608
3.474
3.340
3.207
3.073
2.940
2.806
2.672
2.539
2.405
2.272
2.138
2.004
1.871
1.603
1.336
1.069
0.8017
0.5345
0.2672
0.0000
Specific
enthalpy, h
/ (kJ·kg⫺1)
24.86
24.18
23.51
22.84
22.17
21.49
20.82
20.15
19.81
19.48
19.14
18.80
18.47
18.13
17.80
17.46
17.12
16.79
16.45
16.12
15.78
15.44
15.11
14.77
14.43
14.10
13.76
13.43
13.09
12.75
12.08
11.41
10.74
10.06
9.392
8.720
8.048
Specific
volume, / (m3·kg⫺1)
0.8046
0.8042
0.8039
0.8035
0.8032
0.8029
0.8025
0.8022
0.8020
0.8018
0.8017
0.8015
0.8013
0.8012
0.8010
0.8008
0.8007
0.8005
0.8003
0.8001
0.8000
0.7998
0.7996
0.7995
0.7993
0.7991
0.7990
0.7988
0.7986
0.7984
0.7981
0.7978
0.7974
0.7971
0.7967
0.7964
0.7961
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.072
1.030
0.9872
0.9447
0.9021
0.8595
0.8169
0.7742
0.7529
0.7315
0.7102
0.6888
0.6674
0.6460
0.6246
0.6032
0.5818
0.5604
0.5389
0.5175
0.4960
0.4745
0.4531
0.4316
0.4101
0.3886
0.3671
0.3456
0.3240
0.3025
0.2594
0.2162
0.1731
0.1299
0.0866
0.0433
0.0000
8.0
7.4
6.8
6.2
5.5
4.8
4.1
3.3
2.9
2.5
2.1
1.7
1.2
0.8
0.3
⫺0.1
⫺0.6
⫺1.0
⫺1.5
⫺2.0
⫺2.5
⫺3.0
⫺3.6
⫺4.2
⫺4.8
⫺5.4
⫺6.0
⫺6.7
⫺7.5
⫺8.3
⫺10.0
⫺12.1
⫺14.5
⫺17.6
⫺21.9
⫺28.8
—
8.0
7.7
7.4
7.1
6.7
6.4
6.1
5.8
5.6
5.4
5.3
5.1
4.9
4.8
4.6
4.4
4.2
4.1
3.9
3.7
3.5
3.4
3.2
3.0
2.8
2.6
2.4
2.3
2.1
1.9
1.5
1.1
0.7
0.3
⫺0.6
⫺1.0
⫺1.5
8.0
7.7
7.4
7.2
6.9
6.6
6.3
6.0
5.9
5.7
5.6
5.4
5.3
5.1
5.0
4.8
4.7
4.5
4.4
4.2
4.0
3.9
3.7
3.6
3.4
3.3
3.1
2.9
2.8
2.6
2.3
2.0
1.6
1.3
1.0
0.6
0.3
8.0
7.7
7.4
7.1
6.8
6.4
6.1
5.8
5.6
5.5
5.3
5.2
5.0
4.8
4.6
4.5
4.3
4.1
4.0
3.8
3.6
3.4
3.3
3.1
2.9
2.7
2.6
2.4
2.2
2.0
1.6
1.3
0.9
0.5
0.1
⫺0.8
⫺1.2
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.109
1.065
1.021
0.9774
0.9333
0.8893
0.8452
0.8011
0.7790
0.7569
0.7348
0.7127
0.6906
0.6684
0.6463
0.6241
0.6020
0.5798
0.5576
0.5354
0.5132
0.4910
0.4688
0.4466
0.4244
0.4021
0.3799
0.3576
0.3353
0.3130
0.2684
0.2238
0.1791
0.1344
0.0896
0.0448
0.0000
8.5
7.9
7.3
6.6
6.0
5.3
4.6
3.8
3.4
3.0
2.6
2.1
1.7
1.2
0.8
0.3
⫺0.2
⫺0.6
⫺1.1
⫺1.6
⫺2.1
⫺2.6
⫺3.2
⫺3.7
⫺4.3
⫺5.0
⫺5.6
⫺6.4
⫺7.1
⫺7.9
⫺9.6
⫺11.7
⫺14.1
⫺17.2
⫺21.5
⫺28.5
—
8.5
8.2
7.9
7.5
7.2
6.9
6.6
6.2
6.1
5.9
5.7
5.5
5.4
5.2
5.0
4.8
4.7
4.5
4.3
4.1
3.9
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.3
1.9
1.5
1.1
0.7
0.3
⫺0.7
⫺1.2
8.5
8.2
7.9
7.6
7.4
7.1
6.8
6.5
6.3
6.2
6.0
5.9
5.7
5.6
5.4
5.3
5.1
4.9
4.8
4.6
4.5
4.3
4.1
4.0
3.8
3.7
3.5
3.3
3.2
3.0
2.7
2.3
2.0
1.7
1.3
1.0
0.6
8.5
8.2
7.9
7.6
7.2
6.9
6.6
6.3
6.1
5.9
5.8
5.6
5.4
5.3
5.1
4.9
4.7
4.6
4.4
4.2
4.0
3.9
3.7
3.5
3.3
3.1
2.9
2.8
2.6
2.4
2.0
1.6
1.2
0.9
0.5
0.1
⫺0.9
8.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.08
88.12
84.15
80.18
76.20
72.22
70.23
68.24
66.25
64.25
62.26
60.26
58.27
56.27
54.27
52.27
50.27
48.27
46.27
44.27
42.27
40.26
38.26
36.25
34.25
32.24
30.23
28.22
24.20
20.18
16.15
12.12
8.08
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
6.914
6.638
6.361
6.085
5.808
5.532
5.255
4.978
4.840
4.702
4.564
4.425
4.287
4.149
4.010
3.872
3.734
3.596
3.457
3.319
3.181
3.042
2.904
2.766
2.627
2.489
2.351
2.213
2.074
1.936
1.659
1.383
1.106
0.831
0.553
0.278
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
25.95
25.26
24.56
23.86
23.17
22.47
21.78
21.08
20.73
20.38
20.04
19.69
19.34
18.99
18.64
18.29
17.95
17.60
17.25
16.90
16.55
16.21
15.86
15.51
15.16
14.81
14.47
14.12
13.77
13.42
12.73
12.03
11.33
10.64
9.943
9.247
8.551
Specific
volume, / (m3·kg⫺1)
0.8063
0.8059
0.8056
0.8052
0.8049
0.8045
0.8042
0.8038
0.8037
0.8035
0.8033
0.8031
0.8029
0.8028
0.8026
0.8024
0.8022
0.8021
0.8019
0.8017
0.8015
0.8014
0.8012
0.8010
0.8008
0.8007
0.8005
0.8003
0.8001
0.8000
0.7996
0.7993
0.7989
0.7985
0.7982
0.7978
0.7975
1-26
Reference data
9 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.04
92.08
88.12
84.15
80.18
76.21
72.23
70.24
68.25
66.25
64.26
62.27
60.27
58.28
56.28
54.28
52.28
50.28
48.28
46.28
44.28
42.28
40.27
38.27
36.26
34.26
32.25
30.24
28.23
24.21
20.18
16.15
12.12
8.08
4.04
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
7.155
6.869
6.583
6.296
6.010
5.724
5.438
5.152
5.008
4.865
4.722
4.579
4.436
4.293
4.150
4.007
3.864
3.721
3.578
3.434
3.291
3.148
3.005
2.862
2.719
2.576
2.433
2.290
2.146
2.003
1.717
1.431
1.145
0.857
0.572
0.286
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
27.07
26.35
25.63
24.90
24.18
23.46
22.74
22.02
21.66
21.30
20.94
20.58
20.22
19.86
19.50
19.14
18.78
18.42
18.06
17.70
17.34
16.98
16.62
16.26
15.90
15.54
15.18
14.82
14.46
14.10
13.38
12.66
11.94
11.22
10.50
9.774
9.054
Specific
volume, / (m3·kg⫺1)
0.8080
0.8077
0.8073
0.8069
0.8066
0.8062
0.8058
0.8055
0.8053
0.8051
0.8049
0.8048
0.8046
0.8044
0.8042
0.8040
0.8038
0.8037
0.8035
0.8033
0.8031
0.8029
0.8027
0.8026
0.8024
0.8022
0.8020
0.8018
0.8016
0.8015
0.8011
0.8007
0.8004
0.8000
0.7996
0.7993
0.7989
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.147
1.102
1.056
1.011
0.9655
0.9200
0.8744
0.8287
0.8059
0.7830
0.7602
0.7373
0.7144
0.6915
0.6686
0.6457
0.6228
0.5999
0.5769
0.5540
0.5310
0.5080
0.4851
0.4621
0.4391
0.4160
0.3930
0.3700
0.3470
0.3239
0.2778
0.2316
0.1853
0.1391
0.0928
0.0464
0.0000
9.0
8.4
7.8
7.1
6.5
5.8
5.0
4.3
3.9
3.5
3.0
2.6
2.2
1.7
1.3
0.8
0.3
⫺0.2
⫺0.7
⫺1.2
⫺1.7
⫺2.2
⫺2.8
⫺3.3
⫺3.9
⫺4.6
⫺5.3
⫺6.0
⫺6.7
⫺7.5
⫺9.3
⫺11.3
⫺13.8
⫺16.9
⫺21.1
⫺28.1
—
9.0
8.7
8.4
8.0
7.7
7.4
7.0
6.7
6.5
6.3
6.2
6.0
5.8
5.6
5.4
5.3
5.1
4.9
4.7
4.5
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.2
1.8
1.4
1.0
0.6
0.2
⫺0.9
9.0
8.7
8.4
8.1
7.8
7.5
7.2
6.9
6.8
6.6
6.5
6.3
6.2
6.0
5.8
5.7
5.5
5.4
5.2
5.0
4.9
4.7
4.6
4.4
4.2
4.1
3.9
3.7
3.6
3.4
3.0
2.7
2.4
2.0
1.6
1.3
0.9
9.0
8.7
8.4
8.0
7.7
7.4
7.1
6.7
6.6
6.4
6.2
6.0
5.9
5.7
5.5
5.3
5.2
5.0
4.8
4.6
4.4
4.3
4.1
3.9
3.7
3.5
3.3
3.1
3.0
2.8
2.4
2.0
1.6
1.2
0.8
0.4
⫺0.6
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.188
1.141
1.094
1.047
0.9987
0.9516
0.9044
0.8572
0.8336
0.8100
0.7863
0.7627
0.7390
0.7154
0.6917
0.6680
0.6443
0.6206
0.5968
0.5731
0.5493
0.5256
0.5018
0.4780
0.4542
0.4304
0.4066
0.3828
0.3589
0.3351
0.2874
0.2396
0.1918
0.1439
0.0960
0.0480
0.0000
9.5
8.9
8.3
7.6
7.0
6.3
5.5
4.8
4.4
3.9
3.5
3.1
2.7
2.2
1.7
1.2
0.7
0.2
⫺0.3
⫺0.8
⫺1.3
⫺1.8
⫺2.4
⫺2.9
⫺3.5
⫺4.2
⫺4.9
⫺5.6
⫺6.3
⫺7.1
⫺8.9
⫺10.9
⫺13.4
⫺16.5
⫺20.8
⫺27.8
—
9.5
9.2
8.8
8.5
8.2
7.8
7.5
7.1
7.0
6.8
6.6
6.4
6.2
6.1
5.9
5.7
5.5
5.3
5.1
4.9
4.8
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.6
2.2
1.8
1.3
0.9
0.5
⫺0.6
9.5
9.2
8.9
8.6
8.3
8.0
7.7
7.4
7.2
7.1
6.9
6.8
6.6
6.4
6.3
6.1
6.0
5.8
5.6
5.5
5.3
5.1
5.0
4.8
4.6
4.5
4.3
4.1
3.9
3.8
3.4
3.1
2.7
2.3
2.0
1.6
1.2
9.5
9.2
8.9
8.5
8.2
7.9
7.5
7.2
7.0
6.8
6.7
6.5
6.3
6.1
5.9
5.8
5.6
5.4
5.2
5.0
4.9
4.7
4.5
4.3
4.1
3.9
3.7
3.5
3.3
3.1
2.7
2.3
1.9
1.5
1.1
0.7
0.3
9.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.05
92.09
88.12
84.16
80.19
76.21
72.24
70.25
68.26
66.26
64.27
62.28
60.28
58.29
56.29
54.29
52.29
50.29
48.29
46.29
44.29
42.29
40.28
38.28
36.27
34.26
32.26
30.25
28.24
24.22
20.19
16.16
12.12
8.09
4.05
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
7.403
7.107
6.811
6.515
6.219
5.923
5.626
5.330
5.182
5.034
4.886
4.738
4.590
4.442
4.294
4.146
3.998
3.850
3.702
3.554
3.405
3.257
3.109
2.961
2.813
2.665
2.517
2.369
2.221
2.073
1.777
1.481
1.184
0.888
0.592
0.296
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
28.20
27.45
26.71
25.96
25.22
24.47
23.73
22.98
22.61
22.23
21.86
21.49
21.12
20.74
20.37
20.00
19.62
19.25
18.88
18.51
18.13
17.76
17.39
17.01
16.64
16.27
15.90
15.52
15.15
14.78
14.03
13.29
12.54
11.79
11.05
10.30
9.557
Specific
volume, / (m3·kg⫺1)
0.8098
0.8094
0.8090
0.8087
0.8083
0.8079
0.8075
0.8071
0.8070
0.8068
0.8066
0.8064
0.8062
0.8060
0.8058
0.8056
0.8054
0.8053
0.8051
0.8049
0.8047
0.8045
0.8043
0.8041
0.8039
0.8037
0.8035
0.8034
0.8032
0.8030
0.8026
0.8022
0.8018
0.8015
0.8011
0.8007
0.8003
Properties of humid air
1-27
10 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.05
92.09
88.13
84.16
80.19
76.22
72.24
70.26
68.26
66.27
64.28
62.29
60.29
58.30
56.30
54.30
52.30
50.30
48.30
46.30
44.30
42.30
40.29
38.29
36.28
34.27
32.27
30.26
28.25
24.22
20.20
16.16
12.13
8.09
4.05
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
7.659
7.352
7.046
6.740
6.433
6.127
5.821
5.514
5.361
5.208
5.055
4.902
4.748
4.595
4.442
4.289
4.136
3.983
3.829
3.676
3.523
3.370
3.217
3.064
2.910
2.757
2.604
2.451
2.298
2.144
1.838
1.532
1.225
0.919
0.613
0.306
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
29.35
28.58
27.81
27.04
26.27
25.50
24.72
23.95
23.57
23.18
22.79
22.41
22.02
21.64
21.25
20.86
20.48
20.09
19.71
19.32
18.94
18.55
18.16
17.78
17.39
17.00
16.62
16.23
15.85
15.46
14.69
13.92
13.15
12.38
11.60
10.83
10.06
Specific
volume, / (m3·kg⫺1)
0.8116
0.8112
0.8108
0.8104
0.8100
0.8096
0.8092
0.8088
0.8086
0.8084
0.8082
0.8080
0.8078
0.8076
0.8074
0.8072
0.8070
0.8069
0.8067
0.8065
0.8063
0.8061
0.8059
0.8057
0.8055
0.8053
0.8051
0.8049
0.8047
0.8045
0.8041
0.8037
0.8033
0.8029
0.8025
0.8021
0.8018
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.227
1.180
1.130
1.081
1.034
0.9841
0.9354
0.8866
0.8622
0.8377
0.8133
0.7888
0.7644
0.7398
0.7154
0.6909
0.6664
0.6419
0.6173
0.5928
0.5682
0.5436
0.5190
0.4945
0.4698
0.4452
0.4206
0.3960
0.3713
0.3466
0.2973
0.2478
0.1984
0.1488
0.0993
0.0497
0.0000
10.0
9.4
8.8
8.1
7.5
6.7
6.0
5.2
4.8
4.4
4.0
3.6
3.1
2.7
2.2
1.7
1.2
0.7
0.1
⫺0.4
⫺0.9
⫺1.4
⫺2.0
⫺2.5
⫺3.1
⫺3.8
⫺4.5
⫺5.2
⫺5.9
⫺6.7
⫺8.5
⫺10.5
⫺13.0
⫺16.1
⫺20.4
⫺27.4
—
10.0
9.7
9.3
9.0
8.7
8.3
8.0
7.6
7.4
7.2
7.1
6.9
6.7
6.5
6.3
6.1
5.9
5.7
5.6
5.4
5.2
5.0
4.8
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.0
2.5
2.1
1.7
1.2
0.8
0.3
10.0
9.7
9.4
9.1
8.8
8.5
8.2
7.8
7.7
7.5
7.4
7.2
7.0
6.9
6.7
6.5
6.4
6.2
6.0
5.9
5.7
5.5
5.4
5.2
5.0
4.8
4.7
4.5
4.3
4.1
3.8
3.4
3.1
2.7
2.3
1.9
1.6
10.0
9.7
9.3
9.0
8.7
8.3
8.0
7.6
7.5
7.3
7.1
6.9
6.7
6.6
6.4
6.2
6.0
5.8
5.6
5.5
5.3
5.1
4.9
4.7
4.5
4.3
4.1
3.9
3.7
3.5
3.1
2.7
2.3
1.9
1.4
1.0
0.6
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.269
1.219
1.169
1.118
1.068
1.018
0.9673
0.9168
0.8916
0.8663
0.8410
0.8158
0.7905
0.7652
0.7398
0.7145
0.6892
0.6638
0.6384
0.6131
0.5877
0.5623
0.5368
0.5114
0.4860
0.4605
0.4350
0.4095
0.3840
0.3585
0.3075
0.2560
0.2052
0.1540
0.1027
0.0514
0.0000
10.5
9.9
9.3
8.6
7.9
7.2
6.5
5.7
5.3
4.9
4.5
4.0
3.6
3.1
2.7
2.2
1.7
1.2
0.6
0.1
⫺0.5
⫺1.0
⫺1.6
⫺2.1
⫺2.7
⫺3.4
⫺4.1
⫺4.8
⫺5.5
⫺6.3
⫺8.1
⫺10.2
⫺12.6
⫺15.8
⫺20.1
⫺27.1
—
10.5
10.2
9.8
9.5
9.1
8.8
8.4
8.1
7.9
7.7
7.5
7.3
7.1
6.9
6.7
6.6
6.4
6.2
6.0
5.8
5.6
5.4
5.2
5.0
4.8
4.6
4.4
4.2
3.9
3.7
3.3
2.9
2.4
2.0
1.6
1.1
0.6
10.5
10.2
9.9
9.6
9.3
8.9
8.6
8.3
8.1
8.0
7.8
7.6
7.5
7.3
7.1
7.0
6.8
6.6
6.5
6.3
6.1
5.9
5.8
5.6
5.4
5.2
5.1
4.9
4.7
4.5
4.1
3.8
3.4
3.0
2.6
2.3
1.9
10.5
10.2
9.8
9.5
9.2
8.8
8.5
8.1
7.9
7.7
7.6
7.4
7.2
7.0
6.8
6.6
6.4
6.2
6.1
5.9
5.7
5.5
5.3
5.1
4.9
4.7
4.5
4.3
4.1
3.9
3.5
3.0
2.6
2.2
1.8
1.3
0.9
10.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.05
92.09
88.13
84.17
80.20
76.23
72.25
70.26
68.27
66.28
64.29
62.30
60.30
58.31
56.31
54.31
52.31
50.31
48.31
46.31
44.31
42.31
40.30
38.30
36.29
34.28
32.27
30.27
28.25
24.23
20.20
16.17
12.13
8.09
4.05
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
7.922
7.606
7.289
6.972
6.655
6.338
6.021
5.704
5.546
5.387
5.229
5.070
4.912
4.754
4.595
4.437
4.278
4.120
3.961
3.803
3.644
3.486
3.328
3.169
3.011
2.852
2.694
2.535
2.377
2.218
1.901
1.584
1.268
0.951
0.634
0.317
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
30.53
29.73
28.93
28.13
27.33
26.54
25.74
24.94
24.54
24.14
23.74
23.34
22.94
22.54
22.14
21.74
21.34
20.95
20.55
20.15
19.75
19.35
18.95
18.55
18.15
17.75
17.35
16.95
16.55
16.15
15.35
14.56
13.76
12.96
12.16
11.36
10.56
Specific
volume, / (m3·kg⫺1)
0.8133
0.8129
0.8125
0.8121
0.8117
0.8113
0.8109
0.8105
0.8103
0.8101
0.8099
0.8097
0.8095
0.8093
0.8091
0.8089
0.8087
0.8085
0.8083
0.8080
0.8078
0.8076
0.8074
0.8072
0.8070
0.8068
0.8066
0.8064
0.8062
0.8060
0.8056
0.8052
0.8048
0.8044
0.8040
0.8036
0.8032
1-28
Reference data
11 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.05
92.09
88.14
84.17
80.21
76.24
72.26
70.27
68.28
66.29
64.30
62.31
60.31
58.32
56.32
54.32
52.32
50.33
48.32
46.32
44.32
42.32
40.31
38.31
36.30
34.29
32.28
30.27
28.26
24.24
20.21
16.18
12.14
8.10
4.05
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
8.194
7.866
7.539
7.211
6.883
6.555
6.228
5.900
5.736
5.572
5.408
5.244
5.080
4.916
4.753
4.589
4.425
4.261
4.097
3.933
3.769
3.605
3.442
3.278
3.114
2.950
2.786
2.622
2.458
2.294
1.967
1.639
1.311
0.983
0.655
0.328
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
31.72
30.90
30.07
29.25
28.42
27.59
26.77
25.94
25.53
25.11
24.70
24.29
23.87
23.46
23.05
22.63
22.22
21.81
21.40
20.98
20.57
20.16
19.74
19.33
18.92
18.50
18.09
17.68
17.26
16.85
16.02
15.20
14.37
13.54
12.72
11.89
11.06
Specific
volume, / (m3·kg⫺1)
0.8151
0.8147
0.8143
0.8139
0.8134
0.8130
0.8126
0.8122
0.8120
0.8117
0.8115
0.8113
0.8111
0.8109
0.8107
0.8105
0.8103
0.8101
0.8099
0.8096
0.8094
0.8092
0.8090
0.8088
0.8086
0.8084
0.8082
0.8080
0.8077
0.8075
0.8071
0.8067
0.8063
0.8059
0.8054
0.8050
0.8046
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.312
1.260
1.208
1.156
1.104
1.052
1.000
0.9480
0.9219
0.8959
0.8696
0.8435
0.8174
0.7912
0.7650
0.7388
0.7126
0.6864
0.6602
0.6339
0.6077
0.5814
0.5551
0.5288
0.5025
0.4762
0.4499
0.4235
0.3972
0.3708
0.3180
0.2651
0.2122
0.1592
0.1062
0.0531
0.0000
11.0
10.4
9.8
9.1
8.4
7.7
7.0
6.2
5.8
5.4
5.0
4.5
4.1
3.6
3.1
2.6
2.1
1.6
1.1
0.5
⫺0.1
⫺0.6
⫺1.1
⫺1.7
⫺2.3
⫺3.0
⫺3.7
⫺4.4
⫺5.1
⫺5.9
⫺7.7
⫺9.8
⫺12.3
⫺15.4
⫺19.7
⫺26.8
—
11.0
10.7
10.3
10.0
9.6
9.2
8.9
8.5
8.3
8.1
7.9
7.8
7.6
7.4
7.2
7.0
6.8
6.6
6.4
6.2
6.0
5.8
5.6
5.4
5.2
5.0
4.7
4.5
4.3
4.1
3.7
3.2
2.8
2.3
1.9
1.4
0.9
11.0
10.7
10.4
10.1
9.7
9.4
9.1
8.8
8.6
8.4
8.3
8.1
7.9
7.8
7.6
7.4
7.2
7.1
6.9
6.7
6.5
6.4
6.2
6.0
5.8
5.6
5.4
5.3
5.1
4.9
4.5
4.1
3.8
3.4
3.0
2.6
2.2
11.0
10.7
10.3
10.0
9.6
9.3
8.9
8.6
8.4
8.2
8.0
7.8
7.6
7.4
7.2
7.1
6.9
6.7
6.5
6.3
6.1
5.9
5.7
5.5
5.3
5.1
4.9
4.7
4.5
4.2
3.8
3.4
3.0
2.5
2.1
1.6
1.2
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.356
1.303
1.249
1.195
1.142
1.088
1.034
0.9800
0.9531
0.9261
0.8991
0.8721
0.8451
0.8180
0.7910
0.7639
0.7368
0.7097
0.6826
0.6555
0.6283
0.6012
0.5740
0.5468
0.5196
0.4924
0.4652
0.4379
0.4107
0.3834
0.3288
0.2742
0.2194
0.1647
0.1098
0.0549
0.0000
11.5
10.9
10.3
9.6
8.9
8.2
7.5
6.7
6.3
5.9
5.4
5.0
4.6
4.1
3.6
3.1
2.6
2.1
1.5
1.0
0.4
⫺0.2
⫺0.7
⫺1.3
⫺1.9
⫺2.6
⫺3.3
⫺4.0
⫺4.7
⫺5.5
⫺7.3
⫺9.4
⫺11.9
⫺15.1
⫺19.4
⫺26.4
—
11.5
11.2
10.8
10.4
10.1
9.7
9.3
9.0
8.8
8.6
8.4
8.2
8.0
7.8
7.6
7.4
7.2
7.0
6.8
6.6
6.4
6.2
6.0
5.8
5.6
5.3
5.1
4.9
4.7
4.5
4.0
3.6
3.1
2.7
2.2
1.7
1.2
11.5
11.2
10.9
10.5
10.2
9.9
9.6
9.2
9.1
8.9
8.7
8.5
8.4
8.2
8.0
7.8
7.7
7.5
7.3
7.1
6.9
6.8
6.6
6.4
6.2
6.0
5.8
5.6
5.5
5.3
4.9
4.5
4.1
3.7
3.3
2.9
2.5
11.5
11.2
10.8
10.5
10.1
9.7
9.4
9.0
8.8
8.6
8.4
8.3
8.1
7.9
7.7
7.5
7.3
7.1
6.9
6.7
6.5
6.3
6.1
5.9
5.7
5.5
5.2
5.0
4.8
4.6
4.2
3.7
3.3
2.8
2.4
1.9
1.4
11.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.05
92.10
88.14
84.18
80.21
76.24
72.27
70.28
68.29
66.30
64.31
62.32
60.32
58.33
56.33
54.33
52.34
50.34
48.34
46.33
44.33
42.33
40.32
38.32
36.31
34.30
32.29
30.28
28.27
24.25
20.22
16.18
12.14
8.10
4.05
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
8.474
8.135
7.796
7.457
7.118
6.779
6.440
6.102
5.932
5.762
5.593
5.424
5.254
5.085
4.915
4.746
4.576
4.407
4.237
4.068
3.898
3.729
3.559
3.390
3.220
3.051
2.881
2.712
2.542
2.373
2.034
1.695
1.356
1.017
0.678
0.339
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
32.94
32.09
31.23
30.38
29.52
28.67
27.81
26.96
26.53
26.10
25.67
25.25
24.82
24.39
23.96
23.54
23.11
22.68
22.26
21.83
21.40
20.97
20.55
20.12
19.69
19.26
18.84
18.41
17.98
17.55
16.70
15.84
14.99
14.13
13.28
12.42
11.57
Specific
volume, / (m3·kg⫺1)
0.8169
0.8165
0.8160
0.8156
0.8152
0.8147
0.8143
0.8139
0.8136
0.8134
0.8132
0.8130
0.8128
0.8126
0.8123
0.8121
0.8119
0.8117
0.8115
0.8112
0.8110
0.8108
0.8106
0.8104
0.8102
0.8099
0.8097
0.8095
0.8093
0.8091
0.8086
0.8082
0.8078
0.8073
0.8069
0.8064
0.8060
Properties of humid air
1-29
12 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.05
92.10
88.15
84.19
80.22
76.25
72.28
70.29
68.30
66.31
64.32
62.33
60.33
58.34
56.34
54.35
52.35
50.35
48.35
46.35
44.34
42.34
40.34
38.33
36.32
34.31
32.30
30.29
28.28
24.26
20.22
16.19
12.15
8.10
4.05
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
8.763
8.412
8.062
7.711
7.361
7.010
6.660
6.309
6.134
5.959
5.784
5.608
5.433
5.258
5.082
4.907
4.732
4.557
4.382
4.206
4.031
3.856
3.680
3.505
3.330
3.155
2.979
2.804
2.629
2.454
2.103
1.753
1.402
1.052
0.701
0.350
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
34.18
33.30
32.41
31.53
30.64
29.76
28.87
27.99
27.55
27.11
26.66
26.22
25.78
25.34
24.89
24.45
24.01
23.57
23.13
22.68
22.24
21.80
21.36
20.92
20.47
20.03
19.59
19.15
18.70
18.26
17.38
16.49
15.61
14.72
13.84
12.96
12.07
Specific
volume, / (m3·kg⫺1)
0.8187
0.8183
0.8178
0.8174
0.8169
0.8165
0.8160
0.8156
0.8153
0.8151
0.8149
0.8147
0.8144
0.8142
0.8140
0.8138
0.8135
0.8133
0.8131
0.8129
0.8126
0.8124
0.8122
0.8120
0.8117
0.8115
0.8113
0.8110
0.8108
0.8106
0.8101
0.8097
0.8092
0.8088
0.8083
0.8079
0.8074
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.402
1.346
1.291
1.236
1.180
1.124
1.069
1.013
0.9852
0.9574
0.9294
0.9015
0.8736
0.8457
0.8177
0.7897
0.7617
0.7337
0.7057
0.6777
0.6496
0.6215
0.5934
0.5654
0.5372
0.5091
0.4810
0.4528
0.4246
0.3964
0.3400
0.2835
0.2269
0.1703
0.1136
0.0568
0.0000
12.0
11.4
10.8
10.1
9.4
8.7
8.0
7.2
6.8
6.3
5.9
5.5
5.0
4.6
4.1
3.6
3.1
2.6
2.0
1.4
0.9
0.2
⫺0.3
⫺0.9
⫺1.5
⫺2.2
⫺2.9
⫺3.6
⫺4.3
⫺5.2
⫺6.9
⫺9.0
⫺11.5
⫺14.7
⫺19.0
⫺26.1
—
12.0
11.6
11.3
10.8
10.6
10.2
9.8
9.4
9.2
9.0
8.8
8.6
8.4
8.2
8.0
7.8
7.6
7.4
7.2
7.0
6.8
6.6
6.4
6.2
5.9
5.7
5.5
5.3
5.1
4.8
4.4
3.9
3.5
3.0
2.5
2.0
1.5
12.0
11.7
11.4
11.0
10.7
10.4
10.0
9.7
9.5
9.3
9.2
9.0
8.8
8.6
8.4
8.3
8.1
7.9
7.7
7.5
7.4
7.2
7.0
6.8
6.6
6.4
6.2
5.0
5.8
5.6
5.2
4.8
4.4
4.0
3.6
3.2
2.8
12.0
11.7
11.3
10.9
10.6
10.2
9.8
9.5
9.3
9.1
8.9
8.7
8.5
8.3
8.1
7.9
7.7
7.5
7.3
7.1
6.9
6.7
6.5
6.3
6.1
5.8
5.6
5.4
5.2
5.0
4.5
4.1
3.6
3.2
2.7
2.2
1.7
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.449
1.391
1.334
1.277
1.220
1.162
1.105
1.047
1.018
0.9895
0.9607
0.9319
0.9030
0.8741
0.8452
0.8163
0.7874
0.7584
0.7295
0.7005
0.6715
0.6425
0.6135
0.5844
0.5554
0.5263
0.4972
0.4681
0.4390
0.4098
0.3515
0.2931
0.2346
0.1760
0.1174
0.0587
0.0000
12.5
11.9
11.3
10.6
9.9
9.2
8.4
7.7
7.2
6.8
6.4
6.0
5.5
5.0
4.6
4.1
3.5
3.0
2.5
1.9
1.3
0.7
0.1
⫺0.5
⫺1.1
⫺1.8
⫺2.5
⫺3.2
⫺4.0
⫺4.8
⫺6.6
⫺8.6
⫺11.2
⫺14.3
⫺18.7
⫺25.8
—
12.5
12.1
11.8
11.4
11.0
10.7
10.3
9.9
9.7
9.5
9.3
9.1
8.9
8.7
8.5
8.3
8.1
7.8
7.6
7.4
7.2
7.0
6.8
6.6
6.3
6.1
5.9
5.7
5.4
5.2
4.7
4.3
3.8
3.3
2.8
2.3
1.8
12.5
12.2
11.8
11.5
11.2
10.8
10.5
10.1
10.0
9.8
9.6
9.4
9.2
9.1
8.9
8.7
8.5
8.3
8.1
8.0
7.8
7.6
7.4
7.2
7.0
6.8
6.6
6.4
6.2
6.0
5.6
5.2
4.8
4.4
3.9
3.5
3.1
12.5
12.1
11.8
11.4
11.1
10.7
10.3
9.9
9.7
9.5
9.3
9.1
8.9
8.7
8.5
8.3
8.1
7.9
7.7
7.5
7.3
7.1
6.9
6.7
6.4
6.2
6.0
5.8
5.6
5.3
4.9
4.4
4.0
3.5
3.0
2.5
2.0
12.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.06
92.11
88.15
84.19
80.23
76.26
72.29
70.30
68.31
66.32
64.33
62.34
60.35
58.35
56.36
54.36
52.36
50.36
48.36
46.36
44.36
42.35
40.35
38.34
36.33
34.32
32.31
30.30
28.29
24.26
20.23
16.19
12.15
8.11
4.06
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
9.060
8.698
8.336
7.973
7.611
7.248
6.886
6.524
6.342
6.161
5.980
5.799
5.618
5.436
5.255
5.074
4.893
4.711
4.530
4.349
4.168
3.987
3.805
3.624
3.443
3.262
3.080
2.899
2.718
2.537
2.174
1.812
1.450
1.087
0.724
0.362
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
35.44
34.53
33.61
32.70
31.78
30.87
29.95
29.04
28.58
28.12
27.67
27.21
26.75
26.30
25.84
25.38
24.92
24.47
24.01
23.55
23.09
22.64
22.18
21.72
21.26
20.81
20.35
19.89
19.44
18.98
18.06
17.15
16.23
15.32
14.40
13.49
12.58
Specific
volume, / (m3·kg⫺1)
0.8205
0.8201
0.8196
0.8191
0.8187
0.8182
0.8177
0.8173
0.8170
0.8168
0.8166
0.8163
0.8161
0.8159
0.8156
0.8154
0.8152
0.8149
0.8147
0.8145
0.8142
0.8140
0.8138
0.8135
0.8133
0.8131
0.8128
0.8126
0.8124
0.8121
0.8117
0.8112
0.8107
0.8103
0.8098
0.8093
0.8089
1-30
Reference data
13 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.06
92.11
88.16
84.20
80.24
76.27
72.30
70.31
68.33
66.34
64.34
62.35
60.36
58.36
56.37
54.37
52.37
50.37
48.37
46.37
44.37
42.36
40.36
38.35
36.34
34.34
32.33
30.31
28.30
24.27
20.24
16.20
12.16
8.11
4.06
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
9.367
8.992
8.618
8.243
7.868
7.494
7.119
6.744
6.557
6.370
6.182
5.995
5.808
5.620
5.433
5.245
5.058
4.871
0.4683
4.496
4.309
4.121
3.934
3.747
3.559
3.372
3.185
2.997
2.810
2.623
2.248
1.873
1.499
1.124
0.7493
0.3747
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
36.73
35.78
34.84
33.89
32.94
32.00
31.05
30.11
29.63
29.16
28.69
28.21
27.74
27.27
26.79
26.32
25.85
25.38
24.90
24.43
23.96
23.48
23.01
22.54
22.06
21.59
21.12
20.65
20.17
19.70
18.75
17.81
16.86
15.92
14.97
14.02
13.08
Specific
volume, / (m3·kg⫺1)
0.8224
0.8219
0.8214
0.8209
0.8204
0.8200
0.8195
0.8190
0.8188
0.8185
0.8183
0.8180
0.8178
0.8175
0.8173
0.8171
0.8168
0.8166
0.8163
0.8161
0.8158
0.8156
0.8154
0.8151
0.8149
0.8146
0.8144
0.8141
0.8139
0.8137
0.8132
0.8127
0.8122
0.8117
0.8112
0.8108
0.8103
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.497
1.438
1.379
1.320
1.260
1.201
1.142
1.082
1.052
1.023
0.9929
0.9631
0.9333
0.9034
0.8736
0.8437
0.8138
0.7839
0.7540
0.7240
0.6941
0.6641
0.6341
0.6041
0.5740
0.5440
0.5139
0.4838
0.4537
0.4236
0.3633
0.3029
0.2425
0.1820
0.1214
0.0607
0.0000
13.0
12.4
11.7
11.1
10.4
9.7
8.9
8.1
7.7
7.3
6.9
6.4
6.0
5.5
5.0
4.5
4.0
3.5
2.9
2.4
1.8
1.2
0.5
⫺0.1
⫺0.7
⫺1.4
⫺2.1
⫺2.8
⫺3.6
⫺4.4
⫺6.2
⫺8.3
⫺10.8
⫺14.0
⫺18.3
⫺25.5
—
13.0
12.6
12.3
11.9
11.5
11.1
10.7
10.3
10.1
9.9
9.7
9.5
9.3
9.1
8.9
8.7
8.5
8.3
8.1
7.8
7.6
7.4
7.2
6.9
6.7
6.5
6.3
6.0
5.8
5.6
5.1
4.6
4.1
3.6
3.1
2.6
2.1
13.0
12.7
12.3
12.0
11.6
11.3
11.0
10.6
10.4
10.2
10.1
9.9
9.7
9.5
9.3
9.1
8.9
8.7
8.6
8.4
8.2
8.0
7.8
7.6
7.4
7.2
7.0
6.8
6.6
6.4
6.0
5.6
5.1
4.7
4.3
3.8
3.4
13.0
12.6
12.3
11.9
11.5
11.2
10.8
10.4
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.3
8.1
7.9
7.7
7.5
7.3
7.1
6.8
6.6
6.4
6.2
5.9
5.7
5.2
4.8
4.3
3.8
3.3
2.8
2.3
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.546
1.486
1.424
1.363
1.302
1.241
1.180
1.118
1.088
1.057
1.026
0.9952
0.9644
0.9336
0.9028
0.8719
0.8410
0.8101
0.7792
0.7482
0.7173
0.6863
0.6553
0.6243
0.5933
0.5622
0.5312
0.5000
0.4690
0.4378
0.3755
0.3131
0.2506
0.1881
0.1255
0.0628
0.0000
13.5
12.9
12.2
11.6
10.8
10.2
9.4
8.6
8.2
7.8
7.4
6.9
6.5
6.0
5.5
5.0
4.5
4.0
3.4
2.8
2.2
1.6
1.0
0.3
⫺0.3
⫺1.0
⫺1.7
⫺2.4
⫺3.2
⫺4.0
⫺5.8
⫺7.9
⫺10.4
⫺13.6
⫺18.0
⫺25.1
—
13.5
13.1
12.8
12.4
12.0
11.6
11.2
10.8
10.6
10.4
10.2
10.0
9.8
9.6
9.3
9.1
8.9
8.7
8.5
8.2
8.0
7.8
7.6
7.3
7.1
6.9
6.6
6.4
6.2
5.9
5.4
4.9
4.4
3.9
3.4
2.9
2.4
13.5
13.2
12.8
12.5
12.1
11.8
11.4
11.1
10.9
10.7
10.5
10.3
10.1
9.9
9.7
9.6
9.4
9.2
9.0
8.8
8.6
8.4
8.2
8.0
7.8
7.6
7.4
7.2
7.0
6.8
6.3
5.9
5.5
5.0
4.6
4.1
3.7
13.5
13.1
12.8
12.4
12.0
11.6
11.2
10.8
10.6
10.4
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.3
8.1
7.9
7.7
7.4
7.2
7.0
6.8
6.5
6.3
6.1
5.6
5.1
4.6
4.1
3.6
3.1
2.6
13.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.06
92.11
88.16
84.21
80.25
76.28
72.31
70.32
68.34
66.35
64.36
62.36
60.37
58.38
56.38
54.38
52.39
50.39
48.39
46.38
44.38
42.38
40.37
38.36
36.36
34.35
32.34
30.33
28.31
24.28
20.25
16.21
12.16
8.11
4.06
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
9.683
9.295
8.908
8.521
8.133
7.746
7.359
6.972
6.778
6.584
6.390
6.197
6.003
5.810
5.616
5.422
5.229
5.036
4.841
4.648
4.454
4.260
4.067
3.873
3.679
3.486
3.292
3.098
2.905
2.711
2.324
1.936
1.549
1.162
0.7746
0.3873
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
38.04
37.06
36.08
35.10
34.12
33.14
32.17
31.19
30.70
30.21
29.72
29.23
28.74
28.25
27.76
27.28
26.79
26.30
25.81
25.32
24.83
24.34
23.85
23.36
22.87
22.38
21.90
21.41
20.92
20.43
19.45
18.47
17.49
16.52
15.54
14.56
13.58
Specific
volume, / (m3·kg⫺1)
0.8242
0.8237
0.8232
0.8227
0.8222
0.8217
0.8212
0.8207
0.8205
0.8202
0.8200
0.8197
0.8195
0.8192
0.8190
0.8187
0.8185
0.8182
0.8180
0.8177
0.8175
0.8172
0.8170
0.8167
0.8165
0.8162
0.8160
0.8157
0.8155
0.8152
0.8147
0.8142
0.8137
0.8132
0.8127
0.8122
0.8117
Properties of humid air
1-31
14 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.06
92.12
88.17
84.21
80.26
76.29
72.32
70.34
68.35
66.36
64.37
62.38
60.38
58.39
56.39
54.40
52.40
50.40
48.40
46.40
44.39
42.39
40.38
38.38
36.37
34.36
32.35
30.34
28.32
24.29
20.26
16.22
12.17
8.12
4.06
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
10.010
9.608
9.207
8.807
8.407
8.006
7.606
7.206
7.005
6.805
6.605
6.405
6.205
6.005
5.804
5.604
5.404
5.204
5.004
4.804
4.604
4.403
4.203
4.003
3.803
3.603
3.403
3.202
3.002
2.802
2.402
2.002
1.601
1.201
0.8006
0.4003
0.0000
Specific
enthalpy, h
/ (kJ·kg⫺1)
39.37
38.36
37.37
35.34
35.32
34.31
33.30
32.29
31.78
31.28
30.77
30.27
29.76
29.26
28.75
28.24
27.74
27.23
26.73
26.22
25.72
25.21
24.70
24.20
23.69
23.17
22.68
22.18
21.67
21.16
20.15
19.14
18.13
17.12
16.11
15.10
14.08
Specific
volume, / (m3·kg⫺1)
0.8261
0.8256
0.8251
0.8245
0.8240
0.8235
0.8230
0.8225
0.8222
0.8219
0.8217
0.8214
0.8212
0.8209
0.8206
0.8204
0.8201
0.8199
0.8196
0.8193
0.8191
0.8188
0.8186
0.8183
0.8180
0.8178
0.8175
0.8173
0.8170
0.8167
0.8162
0.8157
0.8152
0.8147
0.8142
0.8136
0.8131
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.598
1.535
1.472
1.409
1.345
1.282
1.219
1.155
1.124
1.092
1.060
1.028
0.9965
0.9647
0.9328
0.9009
0.8690
0.8371
0.8052
0.7732
0.7412
0.7092
0.6772
0.6452
0.6131
0.5810
0.5489
0.5168
0.4846
0.4525
0.3881
0.3236
0.2590
0.1944
0.1297
0.0649
0.0000
14.0
13.4
12.7
12.1
11.4
10.7
9.9
9.1
8.7
8.3
7.8
7.4
6.9
6.5
6.0
5.5
5.0
4.4
3.9
3.3
2.7
2.1
1.4
0.8
0.1
⫺0.6
⫺1.3
⫺2.0
⫺2.8
⫺3.6
⫺5.4
⫺7.5
⫺10.0
⫺13.2
⫺17.6
⫺24.8
—
14.0
13.6
13.2
12.9
12.5
12.1
11.7
11.3
11.0
10.8
10.6
10.4
10.2
10.0
9.8
9.6
9.3
9.1
8.9
8.7
8.4
8.2
8.0
7.7
7.5
7.3
7.0
6.8
6.5
6.3
5.8
5.3
4.8
4.3
3.7
3.2
2.6
14.0
13.7
13.3
13.0
12.6
12.2
11.9
11.5
11.3
11.1
10.9
10.8
10.6
10.4
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.4
8.2
8.0
7.8
7.5
7.3
7.1
6.7
6.3
5.8
5.4
4.9
4.4
4.0
14.0
13.6
13.3
12.9
12.5
12.1
11.7
11.3
11.1
10.9
10.7
10.5
10.3
10.0
9.8
9.6
9.4
9.2
9.0
8.7
8.5
8.3
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.4
5.9
5.5
5.0
4.4
3.9
3.4
2.9
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.650
1.585
1.520
1.455
1.390
1.324
1.259
1.194
1.161
1.128
1.095
1.062
1.030
0.9966
0.9937
0.9308
0.8978
0.8649
0.8329
0.7989
0.7658
0.7328
0.6997
0.6666
0.6335
0.6003
0.5672
0.5340
0.5008
0.4675
0.4010
0.3344
0.2677
0.2009
0.1340
0.0670
0.0000
14.5
13.9
13.2
12.6
11.9
11.1
10.4
9.6
9.2
8.7
8.3
7.9
7.4
6.9
6.4
5.9
5.4
4.9
4.3
3.8
3.2
2.5
1.9
1.2
0.5
⫺0.2
⫺0.9
⫺1.6
⫺2.4
⫺3.2
⫺5.0
⫺7.1
⫺9.7
⫺12.9
⫺17.3
⫺24.5
—
14.5
14.1
13.7
13.3
12.9
12.5
12.1
11.7
11.5
11.3
11.1
10.9
10.6
10.4
10.2
10.0
9.8
9.5
9.3
9.1
8.8
8.6
8.4
8.1
7.9
7.6
7.4
7.2
6.9
6.7
6.1
5.6
5.1
4.6
4.0
3.5
2.9
14.5
14.2
13.8
13.4
13.1
12.7
12.3
12.0
11.8
11.6
11.4
11.2
11.0
10.8
10.6
10.4
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.4
8.1
7.9
7.7
7.5
7.0
6.6
6.1
5.7
5.2
4.7
4.3
14.5
14.1
13.7
13.4
13.0
12.6
12.2
11.8
11.5
11.3
11.1
10.9
10.7
10.5
10.3
10.0
9.8
9.6
9.4
9.2
8.9
8.7
8.5
8.2
8.0
7.8
7.5
7.3
7.0
6.8
6.3
5.8
5.3
4.8
4.2
3.7
3.2
14.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.06
92.12
88.17
84.22
80.26
76.30
72.33
70.35
68.36
66.37
64.38
62.39
60.40
58.40
56.41
54.41
52.41
50.41
48.41
46.41
44.41
42.40
40.40
38.39
36.38
34.37
32.36
30.35
28.33
24.30
20.27
16.22
12.18
8.12
4.06
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
10.340
9.929
9.515
9.102
8.688
8.274
7.860
7.447
7.240
7.033
6.826
6.619
6.412
6.206
5.999
5.792
5.585
5.378
5.171
4.964
4.758
4.551
4.344
4.137
3.930
3.723
3.516
3.310
3.103
2.896
2.482
2.068
1.655
1.241
0.827
0.413
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
40.73
39.68
38.64
37.59
36.55
35.50
34.45
33.41
32.89
32.36
31.84
31.32
30.79
30.27
29.75
29.23
28.70
28.18
27.66
27.13
26.61
26.09
25.57
25.04
24.52
24.00
23.47
22.95
22.43
21.91
20.86
19.81
18.77
17.72
16.68
15.63
14.59
Specific
volume, / (m3·kg⫺1)
0.8280
0.8274
0.8269
0.8264
0.8258
0.8253
0.8248
0.8242
0.8239
0.8237
0.8234
0.8231
0.8229
0.8226
0.8223
0.8221
0.8218
0.8215
0.8213
0.8210
0.8207
0.8204
0.8202
0.8199
0.8196
0.8194
0.8191
0.8188
0.8186
0.8183
0.8178
0.8172
0.8167
0.8161
0.8156
0.8151
0.8145
1-32
Reference data
15 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.06
92.13
88.18
84.23
80.27
76.31
72.34
70.36
68.37
66.38
64.39
62.40
60.41
58.42
56.42
54.42
52.43
50.43
48.43
46.42
44.42
42.42
40.41
38.40
36.39
34.38
32.37
30.36
28.35
24.31
20.27
16.23
12.18
8.13
4.07
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
10.697
10.260
9.833
9.405
8.978
8.550
8.123
7.695
7.481
7.268
7.054
6.840
6.626
6.413
6.199
5.985
5.771
5.558
5.344
5.130
4.916
4.703
4.489
4.275
4.061
3.848
3.634
3.420
3.206
2.993
2.565
2.138
1.710
1.282
0.855
0.427
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
42.11
41.03
39.95
38.87
37.79
36.71
35.63
34.55
34.01
33.47
32.93
32.28
31.84
31.30
30.76
30.22
29.68
29.14
28.60
28.06
27.52
26.98
26.44
25.90
25.36
24.82
24.28
23.74
23.20
22.66
21.58
20.49
19.41
18.33
17.25
16.17
15.09
Specific
volume, / (m3·kg⫺1)
0.8299
0.8293
0.8288
0.8282
0.8276
0.8271
0.8265
0.8260
0.8257
0.8254
0.8251
0.8249
0.8246
0.8243
0.8240
0.8237
0.8235
0.8232
0.8229
0.8226
0.8224
0.8221
0.8218
0.8215
0.8212
0.8210
0.8207
0.8204
0.8201
0.8198
0.8193
0.8187
0.8182
0.8176
0.8171
0.8165
0.8159
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.704
1.637
1.570
1.503
1.435
1.368
1.301
1.233
1.199
1.165
1.131
1.097
1.064
1.030
0.9956
0.9616
0.9275
0.8935
0.8594
0.8253
0.7912
0.7570
0.7229
0.6887
0.6545
0.6202
0.5860
0.5517
0.5174
0.4831
0.4143
0.3455
0.2766
0.2076
0.1385
0.0692
0.0000
15.0
14.4
13.7
13.1
12.4
11.6
10.9
10.1
9.7
9.2
8.8
8.3
7.9
7.4
6.9
6.4
5.9
5.4
4.8
4.2
3.6
3.0
2.3
1.7
1.0
0.2
⫺0.5
⫺1.2
⫺2.0
⫺2.8
⫺4.6
⫺6.7
⫺9.3
⫺12.5
⫺16.9
⫺24.1
—
15.0
14.6
14.2
13.8
13.4
13.0
12.6
12.2
12.0
11.7
11.5
11.3
11.1
10.9
10.6
10.4
10.2
9.9
9.7
9.5
9.2
9.0
8.8
8.5
8.3
8.0
7.8
7.5
7.3
7.0
6.5
6.0
5.4
4.9
4.3
3.8
3.2
15.0
14.6
14.3
13.9
13.6
13.2
12.8
12.4
12.2
12.0
11.8
11.6
11.4
11.2
11.0
10.8
10.6
10.4
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.7
8.5
8.3
8.1
7.9
7.4
6.9
6.5
6.0
5.5
5.0
4.6
15.0
14.6
14.2
13.8
13.4
13.0
12.6
12.2
12.0
11.8
11.6
11.4
11.1
10.9
10.7
10.5
10.3
10.0
9.8
9.6
9.3
9.1
8.9
8.6
8.4
8.1
7.9
7.7
7.4
7.2
6.7
6.1
5.6
5.1
4.5
4.0
3.4
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.760
1.691
1.621
1.552
1.482
1.413
1.343
1.273
1.238
1.204
1.168
1.134
1.098
1.063
1.028
0.9932
0.9581
0.9229
0.8877
0.8525
0.8173
0.7820
0.7467
0.7114
0.6761
0.6407
0.6053
0.5699
0.5345
0.4990
0.4280
0.3570
0.2858
0.2145
0.1431
0.0716
0.0000
15.5
14.9
14.2
13.6
12.9
12.1
11.4
10.6
10.1
9.7
9.3
8.8
8.4
7.9
7.4
6.9
6.4
5.8
5.3
4.7
4.1
3.4
2.8
2.1
1.4
0.7
⫺0.1
⫺0.8
⫺1.6
⫺2.4
⫺4.2
⫺6.4
⫺8.9
⫺12.2
⫺16.6
⫺23.8
—
15.5
15.1
14.7
14.3
13.9
13.5
13.1
12.6
12.4
12.2
12.0
11.7
11.5
11.3
11.1
10.8
10.6
10.4
10.1
9.9
9.6
9.4
9.2
8.9
8.7
8.4
8.2
7.9
7.6
7.4
6.8
6.3
5.8
5.2
4.6
4.0
3.5
15.5
15.1
14.8
14.4
14.0
13.7
13.3
12.9
12.7
12.5
12.3
12.1
11.9
11.7
11.5
11.3
11.1
10.9
10.6
10.4
10.2
10.0
9.8
9.6
9.3
9.1
8.9
8.7
8.4
8.2
7.8
7.3
6.8
6.3
5.8
5.3
4.8
15.5
15.1
14.7
14.3
13.9
13.5
13.1
12.7
12.5
12.2
12.0
11.8
11.6
11.4
11.1
10.9
10.7
10.4
10.2
10.0
9.7
9.5
9.3
9.0
8.8
8.5
8.3
8.0
7.8
7.5
7.0
6.5
5.9
5.4
4.8
4.3
3.7
15.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
00
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.07
92.13
88.19
84.24
80.28
76.32
72.36
70.37
68.38
66.40
64.41
62.42
60.42
58.43
56.44
54.44
52.44
50.44
48.44
46.44
44.44
42.43
40.42
38.42
36.41
34.40
32.39
30.37
28.36
24.32
20.28
16.24
12.19
8.13
4.07
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
11.04
10.60
10.16
9.718
9.276
8.834
8.393
7.951
7.730
7.509
7.288
7.068
6.847
6.626
6.405
6.184
5.963
5.742
5.522
5.301
5.080
4.859
4.638
4.417
4.196
3.976
3.755
3.534
3.313
3.092
2.650
2.209
1.767
1.325
0.883
0.442
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
43.52
42.41
41.29
40.17
39.06
37.94
36.82
35.70
35.14
34.59
34.03
33.47
32.91
32.35
31.79
31.24
30.68
30.12
29.56
29.00
28.44
27.88
27.32
26.77
26.21
25.65
25.09
24.53
23.97
23.41
22.30
21.18
20.06
18.94
17.83
16.71
15.59
Specific
volume, / (m3·kg⫺1)
0.8318
0.8312
0.8306
0.8300
0.8295
0.8289
0.8283
0.8277
0.8275
0.8272
0.8269
0.8266
0.8263
0.8260
0.8257
0.8254
0.8252
0.8249
0.8246
0.8243
0.8240
0.8237
0.8234
0.8231
0.8228
0.8226
0.8223
0.8220
0.8217
0.8214
0.8208
0.8203
0.8197
0.8191
0.8185
0.8179
0.8174
Properties of humid air
1-33
16 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.07
92.13
88.19
84.24
80.29
76.33
72.37
70.38
68.40
66.41
64.42
62.43
60.44
58.45
56.45
54.45
52.46
50.46
48.46
46.45
44.45
42.45
40.44
38.43
36.42
34.41
32.40
30.38
28.37
24.33
20.29
16.25
12.19
8.13
4.07
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
11.41
10.95
10.50
10.04
9.583
9.127
8.671
8.214
7.986
7.758
7.530
7.302
7.074
6.845
6.617
6.389
6.161
5.933
5.704
5.476
5.248
5.020
4.792
4.564
4.335
4.107
3.879
3.651
3.423
3.194
2.738
2.282
1.825
1.369
0.912
0.456
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
44.96
43.81
42.65
41.50
40.34
39.19
38.04
36.88
36.30
35.73
35.15
34.57
33.99
33.42
32.84
32.26
31.68
31.11
30.53
29.95
29.37
28.80
28.22
27.64
27.07
26.49
25.91
25.33
24.76
24.17
23.02
21.87
20.71
19.56
18.40
17.25
16.10
Specific
volume, / (m3·kg⫺1)
0.8337
0.8331
0.8325
0.8319
0.8313
0.8307
0.8301
0.8295
0.8292
0.8289
0.8286
0.8283
0.8280
0.8277
0.8274
0.8271
0.8268
0.8265
0.8262
0.8259
0.8257
0.8254
0.8251
0.8248
0.8245
0.8242
0.8239
0.8236
0.8233
0.8230
0.8224
0.8218
0.8212
0.8206
0.8200
0.8194
0.8188
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.817
1.746
1.674
1.603
1.531
1.459
1.387
1.315
1.279
1.243
1.207
1.171
1.134
1.098
1.062
1.026
0.9895
0.9532
0.9169
0.8805
0.8441
0.8077
0.7713
0.7348
0.6983
0.6618
0.6253
0.5887
0.5521
0.5155
0.4422
0.3688
0.2952
0.2216
0.1478
0.0740
0.0000
16.0
15.4
14.7
14.0
13.3
12.6
11.8
11.0
10.6
10.2
9.7
9.3
8.8
8.4
7.9
7.4
6.8
6.3
5.7
5.1
4.5
3.9
3.3
2.6
1.9
1.1
0.3
⫺0.4
⫺1.2
⫺2.0
⫺3.9
⫺6.0
⫺8.6
⫺11.8
⫺16.2
⫺23.5
—
16.0
15.6
15.2
14.8
14.4
14.0
13.5
13.1
12.9
12.6
12.4
12.2
12.0
11.7
11.5
11.3
11.0
10.8
10.5
10.3
10.1
9.8
9.6
9.3
9.0
8.8
8.5
8.3
8.0
7.7
7.2
6.6
6.1
5.5
4.9
4.3
3.7
16.0
15.6
15.3
14.9
14.5
14.1
13.7
13.3
13.1
12.9
12.7
12.5
12.3
12.1
11.9
11.7
11.5
11.3
11.1
10.8
10.6
10.4
10.2
10.0
9.7
9.5
9.3
9.1
8.8
8.6
8.1
7.6
7.2
6.7
6.2
5.6
5.1
16.0
15.6
15.2
14.8
14.4
14.0
13.6
13.1
12.9
12.7
12.5
12.2
12.0
11.8
11.6
11.3
11.1
10.9
10.6
10.4
10.1
9.9
9.7
9.4
9.2
8.9
8.7
8.4
8.1
7.9
7.4
6.8
6.3
5.7
5.1
4.6
4.0
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.876
1.802
1.728
1.655
1.581
1.506
1.432
1.358
1.321
1.283
1.246
1.209
1.171
1.134
1.097
1.059
1.022
0.9844
0.9469
0.9093
0.8718
0.8342
0.7965
0.7589
0.7212
0.6835
0.6458
0.6080
0.5702
0.5324
0.4567
0.3809
0.3049
0.2289
0.1527
0.0764
0.0000
16.5
15.9
15.2
14.5
13.8
13.1
12.3
11.5
11.1
10.7
10.2
9.8
9.3
8.8
8.3
7.8
7.3
6.8
6.2
5.6
5.0
4.4
3.7
3.0
2.3
1.6
0.8
⫺0.1
⫺0.8
⫺1.7
⫺3.5
⫺5.6
⫺8.2
⫺11.4
⫺15.9
⫺23.1
—
16.5
16.1
15.7
15.3
14.9
14.4
14.0
13.5
13.3
13.1
12.9
12.6
12.4
12.2
11.9
11.7
11.4
11.2
11.0
10.7
10.5
10.2
10.0
9.7
9.4
9.2
8.9
8.6
8.4
8.1
7.5
7.0
6.4
5.8
5.2
4.6
4.0
16.5
16.1
15.8
15.4
15.0
14.6
14.2
13.8
13.6
13.4
13.2
13.0
12.8
12.6
12.3
12.1
11.9
11.7
11.5
11.3
11.0
10.8
10.6
10.4
10.1
9.9
9.7
9.4
9.2
9.0
8.5
8.0
7.5
7.0
6.5
5.9
5.4
16.5
16.1
15.7
15.3
14.9
14.4
14.0
13.6
13.4
13.1
12.9
12.7
12.5
12.2
12.0
11.8
11.5
11.3
11.0
10.8
10.6
10.4
10.1
9.8
9.5
9.3
9.0
8.8
8.5
8.2
7.7
7.2
6.6
6.0
5.4
4.8
4.2
16.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.07
92.14
88.20
84.25
80.30
76.34
72.38
70.40
68.41
66.42
64.43
62.44
60.45
58.46
56.47
54.47
52.47
50.47
48.47
46.47
44.47
42.46
40.45
38.45
36.44
34.42
32.41
30.40
28.38
24.35
20.30
16.25
12.20
8.14
4.07
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
11.79
11.31
10.84
10.37
9.900
9.428
8.957
8.486
8.250
8.014
7.778
7.543
7.307
7.071
6.836
6.600
6.364
6.128
5.893
5.657
5.421
5.186
4.950
4.714
4.478
4.243
4.007
3.771
3.536
3.300
2.828
2.357
1.886
1.414
0.943
0.471
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
46.43
45.24
44.04
42.85
41.66
40.46
39.27
38.08
37.48
36.88
36.29
35.69
35.09
34.50
33.90
33.30
32.71
32.11
31.51
30.92
30.32
29.72
29.13
28.53
27.93
27.34
26.74
26.14
25.55
24.95
23.76
22.56
21.37
20.18
18.98
17.79
16.60
Specific
volume, / (m3·kg⫺1)
0.8356
0.8350
0.8344
0.8338
0.8332
0.8326
0.8319
0.8313
0.8310
0.8307
0.8304
0.8301
0.8298
0.8295
0.8292
0.8289
0.8285
0.8282
0.8279
0.8276
0.8273
0.8270
0.8267
0.8264
0.8261
0.8258
0.8255
0.8251
0.8248
0.8245
0.8239
0.8233
0.8227
0.8221
0.8214
0.8208
0.8202
1-34
Reference data
17 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.07
92.14
88.20
84.26
80.31
76.35
72.39
70.41
68.42
66.44
64.45
62.46
60.47
58.47
56.48
54.48
52.49
50.49
48.49
46.49
44.48
42.48
40.47
38.46
36.45
34.44
32.43
30.41
28.39
24.36
20.31
16.26
12.21
8.14
4.08
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
12.17
11.69
11.20
10.71
10.23
9.739
9.252
8.765
8.521
8.278
8.034
7.791
7.547
7.304
7.060
6.817
6.574
6.330
6.087
5.843
5.600
5.356
5.113
4.869
4.626
4.382
4.139
3.896
3.652
3.409
2.922
2.435
1.948
1.461
0.974
0.487
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
47.93
46.69
45.46
44.23
42.99
41.76
40.53
39.30
38.68
38.06
37.45
36.83
36.21
35.60
34.98
34.36
33.75
33.13
32.51
31.90
31.28
30.66
30.05
29.43
28.81
28.20
27.58
26.97
26.35
25.73
24.50
23.27
22.03
20.80
19.57
18.33
17.10
Specific
volume, / (m3·kg⫺1)
0.8376
0.8370
0.8363
0.8357
0.8350
0.8344
0.8338
0.8331
0.8328
0.8325
0.8322
0.8318
0.8315
0.8312
0.8309
0.8306
0.8303
0.8299
0.8296
0.8293
0.8290
0.8287
0.8283
0.8280
0.8277
0.8274
0.8271
0.8267
0.8264
0.8261
0.8255
0.8248
0.8242
0.8235
0.8229
0.8223
0.8216
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.936
1.860
1.784
1.708
1.632
1.555
1.479
1.402
1.363
1.325
1.287
1.248
1.210
1.171
1.132
1.094
1.055
1.016
0.9777
0.9390
0.9002
0.8614
0.8225
0.7837
0.7448
0.7058
0.6669
0.6279
0.5889
0.5498
0.4717
0.3934
0.3149
0.2364
0.1577
0.0789
0.0000
17.0
16.4
15.7
15.0
14.3
13.6
12.8
12.0
11.6
11.2
10.7
10.3
9.8
9.3
8.8
8.3
7.8
7.2
6.7
6.1
5.5
4.8
4.2
3.5
2.8
2.0
1.2
0.4
⫺0.4
⫺1.3
⫺3.1
⫺5.2
⫺7.8
⫺11.1
⫺15.5
⫺22.8
—
17.0
16.6
16.2
15.8
15.3
14.9
14.5
14.0
13.8
13.5
13.3
13.1
12.8
12.6
12.4
12.1
11.9
11.6
11.4
11.1
10.9
10.6
10.3
10.1
9.8
9.6
9.3
9.0
8.7
8.5
7.9
7.3
6.7
6.1
5.5
4.9
4.3
17.0
16.6
16.2
15.9
15.5
15.1
14.7
14.3
14.0
13.8
13.6
13.4
13.2
13.0
12.8
12.6
12.3
12.1
11.9
11.7
11.4
11.2
11.0
10.7
10.5
10.3
10.0
9.8
9.6
9.3
8.8
8.3
7.8
7.3
6.8
6.2
5.7
17.0
16.6
16.2
15.8
15.4
14.9
14.5
14.0
13.8
13.6
13.4
13.1
12.9
12.7
12.4
12.2
11.9
11.7
11.5
11.2
11.0
10.7
10.4
10.2
9.9
9.7
9.4
9.1
8.9
8.6
8.0
7.5
6.9
6.3
5.7
5.1
4.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
1.999
1.920
1.842
1.763
1.684
1.605
1.526
1.447
1.408
1.368
1.328
1.288
1.249
1.209
1.169
1.129
1.089
1.049
1.009
0.9695
0.9294
0.8894
0.8493
0.8092
0.7690
0.7288
0.6886
0.6484
0.6081
0.5678
0.4871
0.4062
0.3252
0.2441
0.1629
0.0815
0.0000
17.5
16.9
16.2
15.5
14.8
14.1
13.3
12.5
12.1
11.6
11.2
10.7
10.3
9.8
9.3
8.8
8.2
7.7
7.1
6.5
5.9
5.3
4.6
3.9
3.2
2.5
1.7
0.8
0.0
⫺0.9
⫺2.7
⫺4.9
⫺7.4
⫺10.7
⫺15.2
⫺22.5
—
17.5
17.1
16.7
16.2
15.8
15.4
14.9
14.5
14.2
14.0
13.8
13.5
13.3
13.0
12.8
12.5
12.3
12.0
11.8
11.5
11.3
11.0
10.7
10.5
10.2
9.9
9.7
9.4
9.1
8.8
8.2
7.7
7.1
6.4
5.8
5.2
4.5
17.5
17.1
16.7
16.3
15.9
15.5
15.1
14.7
14.5
14.3
14.1
13.9
13.6
13.4
13.2
13.0
12.8
12.5
12.3
12.1
11.8
11.6
11.4
11.1
10.9
10.7
10.4
10.2
9.9
9.7
9.2
8.7
8.1
7.6
7.1
6.5
6.0
17.5
17.1
16.7
16.3
15.8
15.4
14.9
14.5
14.5
14.0
13.8
13.6
13.3
13.1
12.9
12.6
12.4
12.1
11.9
11.6
11.4
11.1
10.8
10.6
10.3
10.1
9.8
9.5
9.2
9.0
8.4
7.8
7.2
6.6
6.0
5.4
4.8
17.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
00
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.08
92.15
88.21
84.27
80.32
76.37
72.40
70.42
68.44
66.45
64.46
62.47
60.48
58.49
56.50
54.50
52.50
50.50
48.50
46.50
44.50
42.49
40.48
38.48
36.46
34.45
32.44
30.42
28.41
24.37
20.32
16.27
12.21
8.15
4.08
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
12.57
12.07
11.57
11.06
10.56
10.06
9.555
9.052
8.801
8.549
8.298
8.046
7.795
7.544
7.292
7.041
6.789
6.538
6.286
6.035
5.783
5.532
5.280
5.029
4.778
4.526
4.275
4.023
3.772
3.520
3.017
2.514
2.012
1.509
1.006
0.503
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
49.45
48.18
46.90
45.63
44.36
43.08
41.81
40.53
39.90
39.26
38.62
37.99
37.35
36.71
36.08
35.44
34.80
34.16
33.53
32.89
32.25
31.62
30.98
30.34
29.71
29.07
28.43
27.80
27.16
26.52
25.25
23.97
22.70
21.43
20.15
18.88
17.60
Specific
volume, / (m3·kg⫺1)
0.8396
0.8389
0.8382
0.8376
0.8369
0.8363
0.8356
0.8349
0.8346
0.8343
0.8340
0.8336
0.8333
0.8330
0.8326
0.8323
0.8320
0.8316
0.8313
0.8310
0.8307
0.8303
0.8300
0.8297
0.8293
0.8290
0.8287
0.8283
0.8280
0.8277
0.8270
0.8264
0.8257
0.8250
0.8244
0.8237
0.8230
Properties of humid air
1-35
18 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.08
92.15
88.22
84.28
80.33
76.38
72.42
70.44
68.45
66.47
64.48
62.49
60.50
58.51
56.51
54.52
52.52
50.52
48.52
46.52
44.51
42.51
40.50
38.49
36.48
34.47
32.45
30.44
28.42
24.38
20.33
16.28
12.22
8.15
4.08
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
12.98
12.46
11.94
11.43
10.91
10.39
9.868
9.348
9.088
8.829
8.569
8.309
8.050
7.790
7.530
7.271
7.011
6.751
6.492
6.232
5.972
5.713
5.453
5.193
4.934
4.674
4.414
4.155
3.895
3.635
3.116
2.597
2.077
1.558
1.039
0.519
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
51.01
49.69
48.38
47.06
45.74
44.43
43.11
41.80
41.14
40.48
39.82
39.16
38.51
37.85
37.19
36.53
35.87
35.22
34.56
33.90
33.24
32.58
31.93
31.27
30.61
29.95
29.29
28.64
27.98
27.32
26.00
24.69
23.37
22.06
20.74
19.42
18.11
Specific
volume, / (m3·kg⫺1)
0.8416
0.8409
0.8402
0.8395
0.8388
0.8381
0.8375
0.8368
0.8364
0.8361
0.8357
0.8354
0.8351
0.8347
0.8344
0.8340
0.8337
0.8334
0.8330
0.8327
0.8323
0.8320
0.8316
0.8313
0.8310
0.8306
0.8303
0.8299
0.8296
0.8293
0.8286
0.8279
0.8272
0.8265
0.8258
0.8252
0.8245
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.063
1.982
1.901
1.820
1.738
1.657
1.576
1.494
1.453
1.412
1.371
1.330
1.289
1.248
1.207
1.166
1.125
1.083
1.042
1.001
0.9595
0.9182
0.8768
0.8354
0.7940
0.7525
0.7110
0.6694
0.6278
0.5862
0.5029
0.4194
0.3358
0.2521
0.1682
0.0842
0.0000
18.0
17.4
16.7
16.0
15.3
14.6
13.8
13.0
12.5
12.1
11.7
11.2
10.7
10.3
9.8
9.2
8.7
8.2
7.6
7.0
6.4
5.7
5.1
4.4
3.7
2.9
2.1
1.3
0.4
⫺0.5
⫺2.5
⫺4.5
⫺7.1
⫺10.3
⫺14.8
⫺22.1
—
18.0
17.6
17.2
16.7
16.3
15.8
15.4
14.9
14.7
14.4
14.2
14.0
13.7
13.5
13.2
13.0
12.7
12.5
12.2
11.9
11.7
11.4
11.1
10.9
10.6
10.3
10.0
9.7
9.5
9.2
8.6
8.0
7.4
6.7
6.1
5.5
4.8
18.0
17.6
17.2
16.8
16.4
16.0
15.6
15.2
15.0
14.7
14.5
14.3
14.1
13.9
13.6
13.4
13.2
13.0
12.7
12.5
12.3
12.0
11.8
11.5
11.3
11.0
10.8
10.5
10.3
10.0
9.5
9.0
8.5
7.9
7.4
6.8
6.3
18.0
17.6
17.2
16.7
16.3
15.9
15.4
15.0
14.7
14.5
14.3
14.0
13.8
13.5
13.3
13.0
12.8
12.5
12.3
12.0
11.8
11.5
11.2
11.0
10.7
10.4
10.2
9.9
9.6
9.3
8.7
8.2
7.6
6.9
6.3
5.7
5.0
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.128
2.045
1.962
1.878
1.794
1.710
1.626
1.542
1.500
1.457
1.415
1.373
1.330
1.288
1.246
1.203
1.161
1.118
1.076
1.033
0.9904
0.9478
0.9051
0.8624
0.8196
0.7278
0.7340
0.6911
0.6482
0.6052
0.5192
0.4330
0.3477
0.2603
0.1747
0.0869
0.0000
18.5
17.9
17.2
16.5
15.8
15.1
14.3
13.5
13.0
12.6
12.1
11.7
11.2
10.7
10.2
9.7
9.2
8.6
8.0
7.5
6.8
6.2
5.5
4.8
4.1
3.4
2.6
1.7
0.8
⫺0.1
⫺2.0
⫺4.1
⫺6.7
⫺10.0
⫺14.5
⫺21.8
—
18.5
18.1
17.6
17.2
16.8
16.3
15.8
15.4
15.1
14.9
14.6
14.4
14.2
13.9
13.7
13.4
13.1
12.9
12.6
12.3
12.1
11.8
11.5
11.3
11.0
10.7
10.4
10.1
9.8
9.5
8.9
8.3
7.7
7.1
6.4
5.7
5.0
18.5
18.1
17.7
17.3
16.9
16.5
16.1
15.6
15.4
15.2
15.0
14.7
14.5
14.3
14.1
13.8
13.6
13.4
13.1
12.9
12.7
12.4
12.2
11.9
11.7
11.4
11.2
10.9
10.7
10.4
9.9
9.3
8.8
8.2
7.7
7.1
6.5
18.5
18.1
17.7
17.2
16.8
16.3
15.9
15.4
15.2
14.9
14.7
14.5
14.2
14.0
13.7
13.5
13.2
13.0
12.7
12.4
12.2
11.9
11.6
11.4
11.1
10.8
10.5
10.2
10.0
9.7
9.1
8.5
7.9
7.3
6.6
6.0
5.3
18.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.08
92.16
88.22
84.29
80.34
76.39
72.43
70.45
68.47
66.48
64.49
62.50
60.51
58.52
56.53
54.53
52.54
50.54
48.54
46.53
44.53
42.52
40.52
38.51
36.50
34.48
32.47
30.45
28.43
24.39
20.34
16.29
12.23
8.16
4.08
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
13.41
12.87
12.33
11.80
11.26
10.73
10.19
9.653
9.384
9.116
8.848
8.580
8.312
8.044
7.776
7.508
7.240
6.971
6.703
6.435
6.167
5.899
5.631
5.363
5.094
4.826
4.558
4.290
4.022
3.754
3.218
2.681
2.145
1.609
1.072
0.536
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
52.59
51.24
49.88
48.52
47.16
45.80
44.44
43.08
42.40
41.72
41.04
40.36
39.68
39.00
38.32
37.64
36.96
36.28
35.60
34.92
34.24
33.56
32.88
32.20
31.52
30.84
30.16
29.49
28.81
28.13
26.77
25.41
24.05
22.69
21.33
19.97
18.61
Specific
volume, / (m3·kg⫺1)
0.8436
0.8429
0.8421
0.8414
0.8407
0.8400
0.8393
0.8386
0.8383
0.8379
0.8376
0.8372
0.8368
0.8365
0.8361
0.8358
0.8354
0.8351
0.8347
0.8344
0.8340
0.8337
0.8333
0.8330
0.8326
0.8323
0.8319
0.8315
0.8312
0.8308
0.8301
0.8294
0.8287
0.8280
0.8273
0.8266
0.8259
1-36
Reference data
19 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.08
92.16
88.23
84.30
80.35
76.40
72.44
70.46
68.48
66.50
64.51
62.52
60.53
58.54
56.55
54.55
52.55
50.55
48.55
46.55
44.55
42.54
40.53
38.52
36.51
34.50
32.48
30.47
28.45
24.41
20.36
16.30
12.24
8.16
4.09
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
13.84
13.29
12.74
12.18
11.63
11.07
10.52
9.966
9.689
9.412
9.136
8.859
8.582
8.305
8.028
7.751
7.475
7.198
6.921
6.644
6.367
6.090
5.814
5.537
5.260
4.983
4.706
4.429
4.153
3.876
3.322
2.768
2.215
1.661
1.107
0.554
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
54.21
52.81
51.41
50.00
48.60
47.19
45.79
44.39
43.68
42.98
42.28
41.58
40.88
40.17
39.47
38.77
38.07
37.37
36.66
35.96
35.26
34.56
33.86
33.15
32.45
31.75
31.05
30.35
29.64
28.94
27.54
26.13
24.73
23.33
21.92
20.52
19.11
Specific
volume, / (m3·kg⫺1)
0.8456
0.8449
0.8441
0.8434
0.8427
0.8419
0.8412
0.8405
0.8401
0.8397
0.8394
0.8390
0.8386
0.8383
0.8379
0.8375
0.8372
0.8368
0.8365
0.8361
0.8357
0.8354
0.8350
0.8346
0.8343
0.8339
0.8335
0.8332
0.8328
0.8324
0.8317
0.8310
0.8302
0.8295
0.8288
0.8280
0.8273
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.196
2.110
2.024
1.938
1.851
1.765
1.678
1.591
1.547
1.504
1.460
1.417
1.373
1.329
1.286
1.242
1.198
1.154
1.110
1.066
1.022
0.9782
0.9342
0.8902
0.8460
0.8018
0.7576
0.7134
0.6691
0.6248
0.5360
0.4470
0.3580
0.2687
0.1792
0.0897
0.0000
19.0
18.4
17.7
17.0
16.3
15.5
14.8
13.9
13.5
13.1
12.6
12.2
11.7
11.2
10.7
10.2
9.6
9.1
8.5
7.9
7.3
6.7
6.0
5.3
4.6
3.8
3.0
2.2
1.3
0.3
⫺1.6
⫺3.7
⫺6.3
⫺9.6
⫺14.1
⫺21.5
—
19.0
18.6
18.1
17.7
17.2
16.8
16.3
15.8
15.6
15.3
15.1
14.8
14.6
14.3
14.1
13.8
13.6
13.3
13.0
12.8
12.5
12.2
11.9
11.6
11.4
11.1
10.8
10.5
10.2
9.9
9.3
8.7
8.0
7.4
6.7
6.0
5.3
19.0
18.6
18.2
17.8
17.4
17.0
16.5
16.1
15.9
15.6
15.4
15.2
15.0
14.7
14.5
14.3
14.0
13.8
13.5
13.3
13.1
12.8
12.6
12.3
12.1
11.8
11.6
11.3
11.0
10.8
10.2
9.7
9.1
8.6
8.0
7.4
6.8
19.0
18.6
18.1
17.7
17.3
16.8
16.3
15.9
15.6
15.4
15.1
14.9
14.7
14.4
14.1
13.9
13.6
13.4
13.1
12.8
12.6
12.3
12.0
11.8
11.5
11.2
10.9
10.6
10.3
10.0
9.4
8.8
8.2
7.6
6.9
6.2
5.6
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.266
2.177
2.088
1.999
1.910
1.821
1.731
1.642
1.597
1.552
1.507
1.462
1.417
1.372
1.327
1.282
1.236
1.191
1.146
1.100
1.055
1.010
0.9642
0.9187
0.8732
0.8276
0.7820
0.7363
0.6906
0.6448
0.5532
0.4614
0.3695
0.2774
0.1851
0.0926
0.0000
19.5
18.9
18.2
17.5
16.8
16.0
15.2
14.4
14.0
13.6
13.1
12.6
12.2
11.7
11.2
10.6
10.1
9.6
9.0
8.4
7.8
7.1
6.5
5.8
5.0
4.3
3.4
2.6
1.7
0.7
⫺1.2
⫺3.4
⫺6.0
⫺9.3
⫺13.8
⫺21.2
—
19.5
19.1
18.6
18.2
17.7
17.3
16.8
16.3
16.0
15.8
15.5
15.3
15.0
14.8
14.5
14.3
14.0
13.7
13.4
13.2
12.9
12.6
12.3
12.0
11.7
11.5
11.2
10.9
10.6
10.2
9.6
9.0
8.3
7.7
7.0
6.3
5.6
19.5
19.1
18.7
18.3
17.9
17.4
17.0
16.5
16.3
16.1
15.9
15.6
15.4
15.2
14.9
14.7
14.5
14.2
14.0
13.7
13.5
13.2
13.0
12.7
12.5
12.2
11.9
11.7
11.4
11.1
10.6
10.0
9.5
8.9
8.3
7.7
7.1
19.5
19.1
18.6
18.2
17.7
17.3
16.8
16.3
16.1
15.8
15.6
15.3
15.1
14.8
14.6
14.3
14.1
13.8
13.5
13.3
13.0
12.7
12.4
12.1
11.9
11.6
11.3
11.0
10.7
10.4
9.8
9.2
8.5
7.9
7.2
6.5
5.8
19.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.09
92.17
88.24
84.30
80.36
76.41
72.46
70.48
68.50
66.51
64.53
62.54
60.55
58.56
56.56
54.57
52.57
50.57
48.57
46.57
44.56
42.56
40.55
38.54
36.53
34.52
32.50
30.48
28.46
24.42
20.37
16.31
12.24
8.17
4.09
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
14.29
13.72
13.15
12.58
12.00
11.43
10.86
10.29
10.00
9.717
9.431
9.146
8.860
8.574
8.288
8.002
7.716
7.431
7.145
6.859
6.573
6.288
6.002
5.716
5.430
5.144
4.859
4.573
4.287
4.001
3.430
2.858
2.286
1.715
1.143
0.572
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
55.87
54.42
52.97
51.52
50.07
48.62
47.17
45.72
44.99
44.27
43.54
42.82
42.09
41.37
40.64
39.92
39.19
38.47
37.74
37.02
36.29
35.57
34.84
34.12
33.39
32.67
31.94
31.22
30.49
29.77
28.32
26.87
25.42
23.97
22.52
21.07
19.62
Specific
volume, / (m3·kg⫺1)
0.8476
0.8469
0.8461
0.8454
0.8446
0.8438
0.8431
0.8423
0.8420
0.8416
0.8412
0.8408
0.8405
0.8401
0.8397
0.8393
0.8389
0.8386
0.8382
0.8378
0.8374
0.8370
0.8367
0.8363
0.8359
0.8355
0.8352
0.8348
0.8344
0.8340
0.8333
0.8325
0.8318
0.8310
0.8302
0.8295
0.8287
Properties of humid air
1-37
20 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.09
92.17
88.25
84.31
80.37
76.43
72.47
70.49
68.51
66.53
64.54
62.55
60.56
58.57
56.58
54.59
52.59
50.59
48.59
46.59
44.58
42.58
40.57
38.56
36.55
34.53
32.52
30.50
28.48
24.43
20.38
16.32
12.25
8.17
4.09
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
14.75
14.16
13.57
12.98
12.39
11.80
11.21
10.62
10.33
10.03
9.736
9.441
9.146
8.851
8.556
8.260
7.966
7.670
7.376
7.080
6.785
6.490
6.195
5.900
5.605
5.310
5.015
4.720
4.425
4.130
3.540
2.950
2.360
1.770
1.180
0.590
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
57.55
56.05
54.56
53.06
51.56
50.06
48.57
47.07
46.32
45.57
44.82
44.08
43.33
42.58
41.83
41.08
40.33
39.58
38.84
38.09
37.34
36.59
35.84
35.09
34.34
33.60
32.85
32.10
31.35
30.60
29.10
27.61
26.11
24.61
23.11
21.62
20.11
Specific
volume, / (m3·kg⫺1)
0.8497
0.8489
0.8481
0.8473
0.8466
0.8458
0.8450
0.8442
0.8438
0.8434
0.8431
0.8427
0.8423
0.8419
0.8415
0.8411
0.8407
0.8403
0.8399
0.8395
0.8391
0.8388
0.8384
0.8380
0.8376
0.8372
0.8368
0.8364
0.8360
0.8356
0.8348
0.8341
0.8333
0.8325
0.8317
0.8309
0.8301
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.337
2.246
2.154
2.062
1.970
1.878
1.786
1.694
1.647
1.601
1.555
1.508
1.462
1.415
1.369
1.322
1.276
1.229
1.182
1.136
1.089
1.042
0.9945
0.9480
0.9011
0.8541
0.8070
0.7600
0.7127
0.6656
0.5710
0.4763
0.3814
0.2863
0.1910
0.0956
0.0000
20.0
19.4
18.7
18.0
17.3
16.5
15.7
14.9
14.5
14.0
13.6
13.1
12.6
12.1
11.6
11.1
10.6
10.0
9.4
8.8
8.2
7.6
6.9
6.2
5.5
4.7
3.9
3.0
2.1
1.2
⫺0.8
⫺3.0
⫺5.6
⫺8.9
⫺13.4
⫺20.8
—
20.0
19.6
19.1
18.7
18.2
17.7
17.2
16.7
16.5
16.2
16.0
15.7
15.5
15.2
14.9
14.7
14.4
14.1
13.9
13.6
13.3
13.0
12.7
12.4
12.1
11.8
11.5
11.2
10.9
10.6
10.0
9.3
8.6
8.0
7.3
6.5
5.8
20.0
19.6
19.2
18.8
18.3
17.9
17.5
17.0
16.8
16.5
16.3
16.1
15.8
15.6
15.4
15.1
14.9
14.6
14.4
14.1
13.9
13.6
13.4
13.1
12.8
12.6
12.3
12.0
11.8
11.5
10.9
10.4
9.8
9.2
8.6
8.0
7.3
20.0
19.6
19.1
18.7
18.2
17.7
17.3
16.8
16.5
16.3
16.0
15.8
15.5
15.3
15.0
14.7
14.5
14.2
13.9
13.7
13.4
13.1
12.8
12.5
12.2
12.0
11.7
11.4
11.1
10.7
10.1
9.5
8.8
8.2
7.5
6.8
6.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.410
2.316
2.222
2.127
2.032
1.938
1.842
1.747
1.699
1.652
1.604
1.556
1.508
1.460
1.412
1.364
1.316
1.268
1.220
1.172
1.123
1.075
1.027
0.9782
0.9298
0.8813
0.8327
0.7841
0.7355
0.6868
0.5892
0.4915
0.3936
0.2955
0.1972
0.0986
0.0000
20.5
19.9
19.2
18.5
17.8
17.0
16.2
15.4
15.0
14.5
14.1
13.6
13.1
12.6
12.1
11.6
11.0
10.5
9.9
9.3
8.7
8.0
7.4
6.7
5.9
5.2
4.3
3.5
2.6
1.6
⫺0.4
⫺2.6
⫺5.2
⫺8.5
⫺13.1
⫺20.5
—
20.5
20.1
19.6
19.1
18.7
18.2
17.7
17.2
17.0
16.7
16.4
16.2
15.9
15.6
15.4
15.1
14.8
14.6
14.3
14.0
13.7
13.4
13.1
12.8
12.5
12.2
11.9
11.6
11.3
11.0
10.3
9.6
9.0
8.3
7.5
6.8
6.1
20.5
20.1
19.7
19.2
18.8
18.4
17.9
17.5
17.2
17.0
16.8
16.5
16.3
16.0
15.8
15.5
15.3
15.0
14.8
14.5
14.3
14.0
13.8
13.5
13.2
13.0
12.7
12.4
12.1
11.8
11.3
10.7
10.1
9.5
8.9
8.2
7.6
20.5
20.1
19.6
19.2
18.7
18.2
17.7
17.2
17.0
16.7
16.5
16.2
16.0
15.7
15.4
15.2
14.9
14.6
14.4
14.1
13.8
13.5
13.2
12.9
12.6
12.3
12.0
11.7
11.4
11.1
10.5
9.8
9.2
8.5
7.8
7.1
6.3
20.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.09
92.18
88.25
84.32
80.39
76.44
72.49
70.51
68.53
66.54
64.56
62.57
60.58
58.59
56.60
54.60
52.61
50.61
48.61
46.61
44.60
42.59
40.59
38.58
36.56
34.55
32.53
30.51
28.49
24.45
20.39
16.33
12.26
8.18
4.09
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
15.22
14.62
14.01
13.49
12.79
12.18
11.57
10.96
10.66
10.35
10.05
9.744
9.440
9.135
8.831
8.526
8.222
7.917
7.613
7.308
7.004
6.699
6.395
6.090
5.786
5.481
5.177
4.872
4.568
4.263
3.654
3.045
2.436
1.827
1.218
0.609
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
59.27
57.73
56.18
54.63
53.09
51.54
50.00
48.45
47.68
46.90
46.13
45.36
44.59
43.81
43.04
42.27
41.49
40.72
39.95
39.18
38.40
37.63
36.86
36.08
35.31
34.54
33.76
32.99
32.22
31.44
29.90
28.35
26.81
25.26
23.71
22.17
20.62
Specific
volume, / (m3·kg⫺1)
0.8518
0.8510
0.8502
0.8493
0.8485
0.8477
0.8469
0.8461
0.8457
0.8453
0.8449
0.8445
0.8441
0.8437
0.8433
0.8429
0.8425
0.8421
0.8417
0.8413
0.8409
0.8405
0.8401
0.8397
0.8393
0.8388
0.8384
0.8380
0.8376
0.8372
0.8364
0.8356
0.8348
0.8340
0.8332
0.8324
0.8316
1-38
Reference data
21 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.09
92.18
88.26
84.33
80.40
76.45
72.50
70.52
68.54
66.56
64.58
62.59
60.60
58.61
56.62
54.62
52.63
50.63
48.63
46.62
44.62
42.61
40.60
38.59
36.58
34.57
32.55
30.53
28.51
24.46
20.40
16.34
12.27
8.19
4.10
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
15.71
15.09
14.46
13.83
13.20
12.57
11.94
11.31
11.00
10.69
10.37
10.06
9.742
9.428
9.114
8.800
8.485
8.171
7.857
7.542
7.228
6.914
6.600
6.285
5.971
5.657
5.343
5.028
4.714
4.400
3.771
3.143
2.514
1.886
1.257
0.628
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
61.03
59.43
57.84
56.24
54.64
53.05
51.45
49.86
49.06
48.26
47.46
46.66
45.87
45.07
44.27
43.47
42.67
41.88
41.08
40.28
39.48
38.68
37.89
37.09
36.29
35.49
34.69
33.89
33.10
32.30
30.70
29.11
27.51
25.91
24.32
22.72
21.13
Specific
volume, / (m3·kg⫺1)
0.8539
0.8530
0.8522
0.8514
0.8505
0.8497
0.8489
0.8480
0.8476
0.8472
0.8468
0.8464
0.8459
0.8455
0.8451
0.8447
0.8443
0.8439
0.8434
0.8430
0.8426
0.8422
0.8418
0.8413
0.8409
0.8405
0.8401
0.8397
0.8393
0.8388
0.8380
0.8372
0.8363
0.8355
0.8347
0.8338
0.8330
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.486
2.389
2.291
2.194
2.096
1.998
1.900
1.802
1.753
1.704
1.654
1.605
1.556
1.506
1.457
1.407
1.358
1.308
1.258
1.209
1.159
1.109
1.059
1.009
0.9593
0.9093
0.8592
0.8091
0.7589
0.7087
0.6080
0.5072
0.4062
0.3049
0.2035
0.1018
0.0000
21.0
20.4
19.7
19.0
18.3
17.5
16.7
15.9
15.4
15.0
14.5
14.1
13.6
13.1
12.6
12.1
11.5
11.0
10.4
9.8
9.1
8.5
7.8
7.1
6.4
5.6
4.8
3.9
3.0
2.1
⫺0.1
⫺2.2
⫺4.9
⫺8.2
⫺12.7
⫺20.2
—
21.0
20.6
20.1
19.6
19.2
18.7
18.2
17.7
17.4
17.1
16.9
16.6
16.4
16.1
15.8
15.5
15.3
15.0
14.7
14.4
14.1
13.8
13.5
13.2
12.9
12.6
12.3
12.0
11.6
11.3
10.7
10.0
9.3
8.6
7.8
7.1
6.3
21.0
20.6
20.2
19.7
19.3
18.8
18.4
17.9
17.7
17.4
17.2
17.0
16.7
16.5
16.2
16.0
15.7
15.5
15.2
14.9
14.7
14.4
14.2
13.9
13.6
13.3
13.1
12.8
12.5
12.2
11.6
11.0
10.4
9.8
9.2
8.5
7.9
21.0
20.6
20.1
19.6
19.2
18.7
18.2
17.7
17.5
17.2
16.9
16.7
16.4
16.1
15.9
15.6
15.3
15.0
14.8
14.5
14.2
13.9
13.6
13.3
13.0
12.7
12.4
12.1
11.8
11.5
10.8
10.1
9.5
8.8
8.1
7.3
6.6
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.563
2.463
2.363
2.262
2.162
2.061
1.960
1.859
1.808
1.757
1.706
1.656
1.605
1.554
1.503
1.452
1.401
1.349
1.298
1.247
1.196
1.144
1.093
1.041
0.9897
0.9381
0.8864
0.8347
0.7829
0.7311
0.6273
0.5233
0.4191
0.3146
0.2100
0.1051
0.0000
21.5
20.9
20.2
19.5
18.7
18.0
17.2
16.4
15.9
15.5
15.0
14.6
14.1
13.6
13.1
12.5
12.0
11.4
10.8
10.2
9.6
9.0
8.3
7.6
6.8
6.1
5.2
4.4
3.5
2.5
0.4
⫺1.9
⫺4.5
⫺7.8
⫺12.4
⫺19.8
—
21.5
21.0
20.6
20.1
19.6
19.1
18.6
18.1
17.9
17.6
17.3
17.1
16.8
16.5
16.2
16.0
15.7
15.4
15.1
14.8
14.5
14.2
13.9
13.6
13.3
13.0
12.7
12.3
12.0
11.7
11.0
10.3
9.6
8.9
8.1
7.3
6.6
21.5
21.1
20.6
20.2
19.8
19.3
18.8
18.4
18.1
17.9
17.7
17.4
17.2
16.9
16.7
16.4
16.1
15.9
15.6
15.4
15.1
14.8
14.5
14.3
14.0
13.7
13.4
13.1
12.9
12.6
12.0
11.4
10.7
10.1
9.5
8.8
8.1
21.5
21.1
20.6
20.1
19.6
19.2
18.7
18.2
17.9
17.6
17.4
17.1
16.9
16.6
16.3
16.0
15.8
15.5
15.2
14.9
14.6
14.3
14.0
13.7
13.4
13.1
12.8
12.5
12.1
11.8
11.2
10.5
9.8
9.1
8.3
7.6
6.8
21.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.10
92.19
88.27
84.34
80.41
76.47
72.52
70.54
68.56
66.58
64.59
62.61
60.62
58.63
56.64
54.64
52.65
50.65
48.65
46.64
44.64
42.63
40.62
38.61
36.60
34.58
32.57
30.55
28.53
24.48
20.42
16.35
12.28
8.19
4.10
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
16.22
15.57
14.92
14.27
13.62
12.97
12.32
11.68
11.35
11.03
10.70
10.38
10.05
9.730
9.405
9.081
8.756
8.432
8.108
7.784
7.459
7.135
6.811
6.486
6.162
5.838
5.513
5.189
4.865
4.540
3.892
3.243
2.594
1.946
1.297
0.648
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
62.82
61.17
59.53
57.88
56.23
54.58
52.94
51.29
50.46
49.64
48.82
47.99
47.17
46.34
45.52
44.70
43.87
43.05
42.23
41.40
40.58
39.75
38.93
38.11
37.28
36.46
35.64
34.81
33.99
33.16
31.52
29.87
28.22
26.57
24.92
23.28
21.63
Specific
volume, / (m3·kg⫺1)
0.8560
0.8551
0.8543
0.8534
0.8525
0.8517
0.8508
0.8500
0.8495
0.8491
0.8487
0.8482
0.8478
0.8474
0.8469
0.8465
0.8461
0.8456
0.8452
0.8448
0.8443
0.8439
0.8435
0.8431
0.8426
0.8422
0.8418
0.8413
0.8409
0.8405
0.8396
0.8387
0.8379
0.8370
0.8361
0.8353
0.8344
Properties of humid air
1-39
22 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.10
92.19
88.28
84.36
80.42
76.48
72.53
70.56
68.58
66.60
64.61
62.63
60.64
58.65
56.66
54.66
52.67
50.67
48.67
46.66
44.66
42.65
40.64
38.63
36.62
34.60
32.58
30.56
28.54
24.49
20.43
16.36
12.28
8.20
4.10
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
16.73
16.06
15.39
14.72
14.06
13.39
12.72
12.05
11.71
11.38
11.04
10.71
10.37
10.04
9.705
9.370
9.036
8.701
8.366
8.032
7.697
7.362
7.028
6.693
6.358
6.024
5.689
5.354
5.020
4.685
4.016
3.346
2.677
2.008
1.339
0.669
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
64.65
62.95
61.25
59.55
57.85
56.15
54.45
52.75
51.90
51.05
50.20
49.35
48.50
47.64
46.79
45.94
45.09
44.24
43.39
42.54
41.69
40.84
39.99
39.14
38.29
37.44
36.59
35.74
34.89
34.04
32.34
30.64
28.94
27.24
25.53
23.83
22.13
Specific
volume, / (m3·kg⫺1)
0.8581
0.8572
0.8564
0.8555
0.8546
0.8537
0.8528
0.8519
0.8515
0.8510
0.8506
0.8501
0.8497
0.8492
0.8488
0.8483
0.8479
0.8474
0.8470
0.8465
0.8461
0.8457
0.8452
0.8448
0.8443
0.8439
0.8434
0.8430
0.8425
0.8421
0.8412
0.8403
0.8394
0.8385
0.8376
0.8367
0.8358
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.643
2.540
2.436
2.333
2.229
2.125
2.021
1.917
1.865
1.812
1.760
1.707
1.655
1.602
1.550
1.497
1.445
1.392
1.339
1.286
1.233
1.180
1.127
1.074
1.021
0.9677
0.9144
0.8611
0.8077
0.7542
0.6472
0.5399
0.4324
0.3246
0.2166
0.1084
0.0000
22.0
21.3
20.7
20.0
19.2
18.5
17.7
16.8
16.4
16.0
15.5
15.0
14.5
14.0
13.5
13.0
12.5
11.9
11.3
10.7
10.1
9.4
8.7
8.0
7.3
6.5
5.7
4.8
3.9
2.9
0.8
⫺1.5
⫺4.1
⫺7.5
⫺12.0
⫺19.5
—
22.0
21.5
21.1
20.6
20.1
19.6
19.1
18.6
18.3
18.1
17.8
17.5
17.2
17.0
16.7
16.4
16.1
15.8
15.5
15.2
14.9
14.6
14.3
14.0
13.7
13.4
13.0
12.7
12.4
12.0
11.3
10.6
9.9
9.2
8.4
7.6
6.8
22.0
21.6
21.1
20.7
20.2
19.8
19.3
18.8
18.6
18.3
18.1
17.9
17.6
17.3
17.1
16.8
16.6
16.3
16.0
15.8
15.5
15.2
14.9
14.7
14.4
14.1
13.8
13.5
13.2
12.9
12.3
11.7
11.1
10.4
9.8
9.1
8.4
22.0
21.5
21.1
20.6
20.1
19.6
19.1
18.6
18.4
18.1
17.8
17.6
17.3
17.0
16.7
16.5
16.2
15.9
15.6
15.3
15.0
14.7
14.4
14.1
13.8
13.5
13.2
12.8
12.5
12.2
11.5
10.8
10.1
9.4
8.6
7.9
7.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.724
2.618
2.512
2.405
2.298
2.191
2.084
1.976
1.923
1.869
1.815
1.761
1.707
1.653
1.598
1.544
1.490
1.435
1.381
1.326
1.272
1.217
1.163
1.108
1.053
0.9981
0.9432
0.8882
0.8331
0.7780
0.6676
0.5570
0.4461
0.3349
0.2235
0.1119
0.0000
22.5
21.8
21.2
20.5
19.7
19.0
18.2
17.3
16.9
16.4
16.0
15.5
15.0
14.5
14.0
13.5
12.9
12.4
11.8
11.2
10.5
9.9
9.2
8.5
7.7
7.0
6.1
5.3
4.3
3.4
1.2
⫺1.1
⫺3.8
⫺7.1
⫺11.7
⫺19.2
—
22.5
22.0
21.6
21.1
20.6
20.1
19.6
19.0
18.8
18.5
18.2
18.0
17.7
17.4
17.1
16.8
16.5
16.2
15.9
15.6
15.3
15.0
14.7
14.4
14.1
13.7
13.4
13.1
12.7
12.4
11.7
11.0
10.2
9.5
8.7
7.9
7.0
22.5
22.1
21.6
21.2
20.7
20.3
19.8
19.3
19.0
18.8
18.5
18.3
18.0
17.8
17.5
17.3
17.0
16.7
16.5
16.2
15.9
15.6
15.3
15.1
14.8
14.5
14.2
13.9
13.6
13.3
12.7
12.0
11.4
10.7
10.1
9.4
8.7
22.5
22.0
21.6
21.1
20.6
20.1
19.6
19.1
18.8
18.6
18.3
18.0
17.7
17.5
17.2
16.9
16.6
16.3
16.0
15.7
15.4
15.1
14.8
14.5
14.2
13.8
13.5
13.2
12.9
12.5
11.8
11.1
10.4
9.7
8.9
8.1
7.3
22.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.10
92.20
88.29
84.37
80.44
76.50
72.55
70.58
68.60
66.62
64.63
62.65
60.66
58.67
56.68
54.68
52.69
50.69
48.69
46.69
44.68
42.67
40.66
38.65
36.64
34.62
32.60
30.58
28.56
24.51
20.44
16.37
12.29
8.20
4.11
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
17.26
16.57
15.88
15.19
14.50
13.81
13.12
12.43
12.08
11.74
11.39
11.05
10.70
10.36
10.01
9.668
9.322
8.977
8.632
8.287
7.941
7.596
7.251
6.906
6.560
6.215
5.870
5.524
5.179
4.834
4.143
3.453
2.762
2.072
1.381
0.690
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
66.52
64.77
63.01
61.26
59.50
57.75
55.99
54.23
53.36
52.48
51.60
50.72
49.85
48.97
48.09
47.21
46.33
45.46
44.58
43.70
42.82
41.95
41.07
40.19
39.31
38.43
37.56
36.68
35.80
34.92
33.17
31.41
29.66
27.90
26.15
24.39
22.64
Specific
volume, / (m3·kg⫺1)
0.8603
0.8594
0.8585
0.8575
0.8566
0.8557
0.8548
0.8539
0.8534
0.8529
0.8525
0.8520
0.8516
0.8511
0.8506
0.8502
0.8497
0.8492
0.8488
0.8483
0.8479
0.8474
0.8469
0.8465
0.8460
0.8456
0.8451
0.8446
0.8442
0.8437
0.8428
0.8419
0.8409
0.8400
0.8391
0.8382
0.8372
1-40
Reference data
23 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.11
92.21
88.30
84.38
80.45
76.51
72.57
70.59
68.61
66.63
64.65
62.67
60.68
58.69
56.70
54.70
52.71
50.71
48.71
46.71
44.70
42.69
40.68
38.67
36.66
34.64
32.62
30.60
28.58
24.52
20.46
16.39
12.30
8.21
4.11
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
17.81
17.10
16.39
15.67
14.96
14.25
13.54
12.82
12.47
12.11
11.76
11.40
11.04
10.69
10.33
9.974
9.618
9.262
8.905
8.549
8.193
7.837
7.480
7.124
6.768
6.412
6.056
5.699
5.343
4.987
4.275
3.562
2.850
2.137
1.425
0.712
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
68.43
66.62
64.81
63.00
61.18
59.37
57.56
55.75
54.84
53.94
53.03
52.13
51.22
50.31
49.41
48.50
47.60
46.69
45.79
44.88
43.97
43.07
42.16
41.26
40.35
39.44
38.54
37.63
36.73
35.82
34.01
32.20
30.39
28.57
26.76
24.95
23.14
Specific
volume, / (m3·kg⫺1)
0.8625
0.8615
0.8606
0.8596
0.8587
0.8577
0.8568
0.8558
0.8554
0.8549
0.8544
0.8539
0.8535
0.8530
0.8525
0.8520
0.8515
0.8511
0.8506
0.8501
0.8496
0.8392
0.8487
0.8482
0.8477
0.8473
0.8468
0.8463
0.8458
0.8453
0.8444
0.8434
0.8425
0.8415
0.8406
0.8396
0.8387
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.808
2.699
2.589
2.479
2.369
2.259
2.149
2.038
1.982
1.927
1.871
1.815
1.760
1.704
1.648
1.592
1.536
1.480
1.424
1.368
1.312
1.255
1.199
1.142
1.086
1.029
0.9727
0.9160
0.8593
0.8024
0.6886
0.5745
0.4601
0.3455
0.2306
0.1154
0.0000
23.0
22.3
21.7
21.0
20.2
19.5
18.6
17.8
17.4
16.9
16.5
16.0
15.5
15.0
14.5
13.9
13.4
12.8
12.2
11.6
11.0
10.3
9.7
8.9
8.2
7.4
6.6
5.7
4.8
3.8
1.7
⫺0.7
⫺3.4
⫺6.8
⫺11.3
⫺18.9
—
23.0
22.5
22.1
21.6
21.1
20.6
20.0
19.5
19.2
19.0
18.7
18.4
18.1
17.8
17.5
17.2
17.0
16.7
16.3
16.0
15.7
15.4
15.1
14.8
14.4
14.1
13.8
13.4
13.1
12.7
12.0
11.3
10.5
9.8
9.0
8.1
7.3
23.0
22.6
22.1
21.7
21.2
20.7
20.2
19.7
19.5
19.2
19.0
18.7
18.5
18.2
18.0
17.7
17.4
17.1
16.9
16.6
16.3
16.0
15.7
15.4
15.2
14.9
14.6
14.3
13.9
13.6
13.0
12.4
11.7
11.0
10.3
9.6
8.9
23.0
22.5
22.1
21.6
21.1
20.6
20.1
19.5
19.3
19.0
18.7
18.5
18.2
17.9
17.6
17.3
17.0
16.7
16.4
16.1
15.8
15.5
15.2
14.9
14.6
14.2
13.9
13.6
13.2
12.9
12.2
11.5
10.7
10.0
9.2
8.4
7.6
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.894
2.782
2.669
2.556
2.442
2.329
2.215
2.101
2.044
1.986
1.929
1.872
1.814
1.757
1.699
1.642
1.584
1.526
1.468
1.410
1.352
1.294
1.236
1.178
1.120
1.062
1.003
0.9447
0.8862
0.8276
0.7102
0.5925
0.4746
0.3564
0.2379
0.1191
0.0000
23.5
22.8
22.2
21.5
20.7
19.9
19.1
18.3
17.9
17.4
16.9
16.5
16.0
15.5
15.0
14.4
13.9
13.3
12.7
12.1
11.5
10.8
10.1
9.4
8.6
7.9
7.0
6.2
5.2
4.3
2.1
⫺0.4
⫺3.0
⫺6.4
⫺11.0
⫺18.5
—
23.5
23.0
22.5
22.0
21.5
21.0
20.5
20.0
19.7
19.4
19.1
18.8
18.6
18.3
18.0
17.7
17.4
17.1
16.8
16.5
16.1
15.8
15.5
15.2
14.8
14.5
14.1
13.8
13.4
13.1
12.4
11.6
10.8
10.1
9.2
8.4
7.5
23.5
23.1
22.6
22.1
21.7
21.2
20.7
20.2
20.0
19.7
19.4
19.2
18.9
18.7
18.4
18.1
17.8
17.6
17.3
17.0
16.7
16.4
16.1
15.8
15.5
15.2
14.9
14.6
14.3
14.0
13.4
12.7
12.0
11.3
10.6
9.9
9.2
23.5
23.0
22.6
22.1
21.6
21.1
20.5
20.0
19.7
19.5
19.2
18.9
18.6
18.3
18.0
17.7
17.4
17.1
16.8
16.5
16.2
15.9
15.6
15.3
14.9
14.6
14.3
13.9
13.6
13.2
12.5
11.8
11.0
10.3
9.5
8.7
7.8
23.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.11
92.21
88.31
84.39
80.46
76.53
72.59
70.61
68.63
66.65
64.67
62.69
60.70
58.71
56.72
54.73
52.73
50.73
48.73
46.73
44.72
42.72
40.71
38.69
36.68
34.66
32.64
30.62
28.59
24.54
20.47
16.40
12.31
8.22
4.11
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
18.37
17.64
16.90
16.17
15.43
14.70
13.96
13.23
12.86
12.49
12.13
11.76
11.39
11.02
10.66
10.29
9.921
9.554
9.187
8.819
8.452
8.804
7.717
7.349
6.982
6.614
6.247
5.879
5.512
5.144
4.410
3.675
2.940
2.205
1.470
0.735
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
70.38
68.51
66.64
64.77
62.90
61.03
59.16
57.29
56.36
55.42
54.49
53.56
52.62
51.69
50.75
49.82
48.88
47.95
47.01
46.08
45.14
44.21
43.27
42.34
41.40
40.47
39.53
38.60
37.66
36.73
34.86
32.99
31.12
29.25
27.38
25.51
23.64
Specific
volume, / (m3·kg⫺1)
0.8467
0.8637
0.8627
0.8618
0.8608
0.8598
0.8588
0.8578
0.8573
0.8568
0.8563
0.8559
0.8554
0.8549
0.8544
0.8539
0.8534
0.8529
0.8524
0.8519
0.8514
0.8509
0.8504
0.8499
0.8495
0.8490
0.8485
0.8480
0.8475
0.8470
0.8460
0.8450
0.8440
0.8430
0.8421
0.8411
0.8401
Properties of humid air
1-41
24 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.11
92.22
88.31
84.40
80.48
76.55
72.60
70.63
68.65
66.67
64.69
62.71
60.72
58.73
56.74
54.75
52.75
50.75
48.75
46.75
44.75
42.74
40.73
38.71
36.70
34.68
32.66
30.64
28.61
24.56
20.49
16.41
12.32
8.22
4.12
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
18.95
18.19
17.44
16.68
15.92
15.16
14.40
13.64
13.27
12.89
12.51
12.13
11.75
11.37
10.99
10.61
10.23
9.855
9.476
9.097
8.718
8.339
7.960
7.580
7.202
6.822
6.444
6.064
5.685
5.306
4.548
3.790
3.032
2.274
1.516
0.758
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
72.37
70.44
68.52
66.59
64.66
62.73
60.80
58.87
57.90
56.94
55.98
55.01
54.05
53.08
52.12
51.15
50.19
49.22
48.26
47.29
46.33
45.37
44.40
43.44
42.47
41.51
40.54
39.58
38.61
37.65
35.72
33.79
31.86
29.93
28.00
26.07
24.14
Specific
volume, / (m3·kg⫺1)
0.8669
0.8659
0.8649
0.8639
0.8629
0.8619
0.8608
0.8598
0.8593
0.8588
0.8583
0.8578
0.8573
0.8568
0.8563
0.8558
0.8553
0.8547
0.8542
0.8537
0.8532
0.8527
0.8522
0.8517
0.8512
0.8507
0.8502
0.8497
0.8491
0.8486
0.8476
0.8466
0.8456
0.8446
0.8435
0.8425
0.8415
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
2.983
2.867
2.751
2.634
2.517
2.400
2.283
2.165
2.107
2.048
1.989
1.930
1.870
1.811
1.752
1.692
1.633
1.573
1.514
1.454
1.394
1.335
1.275
1.215
1.155
1.095
1.034
0.9741
0.9138
0.8534
0.7324
0.6111
0.4894
0.3675
0.2453
0.1228
0.0000
24.0
23.3
22.7
21.9
21.2
20.4
19.6
18.8
18.3
17.9
17.4
16.9
16.5
15.9
15.4
14.9
14.3
13.8
13.2
12.6
11.9
11.3
10.6
9.8
9.1
8.3
7.5
6.6
5.7
4.7
2.5
⫺0.0
⫺2.7
⫺6.0
⫺10.7
⫺18.2
—
24.0
23.5
23.0
22.5
22.0
21.5
21.0
20.4
20.1
19.9
19.6
19.3
19.0
18.7
18.4
18.1
17.8
17.5
17.2
16.9
16.5
16.2
15.9
15.6
15.2
14.9
14.5
14.2
13.8
13.4
12.7
11.9
11.2
10.4
9.5
8.7
7.8
24.0
23.6
23.1
22.6
22.2
21.7
21.2
20.7
20.4
20.2
19.9
19.6
19.4
19.1
18.8
18.5
18.3
18.0
17.7
17.4
17.1
16.8
16.5
16.2
15.9
15.6
15.3
15.0
14.7
14.4
13.7
13.0
12.3
11.6
10.9
10.2
9.4
24.0
23.5
23.0
22.5
22.0
21.5
21.0
20.5
20.2
19.9
19.6
19.3
19.1
18.8
18.5
18.2
17.9
17.6
17.3
16.9
16.6
16.3
16.0
15.7
15.3
15.0
14.6
14.3
13.9
13.6
12.9
12.1
11.4
10.6
9.8
8.9
8.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.073
2.954
2.834
2.714
2.594
2.474
2.353
2.232
2.171
2.111
2.050
1.989
1.928
1.867
1.806
1.745
1.658
1.622
1.561
1.499
1.439
1.376
1.314
1.252
1.190
1.129
1.067
1.004
0.9422
0.8800
0.7552
0.6301
0.5047
0.3790
0.2530
0.1267
0.0000
24.5
23.8
23.2
22.4
21.7
20.9
20.1
19.3
18.8
18.4
17.9
17.4
16.9
16.4
15.9
15.4
14.8
14.2
13.6
13.0
12.4
11.7
11.0
10.3
9.5
8.8
7.9
7.0
6.1
5.1
3.0
0.4
⫺2.3
⫺5.7
⫺10.3
⫺17.9
—
24.5
24.0
23.5
23.0
22.5
22.0
21.4
20.9
20.6
20.3
20.0
19.7
19.4
19.1
18.8
18.5
18.2
17.9
17.6
17.3
16.9
16.6
16.3
15.9
15.6
15.2
14.9
14.5
14.2
13.8
13.0
12.3
11.5
10.6
9.8
8.9
8.0
24.5
24.0
23.6
23.1
22.6
22.1
21.6
21.1
20.9
20.6
20.3
20.1
19.8
19.5
19.3
19.0
18.7
18.4
18.1
17.8
17.5
17.2
16.9
16.6
16.3
16.0
15.7
15.4
15.0
14.7
14.0
13.4
12.7
11.9
11.2
10.4
9.7
24.5
24.0
23.5
23.0
22.5
22.0
21.5
20.9
20.6
20.4
20.1
19.8
19.5
19.2
18.9
18.6
18.3
18.0
17.7
17.4
17.0
16.7
16.4
16.0
15.7
15.4
15.0
14.7
14.3
13.9
13.2
12.4
11.7
10.9
10.0
9.2
8.3
24.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.12
92.23
88.32
84.41
80.49
76.56
72.62
70.65
68.67
66.69
64.71
62.73
60.74
58.76
56.77
54.77
52.78
50.78
48.78
46.77
44.77
42.76
40.75
38.74
36.72
34.70
32.68
30.66
28.63
24.57
20.50
16.42
12.33
8.23
4.12
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
19.55
18.76
17.98
17.20
16.42
15.64
14.86
14.07
13.68
13.29
12.90
12.51
12.12
11.73
11.34
10.95
10.56
10.16
9.773
9.382
8.991
8.600
8.209
7.818
7.428
7.037
6.646
6.255
5.864
5.473
4.691
3.909
3.127
2.346
1.564
0.782
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
74.41
72.42
70.43
68.44
66.45
64.46
62.47
60.48
59.48
58.48
57.49
56.49
55.50
54.50
53.51
52.51
51.52
50.52
49.53
48.53
47.54
46.54
45.55
44.55
43.56
42.56
41.57
40.57
39.58
38.58
36.59
34.60
32.61
30.62
28.63
26.64
24.65
Specific
volume, / (m3·kg⫺1)
0.8692
0.8682
0.8671
0.8661
0.8650
0.8640
0.8629
0.8619
0.8613
0.8608
0.8603
0.8598
0.8592
0.8587
0.8582
0.8577
0.8571
0.8566
0.8561
0.8556
0.8550
0.8545
0.8540
0.8535
0.8529
0.8524
0.8519
0.8513
0.8508
0.8503
0.8492
0.8482
0.8471
0.8461
0.8450
0.8440
0.8429
1-42
Reference data
25 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.12
92.23
88.33
84.43
80.51
76.58
72.64
70.67
68.69
66.72
64.74
62.75
60.77
58.78
56.79
54.80
52.80
50.80
48.80
46.80
44.79
42.78
40.77
38.76
36.74
34.72
32.70
30.68
28.65
24.59
20.52
16.44
12.34
8.24
4.12
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
20.16
19.35
18.55
17.74
16.93
16.13
15.32
14.51
14.11
13.71
13.30
12.90
12.50
12.10
11.69
11.29
10.89
10.48
10.08
9.676
9.273
8.870
8.466
8.063
7.660
7.257
6.854
6.450
6.047
5.644
4.838
4.032
3.225
2.419
1.613
0.806
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
76.49
74.43
72.38
70.33
68.27
66.22
64.17
62.11
61.09
60.06
59.03
58.01
56.98
55.95
54.93
53.90
52.87
51.85
50.82
49.79
48.76
47.74
46.71
45.69
44.66
43.63
42.60
41.58
40.55
39.52
37.47
35.42
33.36
31.31
29.26
27.20
25.15
Specific
volume, / (m3·kg⫺1)
0.8715
0.8704
0.8693
0.8682
0.8672
0.8661
0.8650
0.8639
0.8634
0.8628
0.8623
0.8617
0.8612
0.8606
0.8601
0.8596
0.8590
0.8585
0.8579
0.8574
0.8568
0.8563
0.8558
0.8552
0.8547
0.8541
0.8536
0.8530
0.8525
0.8520
0.8509
0.8498
0.8487
0.8476
0.8465
0.8454
0.8443
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.166
3.044
2.921
2.797
2.673
2.549
2.425
2.300
2.238
2.175
2.113
2.050
1.987
1.924
1.861
1.798
1.735
1.672
1.609
1.545
1.482
1.418
1.355
1.291
1.227
1.163
1.100
1.036
0.9714
0.9072
0.7786
0.6497
0.5204
0.3908
0.2609
0.1306
0.0000
25.0
24.3
23.7
22.9
22.2
21.4
20.6
19.7
19.3
18.8
18.4
17.9
17.4
16.9
16.4
15.8
15.3
14.7
14.1
13.5
12.8
12.2
11.5
10.8
10.0
9.2
8.4
7.5
6.6
5.6
3.4
0.9
⫺1.9
⫺5.3
⫺10.0
⫺17.5
—
25.0
24.5
24.0
23.5
23.0
22.4
21.9
21.3
21.1
20.8
20.5
20.2
19.9
19.6
19.3
19.0
18.7
18.3
18.0
17.7
17.4
17.0
16.7
16.3
16.0
15.6
15.3
14.9
14.5
14.2
13.4
12.6
11.8
10.9
10.1
9.2
8.2
25.0
24.5
24.1
23.6
23.1
22.6
22.1
21.6
21.3
21.1
20.8
20.5
20.2
20.0
19.7
19.4
19.1
18.8
18.5
18.2
17.9
17.6
17.3
17.0
16.7
16.4
16.1
15.7
15.4
15.1
14.4
13.7
13.0
12.2
11.5
10.7
9.9
25.0
24.5
24.0
23.5
23.0
22.5
21.9
21.4
21.1
20.8
20.5
20.2
19.9
19.6
19.3
19.0
18.7
18.4
18.1
17.8
17.4
17.1
16.8
16.4
16.1
15.7
15.4
15.0
14.7
14.3
13.5
12.8
12.0
11.2
10.3
9.4
8.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.262
3.136
3.009
2.882
2.754
2.627
2.499
2.370
2.306
2.242
2.177
2.112
2.048
1.983
1.918
1.853
1.788
1.723
1.658
1.593
1.527
1.462
1.396
1.331
1.265
1.199
1.133
1.067
1.001
0.9353
0.8027
0.6698
0.5366
0.4030
0.2690
0.1347
0.0000
25.5
24.8
24.1
23.4
22.7
21.9
21.1
20.2
19.8
19.3
18.9
18.4
17.9
17.4
16.9
16.3
15.7
15.2
14.6
14.0
13.3
12.6
11.9
11.2
10.5
9.7
8.8
7.9
7.0
6.0
3.8
1.3
⫺1.6
⫺5.0
⫺9.6
⫺17.2
—
25.5
25.0
24.5
24.0
23.5
22.9
22.4
21.8
21.5
21.2
20.9
20.6
20.3
20.0
19.7
19.4
19.1
18.8
18.4
18.1
17.8
17.4
17.1
16.7
16.4
16.0
15.6
15.3
14.9
14.5
13.7
12.9
12.1
11.2
10.3
9.4
8.5
25.5
25.0
24.6
24.1
23.6
23.1
22.6
22.0
21.8
21.5
21.2
21.0
20.7
20.4
20.1
19.8
19.5
19.2
18.9
18.6
18.3
18.0
17.7
17.4
17.1
16.8
16.4
16.1
15.8
15.4
14.7
14.0
13.3
12.5
11.8
11.0
10.2
25.5
25.0
24.5
24.0
23.5
22.9
22.4
21.8
21.6
21.3
21.0
20.7
20.4
20.1
19.8
19.5
19.2
18.8
18.5
18.2
17.9
17.5
17.2
16.8
16.5
16.1
15.8
15.4
15.0
14.7
13.9
13.1
12.3
11.4
10.6
9.7
8.8
25.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.12
92.24
88.34
84.44
80.52
76.60
72.66
70.69
68.71
66.74
64.76
62.78
60.79
58.80
56.81
54.82
52.82
50.83
48.83
46.82
44.82
42.81
40.80
38.78
36.77
34.75
32.72
30.70
28.67
24.61
20.53
16.45
12.35
8.25
4.13
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
20.79
20.00
19.12
18.29
17.46
16.63
15.80
14.97
14.55
14.14
13.72
13.30
12.89
12.47
12.06
11.64
11.22
10.81
10.39
9.978
9.562
9.146
8.730
8.315
7.899
7.483
7.068
6.652
6.236
5.820
4.989
4.157
3.326
2.494
1.663
0.831
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
78.61
76.49
74.37
72.26
70.14
68.02
65.90
63.78
62.72
61.66
60.61
59.55
58.49
57.43
56.37
55.31
54.25
53.19
52.13
51.07
50.01
48.95
47.90
46.84
45.78
44.72
43.66
42.60
41.54
40.48
38.36
36.25
34.13
32.01
29.89
27.77
25.65
Specific
volume, / (m3·kg⫺1)
0.8738
0.8727
0.8716
0.8704
0.8693
0.8682
0.8671
0.8660
0.8654
0.8648
0.8643
0.8637
0.8632
0.8626
0.8620
0.8615
0.8609
0.8604
0.8598
0.8592
0.8587
0.8581
0.8576
0.8570
0.8564
0.8559
0.8553
0.8548
0.8542
0.8536
0.8525
0.8514
0.8503
0.8491
0.8480
0.8469
0.8458
Properties of humid air
1-43
26 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.13
92.25
88.35
84.45
80.54
76.62
72.68
70.71
68.74
66.76
64.78
62.80
60.81
58.83
56.84
54.85
52.85
50.85
48.85
46.85
44.84
42.83
40.82
38.81
36.79
34.77
32.75
30.72
28.69
24.63
20.55
16.46
12.36
8.25
4.13
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
21.43
20.58
19.72
18.86
18.00
17.15
16.29
15.43
15.00
14.58
14.15
13.72
13.29
12.86
12.43
12.00
11.57
11.15
10.72
10.29
9.860
9.431
9.002
8.574
8.145
7.716
7.288
6.859
6.430
6.002
5.144
4.287
3.429
2.572
1.715
0.857
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
80.78
78.60
76.41
74.23
72.04
69.86
67.67
65.49
64.39
63.30
62.21
61.12
60.02
58.93
57.84
56.75
55.65
54.56
53.47
52.38
51.28
50.19
49.10
48.01
46.91
45.82
44.73
43.64
42.54
41.45
39.27
37.08
34.90
32.71
30.53
28.34
26.16
Specific
volume, / (m3·kg⫺1)
0.8761
0.8750
0.8738
0.8727
0.8715
0.8704
0.8692
0.8680
0.8675
0.8669
0.8663
0.8657
0.8652
0.8646
0.8640
0.8634
0.8628
0.8623
0.8617
0.8611
0.8605
0.8599
0.8594
0.8588
0.8582
0.8576
0.8570
0.8565
0.8559
0.8553
0.8541
0.8530
0.8518
0.8507
0.8495
0.8483
0.8472
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.360
3.230
3.100
2.969
2.838
2.706
2.574
2.442
2.376
2.310
2.243
2.177
2.110
2.043
1.977
1.910
1.843
1.776
1.709
1.641
1.574
1.507
1.439
1.372
1.304
1.236
1.168
1.100
1.032
0.9641
0.8275
0.6905
0.5532
0.4155
0.2774
0.1389
0.0000
26.0
25.3
24.6
23.9
23.2
22.4
21.6
20.7
20.3
19.8
19.3
18.9
18.4
17.9
17.3
16.8
16.2
15.6
15.0
14.4
13.8
13.1
12.4
11.7
10.9
10.1
9.3
8.4
7.4
6.4
4.3
1.7
⫺1.2
⫺4.6
⫺9.3
⫺16.9
—
26.0
25.5
25.0
24.5
23.9
23.4
22.8
22.3
22.0
21.7
21.4
21.1
20.8
20.5
20.1
19.8
19.5
19.2
18.8
18.5
18.2
17.8
17.5
17.1
16.8
16.4
16.0
15.6
15.3
14.9
14.1
13.2
12.4
11.5
10.6
9.7
8.7
26.0
25.5
25.1
24.6
24.1
23.6
23.0
22.5
22.2
22.0
21.7
21.4
21.1
20.8
20.6
20.3
20.0
19.7
19.4
19.1
18.7
18.4
18.1
17.8
17.5
17.1
16.8
16.5
16.1
15.8
15.1
14.3
13.6
12.8
12.1
11.2
10.4
26.0
25.5
25.0
24.5
24.0
23.4
22.9
22.3
22.0
21.7
21.4
21.1
20.8
20.5
20.2
19.9
19.6
19.3
18.9
18.6
18.3
17.9
17.6
17.2
16.9
16.5
16.1
15.8
15.4
15.0
14.2
13.4
12.6
11.7
10.9
9.9
9.0
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.461
3.327
3.193
3.058
2.923
2.788
2.652
2.516
2.448
2.380
2.311
2.243
2.174
2.106
2.037
1.968
1.899
1.830
1.761
1.692
1.622
1.553
1.483
1.414
1.344
1.274
1.204
1.134
1.064
0.9937
0.8530
0.7118
0.5703
0.4283
0.2860
0.1432
0.0000
26.5
25.8
25.1
24.4
23.7
22.9
22.1
21.2
20.8
20.3
19.8
19.3
18.8
18.3
17.8
17.3
16.7
16.1
15.5
14.9
14.2
13.6
12.9
12.1
11.4
10.6
9.7
8.8
7.9
6.9
4.7
2.1
⫺0.8
⫺4.2
⫺8.9
⫺16.6
—
26.5
26.0
25.5
25.0
24.4
23.9
23.3
22.7
22.4
22.1
21.8
21.5
21.2
20.9
20.6
20.3
19.9
19.6
19.3
18.9
18.6
18.2
17.9
17.5
17.1
16.8
16.4
16.0
15.6
15.2
14.4
13.6
12.7
11.8
10.9
9.9
8.9
26.5
26.0
25.5
25.0
24.5
24.0
23.5
23.0
22.7
22.4
22.1
21.9
21.6
21.3
21.0
20.7
20.4
20.1
19.8
19.5
19.2
18.8
18.5
18.2
17.9
17.5
17.2
16.8
16.5
16.1
15.4
14.7
13.9
13.1
12.3
11.5
10.7
26.5
26.0
25.5
25.0
24.4
23.9
23.3
22.8
22.5
22.2
21.9
21.6
21.3
21.0
20.6
20.3
20.0
19.7
19.3
19.0
18.7
18.3
18.0
17.6
17.3
16.9
16.5
16.1
15.8
15.4
14.6
13.8
12.9
12.0
11.1
10.2
9.2
26.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.13
92.26
88.37
84.47
80.56
76.63
72.70
70.73
68.76
66.78
64.81
62.82
60.84
58.85
56.86
54.87
52.88
50.88
48.88
46.87
44.87
42.86
40.85
38.83
36.81
34.79
32.77
30.74
28.71
24.65
20.57
16.48
12.38
8.26
4.14
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
22.10
21.22
20.33
19.45
18.56
17.68
16.80
15.91
15.47
15.03
14.59
14.14
13.70
13.26
12.82
12.38
11.93
11.49
11.05
10.61
10.18
9.723
9.281
8.840
8.400
7.956
7.514
7.072
6.630
6.188
5.304
4.420
3.536
2.652
1.768
0.884
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
83.00
80.75
78.49
76.24
73.99
71.73
69.48
67.23
66.10
64.97
63.84
62.72
61.59
60.46
59.34
58.21
57.08
55.96
54.83
53.70
52.58
51.45
50.32
49.20
48.07
46.94
45.82
44.69
43.56
42.44
40.18
37.93
35.67
33.42
31.17
28.91
26.66
Specific
volume, / (m3·kg⫺1)
0.8785
0.8773
0.8761
0.8749
0.8737
0.8725
0.8713
0.8702
0.8696
0.8690
0.8684
0.8678
0.8672
0.8666
0.8660
0.8654
0.8648
0.8642
0.8636
0.8630
0.8624
0.8618
0.8612
0.8606
0.8600
0.8594
0.8588
0.8582
0.8576
0.8570
0.8558
0.8546
0.8534
0.8522
0.8510
0.8498
0.8486
1-44
Reference data
27 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.14
92.26
88.38
84.48
80.57
76.66
72.72
70.76
68.78
66.81
64.83
62.85
60.87
58.88
56.89
54.90
52.90
50.91
48.90
46.90
44.89
42.88
40.87
38.86
36.84
34.82
32.79
30.77
28.74
24.67
20.59
16.49
12.39
8.27
4.14
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
22.78
21.87
20.96
20.05
19.14
18.23
17.32
16.40
15.95
15.49
15.04
14.58
14.13
13.67
13.21
12.76
12.30
11.85
11.39
10.94
10.48
10.02
9.569
9.113
8.658
8.202
7.746
7.291
6.835
6.379
5.468
4.557
3.645
2.734
1.823
0.911
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
85.29
82.94
80.62
78.30
75.97
73.65
71.32
69.00
67.84
66.67
65.51
64.35
63.19
62.03
60.86
59.70
58.54
57.38
56.22
55.05
53.89
52.73
51.57
50.41
49.24
48.08
46.92
45.76
44.60
43.43
41.11
38.78
36.46
34.14
31.81
29.49
27.16
Specific
volume, / (m3·kg⫺1)
0.8809
0.8797
0.8784
0.8772
0.8760
0.8747
0.8735
0.8723
0.8717
0.8710
0.8704
0.8698
0.8692
0.8686
0.8680
0.8673
0.8667
0.8661
0.8655
0.8649
0.8642
0.8636
0.8630
0.8624
0.8618
0.8612
0.8605
0.8599
0.8593
0.8587
0.8574
0.8562
0.8550
0.8537
0.8525
0.8513
0.8500
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.564
3.426
3.288
3.150
3.011
2.872
2.732
2.592
2.522
2.452
2.381
2.311
2.240
2.169
2.099
2.028
1.957
1.886
1.814
1.743
1.672
1.600
1.528
1.459
1.385
1.313
1.241
1.169
1.097
1.024
0.8792
0.7337
0.5878
0.4415
0.2948
0.1476
0.0000
27.0
26.3
25.6
24.9
24.2
23.4
22.5
21.7
21.2
20.8
20.3
19.8
19.3
18.8
18.3
17.7
17.2
16.6
16.0
15.3
14.7
14.0
13.3
12.6
11.8
11.0
10.2
9.3
8.3
7.3
5.1
2.6
⫺0.5
⫺3.9
⫺8.6
⫺16.2
—
27.0
26.5
26.0
25.4
24.9
24.3
23.8
23.2
22.9
22.6
22.3
22.0
21.7
21.3
21.0
20.7
20.4
20.0
19.7
19.3
19.0
18.6
18.3
17.9
17.5
17.2
16.8
16.4
16.0
15.6
14.8
13.9
13.0
12.1
11.2
10.2
9.2
27.0
26.5
26.0
25.5
25.0
24.5
24.0
23.4
23.1
22.9
22.6
22.3
22.0
21.7
21.4
21.1
20.8
20.5
20.2
19.9
19.6
19.2
18.9
18.6
18.2
17.9
17.6
17.2
16.9
16.5
15.8
15.0
14.2
13.4
12.6
11.8
10.9
27.0
26.5
26.0
25.5
24.9
24.4
23.8
23.2
22.9
22.6
22.3
22.0
21.7
21.4
21.1
20.8
20.4
20.1
19.8
19.4
19.1
18.7
18.4
18.0
17.6
17.3
16.9
16.5
16.1
15.7
14.9
14.1
13.2
12.3
11.4
10.4
9.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.670
3.528
3.386
3.244
3.101
2.958
2.814
2.670
2.598
2.525
2.453
2.380
2.308
2.235
2.162
2.089
2.016
1.943
1.869
1.796
1.722
1.649
1.575
1.501
1.427
1.353
1.279
1.204
1.130
1.055
0.9060
0.7562
0.6059
0.4551
0.3039
0.1522
0.0000
27.5
26.8
26.1
25.4
24.7
23.9
23.0
22.2
21.7
21.3
20.8
20.3
19.8
19.3
18.7
18.2
17.6
17.0
16.4
15.8
15.2
14.5
13.8
13.0
12.3
11.5
10.6
9.7
8.8
7.8
5.6
3.0
⫺0.1
⫺3.5
⫺8.2
⫺15.9
—
27.5
27.0
26.5
25.9
25.4
24.8
24.2
23.7
23.3
23.0
22.7
22.4
22.1
21.8
21.5
21.1
20.8
20.4
20.1
19.7
19.4
19.0
18.7
18.3
17.9
17.5
17.1
16.7
16.3
15.9
15.1
14.2
13.3
12.4
11.4
10.4
9.4
27.5
27.0
26.5
26.0
25.5
25.0
24.4
23.9
23.6
23.3
23.0
22.7
22.5
22.2
21.9
21.5
21.2
20.9
20.6
20.3
20.0
19.6
19.3
19.0
18.6
18.3
17.9
17.6
17.2
16.8
16.1
15.3
14.5
13.7
12.9
12.0
11.1
27.5
27.0
26.5
25.9
25.4
24.8
24.3
23.7
23.4
23.1
22.8
22.5
22.2
21.8
21.5
21.2
20.9
20.5
20.2
19.8
19.5
19.1
18.8
18.4
18.0
17.6
17.3
16.9
16.5
16.1
15.3
14.4
13.5
12.6
11.7
10.7
9.7
27.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.14
92.27
88.39
84.50
80.59
76.68
72.75
70.78
68.81
66.83
64.86
62.88
60.89
58.91
56.92
54.93
52.93
50.93
48.93
46.93
44.92
42.91
40.90
38.88
36.86
34.84
32.82
30.79
28.76
24.69
20.60
16.51
12.40
8.28
4.15
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
23.49
22.55
21.61
20.67
19.73
18.79
17.85
16.91
16.44
15.97
15.50
15.03
14.56
14.09
13.62
13.15
12.68
12.21
11.74
11.27
10.80
10.33
9.864
9.395
8.925
8.455
7.986
7.516
7.046
6.576
5.637
4.697
3.758
2.818
1.879
0.939
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
87.59
85.19
82.79
80.40
78.00
75.60
73.21
70.81
69.61
68.41
67.21
66.02
64.82
63.62
62.42
61.22
60.02
58.82
57.63
56.43
55.23
54.03
52.83
51.63
50.44
49.24
48.04
46.84
45.64
44.44
42.05
39.65
37.25
34.86
32.46
30.06
27.67
Specific
volume, / (m3·kg⫺1)
0.8833
0.8821
0.8808
0.8795
0.8782
0.8770
0.8757
0.8744
0.8738
0.8731
0.8725
0.8719
0.8712
0.8706
0.8700
0.8693
0.8687
0.8680
0.8674
0.8668
0.8661
0.8655
0.8649
0.8642
0.8636
0.8629
0.8623
0.8617
0.8610
0.8604
0.8591
0.8578
0.8566
0.8553
0.8540
0.8527
0.8514
Properties of humid air
1-45
28 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.14
92.28
88.40
84.51
80.61
76.70
72.77
70.80
68.83
66.86
64.88
62.90
60.92
58.94
56.95
54.95
52.96
50.96
48.96
46.96
44.95
42.94
40.93
38.91
36.89
34.87
32.84
30.81
28.78
24.71
20.62
16.52
12.41
8.29
4.15
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
24.21
23.24
22.27
21.30
20.34
19.37
18.40
17.43
16.95
16.46
15.98
15.49
15.01
14.53
14.04
13.56
13.07
12.59
12.10
11.62
11.14
10.65
10.17
9.684
9.200
8.716
8.231
7.747
7.263
6.779
5.810
4.842
3.874
2.905
1.937
0.968
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
89.96
87.49
85.01
82.54
80.07
77.60
75.13
72.66
71.42
70.18
68.95
67.71
66.48
65.24
64.01
62.77
61.53
60.30
59.06
57.83
56.59
55.36
54.12
52.88
51.65
50.41
49.18
47.94
46.70
45.47
43.00
40.53
38.06
35.58
33.11
30.64
28.17
Specific
volume, / (m3·kg⫺1)
0.8858
0.8845
0.8832
0.8818
0.8805
0.8792
0.8779
0.8766
0.8759
0.8753
0.8746
0.8740
0.8733
0.8726
0.8720
0.8713
0.8707
0.8700
0.8693
0.8687
0.8680
0.8674
0.8667
0.8661
0.8654
0.8647
0.8641
0.8634
0.8628
0.8621
0.8608
0.8595
0.8581
0.8568
0.8555
0.8542
0.8529
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.779
3.633
3.487
3.340
3.194
3.046
2.898
2.750
2.675
2.601
2.526
2.452
2.377
2.302
2.227
2.152
2.077
2.001
1.926
1.850
1.774
1.699
1.624
1.547
1.470
1.394
1.318
1.241
1.164
1.088
0.9337
0.7793
0.6244
0.4690
0.3132
0.1568
0.0000
28.0
27.3
26.6
25.9
25.1
24.4
23.5
22.7
22.2
21.7
21.3
20.8
20.3
19.8
19.2
18.7
18.1
17.5
16.9
16.3
15.6
14.9
14.2
13.5
12.7
11.9
11.1
10.2
9.2
8.2
6.0
3.4
0.3
⫺3.2
⫺7.9
⫺15.6
—
28.0
27.5
27.0
26.4
25.9
25.3
24.7
24.1
23.8
23.5
23.2
22.9
22.5
22.2
21.9
21.6
21.2
20.9
20.5
20.2
19.8
19.4
19.1
18.7
18.3
17.9
17.5
17.1
16.7
16.3
15.4
14.6
13.6
12.7
11.7
10.7
9.6
28.0
27.5
27.0
26.5
26.0
25.5
24.9
24.3
24.1
23.8
23.5
23.2
22.9
22.6
22.3
22.0
21.7
21.3
21.0
20.7
20.4
20.0
19.7
19.4
19.0
18.7
18.3
17.9
17.6
17.2
16.4
15.7
14.9
14.0
13.2
12.3
11.4
28.0
27.5
27.0
26.4
25.9
25.3
24.7
24.2
23.8
23.5
23.2
22.9
22.6
22.3
22.0
21.6
21.3
20.9
20.6
20.2
19.9
19.5
19.2
18.8
18.4
18.0
17.6
17.2
16.8
16.4
15.6
14.7
13.8
12.9
11.9
10.9
9.9
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
3.890
3.740
3.590
3.439
3.288
3.137
2.985
2.832
2.755
2.679
2.602
2.525
2.448
2.371
2.294
2.216
2.139
2.061
1.984
1.906
1.828
1.750
1.672
1.593
1.515
1.436
1.358
1.279
1.200
1.121
0.9621
0.8030
0.6434
0.4834
0.3228
0.1616
0.0000
28.5
27.8
27.1
26.4
25.6
24.8
24.0
23.1
22.7
22.2
21.7
21.3
20.8
20.2
19.7
19.1
18.6
18.0
17.4
16.7
16.1
15.4
14.7
14.0
13.2
12.4
11.5
10.6
9.7
8.7
6.4
3.8
0.7
⫺2.8
⫺7.5
⫺15.3
—
28.5
28.0
27.4
26.9
26.3
25.8
25.2
24.6
24.3
24.0
23.6
23.3
23.0
22.7
22.3
22.0
21.6
21.3
20.9
20.6
20.2
19.8
19.5
19.1
18.7
18.3
17.9
17.5
17.1
16.6
15.8
14.9
13.9
13.0
12.0
10.9
9.8
28.5
28.0
27.5
27.0
26.5
25.9
25.4
24.8
24.5
24.2
23.9
23.6
23.3
23.0
22.7
22.4
22.1
21.8
21.4
21.1
20.8
20.4
20.1
19.8
19.4
19.0
18.7
18.3
17.9
17.6
16.8
16.0
15.2
14.3
13.4
12.5
11.6
28.5
28.0
27.5
26.9
26.4
25.8
25.2
24.6
24.3
24.0
23.7
23.4
23.0
22.7
22.4
22.1
21.7
21.4
21.0
20.7
20.3
19.9
19.6
19.2
18.8
18.4
18.0
17.6
17.2
16.8
15.9
15.1
14.1
13.2
12.2
11.2
10.1
28.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.15
92.29
88.41
84.53
80.63
76.72
72.79
70.83
68.86
66.89
64.91
62.93
60.95
58.96
56.98
54.98
52.99
50.99
48.99
46.99
44.98
42.97
40.96
38.94
36.92
34.90
32.87
30.84
28.81
24.73
20.64
16.54
12.42
8.30
4.16
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
24.95
23.96
22.96
21.96
20.96
19.96
18.96
17.97
17.47
16.97
16.47
15.97
15.47
14.97
14.47
13.97
13.47
12.98
12.48
11.98
11.48
10.98
10.48
9.981
9.482
8.983
8.484
7.985
7.486
6.987
5.989
4.991
3.992
2.994
1.996
0.998
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
92.38
89.83
87.28
84.74
82.19
79.64
77.09
74.54
73.27
71.99
70.72
69.45
68.17
66.90
65.62
64.35
63.07
61.80
60.53
59.25
57.98
56.70
55.43
54.16
52.88
51.61
50.33
49.06
47.78
46.51
43.96
41.41
38.87
36.32
33.77
31.22
28.67
Specific
volume, / (m3·kg⫺1)
0.8883
0.8869
0.8856
0.8842
0.8828
0.8815
0.8801
0.8788
0.8781
0.8774
0.8767
0.8761
0.8754
0.8747
0.8740
0.8733
0.8727
0.8720
0.8713
0.8706
0.8699
0.8693
0.8686
0.8679
0.8672
0.8665
0.8659
0.8652
0.8645
0.8638
0.8625
0.8611
0.8597
0.8584
0.8570
0.8556
0.8543
1-46
Reference data
29 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.15
92.30
88.43
84.54
80.65
76.74
72.82
70.85
68.88
66.91
64.94
62.96
60.98
58.99
57.01
55.01
53.02
51.02
49.02
47.02
45.01
43.00
40.98
38.97
36.95
34.92
32.90
30.86
28.83
24.75
20.66
16.56
12.44
8.31
4.16
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
25.72
24.69
23.66
22.63
21.60
20.57
19.55
18.52
18.00
17.49
16.97
16.46
15.94
15.43
14.92
14.40
13.89
13.37
12.86
12.34
11.83
11.32
10.80
10.29
9.773
9.258
8.744
8.230
7.715
7.201
6.172
5.144
4.115
3.086
2.057
1.029
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
94.86
92.23
89.60
86.98
84.35
81.72
79.09
76.47
75.15
73.84
72.53
71.21
69.90
68.58
67.27
65.96
64.64
63.33
62.02
60.70
59.39
58.08
56.76
55.45
54.13
52.82
51.51
50.19
48.88
47.57
44.94
42.31
39.68
37.06
34.43
31.80
29.18
Specific
volume, / (m3·kg⫺1)
0.8908
0.8894
0.8880
0.8866
0.8852
0.8838
0.8824
0.8810
0.8803
0.8796
0.8789
0.8782
0.8775
0.8768
0.8761
0.8754
0.8747
0.8740
0.8733
0.8726
0.8719
0.8712
0.8705
0.8698
0.8691
0.8684
0.8677
0.8670
0.8662
0.8655
0.8641
0.8627
0.8613
0.8599
0.8585
0.8571
0.8557
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.005
3.850
3.696
3.541
3.386
3.230
3.073
2.916
2.837
2.759
2.680
2.600
2.521
2.442
2.362
2.283
2.203
2.123
2.043
1.963
1.883
1.802
1.722
1.641
1.560
1.480
1.398
1.317
1.236
1.155
0.9912
0.8274
0.6630
0.4981
0.3326
0.1666
0.0000
29.0
28.3
27.6
26.9
26.1
25.3
24.5
23.6
23.2
22.7
22.2
21.7
21.2
20.7
20.2
19.6
19.1
18.5
17.8
17.2
16.6
15.9
15.2
14.4
13.6
12.8
12.0
11.1
10.1
9.1
6.9
4.3
1.1
⫺2.4
⫺7.2
⫺14.9
—
29.0
28.5
27.9
27.4
26.8
26.2
25.6
25.0
24.7
24.4
24.1
23.8
23.4
23.1
22.8
22.4
22.1
21.7
21.4
21.0
20.6
20.2
19.9
19.5
19.1
18.7
18.3
17.9
17.4
17.0
16.1
15.2
14.3
13.3
12.2
11.2
10.1
29.0
28.5
28.0
27.5
26.9
26.4
25.8
25.3
25.0
24.7
24.4
24.1
23.8
23.5
23.2
22.8
22.5
22.2
21.9
21.5
21.2
20.8
20.5
20.1
19.8
19.4
19.1
18.7
18.3
17.9
17.1
16.3
15.5
14.6
13.7
12.8
11.9
29.0
28.5
27.9
27.4
26.8
26.3
25.7
25.1
24.8
24.5
24.1
23.8
23.5
23.2
22.8
22.5
22.1
21.8
21.4
21.1
20.7
20.3
20.0
19.6
19.2
18.8
18.4
18.0
17.6
17.1
16.3
15.4
14.5
13.5
12.5
11.4
10.4
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.122
3.963
3.805
3.645
3.485
3.325
3.164
3.002
2.922
2.840
2.759
2.678
2.596
2.515
2.433
2.351
2.269
2.187
2.104
2.022
1.939
1.856
1.774
1.691
1.607
1.524
1.441
1.357
1.273
1.189
1.021
0.8524
0.6831
0.5132
0.3427
0.1717
0.0000
29.5
28.8
28.1
27.4
26.6
25.8
25.0
24.1
23.7
23.2
22.7
22.2
21.7
21.2
20.7
20.1
19.5
18.9
18.3
17.7
17.0
16.3
15.6
14.9
14.1
13.3
12.4
11.5
10.6
9.5
7.3
4.7
1.6
⫺2.1
⫺6.8
⫺14.6
—
29.5
29.0
28.4
27.9
27.3
26.7
26.1
25.5
25.2
24.9
24.5
24.2
23.9
23.5
23.2
22.9
22.5
22.1
21.8
21.4
21.0
20.7
20.3
19.9
19.5
19.1
18.6
18.2
17.8
17.4
16.5
15.5
14.6
13.6
12.5
11.4
10.3
29.5
29.0
28.5
28.0
27.4
26.9
26.3
25.7
25.4
25.1
24.8
24.5
24.2
23.9
23.6
23.3
22.9
22.6
22.3
21.9
21.6
21.3
20.9
20.5
20.2
19.8
19.4
19.1
18.7
18.3
17.5
16.6
15.8
14.9
14.0
13.1
12.1
29.5
29.0
28.4
27.9
27.3
26.7
26.1
25.5
25.2
24.9
24.6
24.3
23.9
23.6
23.3
22.9
22.6
22.2
21.9
21.5
21.1
20.7
20.4
20.0
19.6
19.2
18.8
18.4
17.9
17.5
16.6
15.7
14.8
13.8
12.8
11.7
10.6
29.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.16
92.30
88.44
84.56
80.67
76.76
72.84
70.88
68.91
66.94
64.97
62.99
61.01
59.02
57.04
55.04
53.05
51.05
49.05
47.05
45.04
43.03
41.01
39.00
36.98
34.95
32.92
30.89
28.86
24.78
20.68
16.57
12.45
8.32
4.16
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
26.50
25.44
24.38
23.32
22.26
21.20
20.14
19.08
18.55
18.02
17.49
16.96
16.43
15.90
15.37
14.84
14.31
13.78
13.25
12.72
12.19
11.66
11.13
10.60
10.07
9.541
9.011
8.481
7.951
7.421
6.361
5.301
4.240
3.180
2.120
1.060
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
97.39
94.68
91.97
89.27
86.56
83.85
81.14
78.43
77.08
75.72
74.37
73.01
71.66
70.31
68.95
67.60
66.24
64.89
63.54
62.18
60.83
59.47
58.12
56.76
55.41
54.06
52.70
51.35
49.99
48.64
45.93
43.22
40.51
37.80
35.10
32.39
29.68
Specific
volume, / (m3·kg⫺1)
0.8933
0.8919
0.8905
0.8890
0.8876
0.8861
0.8847
0.8832
0.8825
0.8818
0.8810
0.8803
0.8796
0.8789
0.8782
0.8774
0.8767
0.8760
0.8753
0.8745
0.8738
0.8731
0.8724
0.8716
0.8709
0.8702
0.8695
0.8687
0.8680
0.8673
0.8658
0.8644
0.8629
0.8615
0.8600
0.8586
0.8571
Properties of humid air
1-47
30 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.16
92.31
88.45
84.57
80.69
76.78
72.87
70.91
68.94
66.97
65.00
63.02
61.04
59.05
57.07
55.08
53.08
51.08
49.08
47.08
45.07
43.06
41.05
39.03
37.00
34.98
32.95
30.92
28.88
24.80
20.70
16.59
12.47
8.32
4.17
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
27.31
26.22
25.13
24.03
22.94
21.85
20.76
19.66
19.12
18.57
18.02
17.48
16.93
16.39
15.84
15.29
14.75
14.20
13.66
13.11
12.56
12.02
11.47
10.92
10.38
9.832
9.286
8.739
8.193
7.647
6.554
5.462
4.370
3.277
2.185
1.092
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
99.98
97.19
94.40
91.61
88.81
86.02
83.23
80.44
79.04
77.65
76.25
74.85
73.46
72.06
70.67
69.27
67.87
66.48
65.08
63.69
62.29
60.89
59.50
58.10
56.71
55.31
53.91
52.52
51.12
49.73
46.93
44.14
41.35
38.56
35.77
32.97
30.18
Specific
volume, / (m3·kg⫺1)
0.8959
0.8944
0.8929
0.8915
0.8900
0.8885
0.8870
0.8855
0.8847
0.8840
0.8832
0.8825
0.8817
0.8810
0.8802
0.8795
0.8788
0.8780
0.8773
0.8765
0.8758
0.8750
0.8743
0.8735
0.8728
0.8720
0.8713
0.8705
0.8698
0.8690
0.8675
0.8660
0.8645
0.8630
0.8615
0.8600
0.8585
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.242
4.079
3.916
3.752
3.588
3.423
3.257
3.091
3.008
2.924
2.841
2.757
2.673
2.589
2.505
2.421
2.336
2.252
2.167
2.092
1.997
1.912
1.827
1.741
1.656
1.570
1.484
1.398
1.312
1.225
1.052
0.8782
0.7038
0.5288
0.3531
0.1769
0.0000
30.0
29.3
28.6
27.9
27.1
26.3
25.5
24.6
24.1
23.7
23.2
22.7
22.2
21.7
21.1
20.6
20.0
19.4
18.8
18.1
17.5
16.8
16.1
15.3
14.6
13.7
12.9
12.0
11.0
10.0
7.7
5.1
2.0
⫺1.7
⫺6.5
⫺14.3
—
30.0
29.5
28.9
28.4
27.8
27.2
26.6
26.0
25.6
25.3
25.0
24.7
24.3
24.0
23.6
23.3
22.9
22.6
22.2
21.8
21.4
21.1
20.7
20.3
19.9
19.4
19.0
18.6
18.2
17.7
16.8
15.9
14.9
13.8
12.8
11.7
10.5
30.0
29.5
29.0
28.4
27.9
27.3
26.8
26.2
25.9
25.6
25.3
25.0
24.7
24.4
24.0
23.7
23.4
23.0
22.7
22.4
22.0
21.7
21.3
20.9
20.6
20.2
19.8
19.4
19.0
18.6
17.8
17.0
16.1
15.2
14.3
13.3
12.3
30.0
29.5
28.9
28.4
27.8
27.2
26.6
26.0
25.7
25.4
25.0
24.7
24.4
24.0
23.7
23.4
23.0
22.6
22.3
21.9
21.5
21.2
20.8
20.4
20.0
19.6
19.1
18.7
18.3
17.9
17.0
16.0
15.1
14.1
13.0
11.9
10.8
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.365
4.198
4.030
3.862
3.693
3.523
3.353
3.182
3.096
3.011
2.925
2.839
2.752
2.666
2.579
2.493
2.406
2.319
2.231
2.144
2.057
1.969
1.881
1.793
1.705
1.617
1.528
1.435
1.351
1.262
1.084
0.9046
0.7250
0.5448
0.3638
0.1823
0.0000
30.5
29.8
29.1
28.4
27.6
26.8
26.0
25.1
24.6
24.2
23.7
23.2
22.7
22.1
21.6
21.0
20.5
19.9
19.3
18.6
18.0
17.3
16.5
15.8
15.0
14.2
13.3
12.4
11.4
10.4
8.2
5.5
2.4
⫺1.4
⫺6.2
⫺14.0
—
30.5
30.0
29.4
28.8
28.3
27.7
27.1
26.4
26.1
25.8
25.5
25.1
24.8
24.4
24.1
23.7
23.4
23.0
22.6
22.2
21.9
21.5
21.1
20.7
20.2
19.8
19.4
19.0
18.5
18.1
17.1
16.2
15.2
14.1
13.0
11.9
10.7
30.5
30.0
29.5
28.9
28.4
27.8
27.2
26.7
26.4
26.1
25.7
25.4
25.1
24.8
24.5
24.1
23.8
23.5
23.1
22.8
22.4
22.1
21.7
21.3
21.0
20.6
20.2
19.8
19.4
19.0
18.2
17.3
16.4
15.5
14.5
13.6
12.5
30.5
30.0
29.4
28.9
28.3
27.7
27.1
26.5
26.1
25.8
25.5
25.2
24.8
24.5
24.1
23.8
23.4
23.1
22.7
22.3
21.9
21.6
21.2
20.8
20.4
19.9
19.5
19.1
18.7
18.2
17.3
16.4
15.4
14.4
13.3
12.2
11.0
30.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.17
92.31
88.46
84.59
80.71
76.81
72.89
70.93
68.97
67.00
65.03
63.05
61.07
59.09
57.10
55.11
53.11
51.12
49.12
47.11
45.10
43.09
41.08
39.06
37.04
35.01
32.98
30.95
28.91
24.82
20.72
16.61
12.48
8.33
4.17
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
28.14
27.02
25.89
24.76
23.64
22.51
21.39
20.26
19.70
19.14
18.57
18.01
17.45
16.88
16.32
15.76
15.20
14.63
14.07
13.51
12.94
12.38
11.82
11.26
10.69
10.13
9.568
9.005
8.442
7.879
6.754
5.628
4.502
3.377
2.251
1.125
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
102.63
99.75
96.88
94.00
91.12
88.24
85.36
82.49
81.05
79.61
78.17
76.73
75.29
73.85
72.41
70.98
69.54
68.10
66.66
65.22
63.78
62.34
60.90
59.46
58.02
56.59
55.15
53.71
52.27
50.83
47.95
45.07
42.40
39.32
36.44
33.56
30.68
Specific
volume, / (m3·kg⫺1)
0.8985
0.8970
0.8955
0.8939
0.8924
0.8908
0.8893
0.8878
0.8870
0.8862
0.8854
0.8847
0.8839
0.8831
0.8824
0.8816
0.8808
0.8800
0.8793
0.8785
0.8777
0.8770
0.8762
0.8754
0.8746
0.8739
0.8731
0.8723
0.8716
0.8708
0.8692
0.8677
0.8661
0.8646
0.8631
0.8615
0.8600
1-48
Reference data
31 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.17
92.33
88.48
84.61
80.73
76.83
72.92
70.96
69.00
67.03
65.06
63.08
61.10
59.12
57.13
55.14
53.15
51.15
49.15
47.15
45.14
43.12
41.11
39.09
37.07
35.04
33.01
30.97
28.94
24.85
20.75
16.63
12.49
8.34
4.18
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
29.00
27.83
26.67
25.51
24.35
23.19
22.04
20.88
20.30
19.72
19.14
18.56
17.98
17.40
16.82
16.24
15.66
15.08
14.50
13.92
13.34
12.76
12.18
11.60
11.02
10.44
9.858
9.278
8.698
8.118
6.958
5.799
4.639
3.479
2.320
1.160
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
105.3
102.4
99.41
96.44
93.48
90.51
87.55
84.58
83.10
81.61
80.13
78.65
77.16
75.68
74.20
72.71
71.23
69.75
68.27
66.78
65.30
63.82
62.33
60.85
59.37
57.88
56.40
54.92
53.45
51.95
48.99
46.02
43.05
40.09
37.12
34.15
31.19
Specific
volume, / (m3·kg⫺1)
0.9012
0.8996
0.8980
0.8964
0.8948
0.8932
0.8917
0.8901
0.8893
0.8885
0.8877
0.8869
0.8861
0.8853
0.8845
0.8837
0.8829
0.8821
0.8813
0.8805
0.8797
0.8789
0.8781
0.8773
0.8765
0.8757
0.8749
0.8741
0.8733
0.8725
0.8710
0.8694
0.8678
0.8662
0.8646
0.8630
0.8614
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.492
4.320
4.147
3.974
3.800
3.626
3.451
3.275
3.187
3.099
3.011
2.922
2.833
2.744
2.655
2.566
2.477
2.387
2.298
2.208
2.118
2.027
1.937
1.846
1.756
1.665
1.574
1.483
1.391
1.300
1.116
0.9318
0.7468
0.5612
0.3748
0.1878
0.0000
31.0
30.3
29.6
28.9
28.1
27.3
26.5
25.6
25.1
24.6
24.2
23.7
23.1
22.6
22.1
21.5
20.9
20.3
19.7
19.1
18.4
17.7
17.0
16.3
15.5
14.6
13.8
12.9
11.9
10.9
8.6
6.0
2.8
⫺1.0
⫺5.8
⫺13.6
—
31.0
30.5
29.9
29.3
28.7
28.1
27.5
26.9
26.6
26.2
25.9
25.6
25.2
24.9
24.5
24.2
23.8
23.4
23.0
22.7
22.3
21.9
21.5
21.1
20.6
20.2
19.8
19.3
18.9
18.4
17.5
16.5
15.5
14.4
13.3
12.1
10.9
31.0
30.5
30.0
29.4
28.9
28.3
27.7
27.1
26.8
26.5
26.2
25.9
25.6
25.2
24.9
24.6
24.2
23.9
23.5
23.2
22.8
22.5
22.1
21.7
21.3
21.0
20.6
20.2
19.8
19.3
18.5
17.6
16.7
15.8
14.8
13.8
12.8
31.0
30.5
29.9
29.3
28.8
28.2
27.6
26.9
26.6
26.3
26.0
25.6
25.3
24.9
24.6
24.2
23.9
23.5
23.1
22.7
22.4
22.0
21.6
21.2
20.7
20.3
19.9
19.5
19.0
18.6
17.6
16.7
15.7
14.6
13.6
12.4
11.2
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.621
4.444
4.267
4.089
3.911
3.731
3.552
3.371
3.280
3.190
3.099
3.008
2.917
2.825
2.734
2.642
2.550
2.458
2.365
2.273
2.180
2.087
1.994
1.901
1.808
1.714
1.621
1.527
1.433
1.338
1.150
0.9597
0.7692
0.5780
0.3861
0.1934
0.0000
31.5
30.8
30.1
29.4
28.6
27.8
26.9
26.1
25.6
25.1
24.6
24.1
23.6
23.1
22.6
22.0
21.4
20.8
20.2
19.6
18.9
18.2
17.5
16.7
15.9
15.1
14.2
13.3
12.3
11.3
9.0
6.4
3.2
⫺0.7
⫺5.5
⫺13.3
—
31.5
31.0
30.4
29.8
29.2
28.6
28.0
27.4
27.0
26.7
26.4
26.0
25.7
25.3
25.0
24.6
24.2
23.8
23.5
23.1
22.7
22.3
21.9
21.5
21.0
20.6
20.2
19.7
19.3
18.8
17.8
16.8
15.8
14.7
13.6
12.4
11.1
31.5
31.0
30.4
29.9
29.3
28.8
28.2
27.6
27.3
27.0
26.6
26.3
26.0
25.7
25.3
25.0
24.7
24.3
24.0
23.6
23.2
22.9
22.5
22.1
21.7
21.3
20.9
20.5
20.1
19.7
18.8
18.0
17.0
16.1
15.1
14.1
13.0
31.5
31.0
30.4
29.8
29.2
28.6
28.0
27.4
27.1
26.7
26.4
26.1
25.7
25.4
25.0
24.7
24.3
23.9
23.5
23.2
22.8
22.4
22.0
21.6
21.1
20.7
20.3
19.8
19.4
18.9
18.0
17.0
16.0
14.9
13.8
12.7
11.5
31.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.18
92.34
88.49
84.63
80.75
76.85
72.95
70.99
69.02
67.06
65.09
63.11
61.13
59.15
57.17
55.18
53.18
51.19
49.18
47.18
45.17
43.16
41.14
39.12
37.10
35.07
33.04
31.00
28.96
24.87
20.77
16.65
12.51
8.36
4.19
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
29.87
28.68
27.48
26.29
25.09
23.90
22.70
21.51
20.91
20.31
19.71
19.12
18.52
17.92
17.32
16.73
16.13
15.53
14.94
14.34
13.74
13.14
12.55
11.95
11.35
10.75
10.16
9.559
8.961
8.364
7.169
5.974
4.780
3.584
2.390
1.194
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
108.1
105.0
102.0
98.94
95.89
92.83
89.77
86.72
85.19
83.66
82.13
80.60
79.07
77.55
76.02
74.49
72.96
71.43
69.90
68.38
66.85
65.32
63.79
62.26
60.73
59.20
57.68
56.15
54.62
53.09
50.03
46.98
43.92
40.86
37.81
34.75
31.69
Specific
volume, / (m3·kg⫺1)
0.9039
0.9022
0.9006
0.8990
0.8973
0.8957
0.8940
0.8924
0.8916
0.8908
0.8899
0.8891
0.8883
0.8875
0.8867
0.8858
0.8850
0.8842
0.8834
0.8825
0.8817
0.8809
0.8801
0.8793
0.8784
0.8776
0.8768
0.8760
0.8751
0.8743
0.8727
0.8710
0.8694
0.8677
0.8661
0.8644
0.8628
Properties of humid air
1-49
32 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.18
92.35
88.50
84.64
80.77
76.88
72.97
71.02
69.05
67.09
65.12
63.15
61.17
59.19
57.20
55.21
53.22
51.22
49.22
47.21
45.21
43.19
41.18
39.16
37.13
35.10
33.07
31.03
28.99
24.90
20.79
16.67
12.52
8.37
4.19
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
30.77
29.54
28.31
27.08
25.85
24.62
23.39
22.16
21.54
20.92
20.31
19.69
19.08
18.46
17.85
17.23
16.62
16.00
15.39
14.77
14.15
13.54
12.92
12.31
11.69
11.08
10.46
9.847
9.232
8.616
7.385
6.154
4.924
3.693
2.462
1.231
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
111.0
107.8
104.6
101.5
98.35
95.20
92.05
88.90
87.33
85.75
84.17
82.60
81.02
79.45
77.87
76.30
74.72
73.15
71.57
70.00
68.42
66.85
65.27
63.70
62.12
60.55
58.97
57.40
55.82
54.25
51.10
47.95
44.80
41.65
38.50
35.35
32.20
Specific
volume, / (m3·kg⫺1)
0.9066
0.9049
0.9032
0.9015
0.8998
0.8981
0.8965
0.8948
0.8939
0.8931
0.8922
0.8914
0.8905
0.8897
0.8888
0.8880
0.8871
0.8863
0.8854
0.8846
0.8837
0.8829
0.8820
0.8812
0.8804
0.8795
0.8787
0.8778
0.8770
0.8761
0.8744
0.8727
0.8710
0.8693
0.8676
0.8659
0.8642
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.754
4.572
4.390
4.207
4.024
3.840
3.655
3.469
3.376
3.283
3.189
3.096
3.002
2.908
2.814
2.719
2.625
2.530
2.435
2.340
2.245
2.149
2.053
1.957
1.861
1.765
1.669
1.572
1.475
1.378
1.183
0.9884
0.7923
0.5954
0.3977
0.1992
0.0000
32.0
31.3
30.6
29.9
29.1
28.3
27.4
26.5
26.1
25.6
25.1
24.6
24.1
23.6
23.0
22.5
21.9
21.3
20.7
20.0
19.3
18.7
17.9
17.2
16.4
15.5
14.7
13.8
12.8
11.7
9.5
6.8
3.6
⫺0.3
⫺5.1
⫺13.0
—
32.0
31.4
30.9
30.3
29.7
29.1
28.5
27.8
27.5
27.2
26.8
26.5
26.1
25.8
25.4
25.0
24.7
24.3
23.9
23.5
23.1
22.7
22.3
21.9
21.4
21.0
20.5
20.1
19.6
19.1
18.2
17.2
16.1
15.0
13.8
12.6
11.4
32.0
31.5
30.9
30.4
29.8
29.2
28.7
28.0
27.7
27.4
27.1
26.8
26.5
26.1
25.8
25.4
25.1
24.7
24.4
24.0
23.7
23.3
22.9
22.5
22.1
21.7
21.3
20.9
20.5
20.1
19.2
18.3
17.3
16.4
15.4
14.3
13.2
32.0
31.5
30.9
30.3
29.7
29.1
28.5
27.9
27.5
27.2
26.9
26.5
26.2
25.8
25.5
25.1
24.7
24.4
24.0
23.6
23.2
22.8
22.4
22.0
21.5
21.1
20.7
20.2
19.8
19.3
18.3
17.3
16.3
15.2
14.1
12.9
11.7
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
4.890
4.703
4.516
4.329
4.140
3.951
3.761
3.570
3.474
3.378
3.282
3.186
3.089
2.993
2.896
2.799
2.702
2.604
2.506
2.409
2.311
2.213
2.114
2.015
1.916
1.817
1.718
1.619
1.519
1.419
1.219
1.018
0.8159
0.6132
0.4096
0.4096
0.0000
32.5
31.8
31.1
30.4
29.6
28.8
27.9
27.0
26.6
26.1
25.6
25.1
24.6
24.1
23.5
22.9
22.4
21.8
21.1
20.5
19.8
19.1
18.4
17.6
16.8
16.0
15.1
14.2
13.2
12.2
9.9
7.2
4.1
0.1
⫺4.8
⫺12.6
—
32.5
31.9
31.4
30.8
30.2
29.6
28.9
28.3
28.0
27.6
27.3
26.9
26.6
26.2
25.8
25.5
25.1
24.7
24.3
23.9
23.5
23.1
22.7
22.2
21.8
21.4
20.9
20.5
20.0
19.5
18.5
17.5
16.4
15.3
14.1
12.9
11.6
32.5
32.0
31.4
30.9
30.3
29.7
29.1
28.5
28.2
27.9
27.6
27.2
26.9
26.6
26.2
25.9
25.5
25.2
24.8
24.4
24.1
23.7
23.3
22.9
22.5
22.1
21.7
21.3
20.8
20.4
19.5
18.6
17.7
16.7
15.6
14.6
13.5
32.5
32.0
31.4
30.8
30.2
29.6
29.0
28.3
28.0
27.7
27.3
27.0
26.6
26.3
25.9
25.5
25.2
24.8
24.4
24.0
23.6
23.2
22.8
22.4
21.9
21.5
21.0
20.6
20.1
19.6
18.7
17.7
16.6
15.5
14.4
13.1
11.9
32.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.19
92.36
88.52
84.66
80.79
76.90
73.00
71.05
69.08
67.12
65.15
63.18
61.20
59.22
57.24
55.25
53.25
51.26
49.26
47.25
45.24
43.23
41.21
39.19
37.16
35.14
33.10
31.06
29.02
24.93
20.81
16.69
12.54
8.38
4.20
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
31.70
30.43
29.16
27.89
26.63
25.36
24.09
22.82
22.19
21.55
20.92
20.29
19.65
19.02
18.38
17.75
17.12
16.48
15.85
15.22
14.58
13.95
13.31
12.68
12.05
11.41
10.78
10.14
9.509
8.875
7.608
6.340
5.072
3.804
2.536
1.268
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
113.9
110.6
107.4
104.1
100.9
97.62
94.38
91.13
89.51
87.88
86.26
84.64
83.02
81.39
79.77
78.15
76.52
74.90
73.28
71.65
70.03
68.41
66.78
65.16
63.54
61.92
60.29
58.67
57.05
55.42
52.18
48.93
45.68
42.44
39.19
35.94
32.70
Specific
volume, / (m3·kg⫺1)
0.9094
0.9076
0.9059
0.9041
0.9024
0.9006
0.8989
0.8972
0.8963
0.8954
0.8945
0.8937
0.8928
0.8919
0.8910
0.8902
0.8893
0.8884
0.8875
0.8867
0.8858
0.8849
0.8840
0.8832
0.8823
0.8814
0.8805
0.8797
0.8788
0.8779
0.8762
0.8744
0.8727
0.8709
0.8691
0.8674
0.8656
1-50
Reference data
33 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.19
92.37
88.53
84.68
80.81
76.93
73.03
71.08
69.12
67.15
65.18
63.21
61.24
59.26
57.27
55.28
53.29
51.29
49.29
47.29
45.28
43.26
41.25
39.23
37.20
35.17
33.13
31.10
29.05
24.95
20.84
16.71
12.56
8.39
4.20
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
32.65
31.34
30.04
28.73
27.43
26.12
24.81
23.51
22.85
22.20
21.55
20.90
20.24
19.59
18.94
18.28
17.63
16.98
16.32
15.67
15.02
14.37
13.71
13.06
12.41
11.75
11.10
10.45
9.795
9.142
7.836
6.530
5.224
3.918
2.612
1.306
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
116.8
113.5
110.1
106.8
103.4
100.1
96.76
93.41
91.74
90.06
88.39
86.72
85.05
83.38
81.70
80.03
78.36
76.69
75.01
73.34
71.67
70.00
68.32
66.65
64.98
63.31
61.63
59.96
58.29
56.62
53.27
49.93
46.58
43.24
39.89
36.55
32.20
Specific
volume, / (m3·kg⫺1)
0.9122
0.9104
0.9086
0.9068
0.9050
0.9032
0.9014
0.8996
0.8987
0.8978
0.8969
0.8960
0.8951
0.8942
0.8933
0.8924
0.8915
0.8906
0.8896
0.8887
0.8878
0.8869
0.8860
0.8851
0.8842
0.8833
0.8824
0.8815
0.8806
0.8797
0.8779
0.8761
0.8743
0.8725
0.8707
0.8689
0.8671
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.029
4.838
4.646
4.453
4.259
4.064
3.869
3.673
3.575
3.476
3.377
3.278
3.179
3.080
2.980
2.880
2.780
2.680
2.580
2.479
2.378
2.277
2.176
2.074
1.973
1.871
1.769
1.666
1.564
1.461
1.255
1.048
0.8402
0.6315
0.4219
0.2114
0.0000
33.0
32.3
31.6
30.8
30.1
29.3
28.4
27.5
27.1
26.6
26.1
25.6
25.1
24.5
24.0
23.4
22.8
22.2
21.6
21.0
20.3
19.6
18.9
18.1
17.3
16.5
15.6
14.7
13.7
12.6
10.3
7.7
4.5
0.5
⫺4.4
⫺12.3
—
33.0
32.4
31.9
31.3
30.7
30.1
29.4
28.8
28.4
28.1
27.7
27.4
27.0
26.7
26.3
25.9
25.5
25.1
24.7
24.3
23.9
23.5
23.1
22.6
22.2
21.8
21.3
20.8
20.3
19.9
18.9
17.8
16.7
15.6
14.4
13.1
11.8
33.0
32.5
31.9
31.4
30.8
30.2
29.6
29.0
28.7
28.3
28.0
27.7
27.3
27.0
26.7
26.3
26.0
25.6
25.2
24.9
24.5
24.1
23.7
23.3
22.9
22.5
22.1
21.6
21.2
20.8
19.9
18.9
18.0
17.0
15.9
14.8
13.7
33.0
32.4
31.9
31.3
30.7
30.1
29.4
28.8
28.5
28.1
27.8
27.4
27.1
26.7
26.3
26.0
25.6
25.2
24.8
24.4
24.0
23.6
23.2
22.8
22.3
21.9
21.4
21.0
20.5
20.0
19.0
18.0
16.9
15.8
14.6
13.4
12.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.172
4.976
4.778
4.580
4.381
4.181
3.980
3.779
3.678
3.576
3.475
3.373
3.271
3.169
3.067
2.964
2.861
2.758
2.655
2.551
2.448
2.344
2.240
2.135
2.031
1.926
1.821
1.716
1.610
1.504
1.292
1.079
0.8652
0.6503
0.4345
0.2177
0.0000
33.5
32.8
32.1
31.3
30.6
29.7
28.9
28.0
27.5
27.1
26.6
26.1
25.5
25.0
24.5
23.9
23.3
22.7
22.1
21.4
20.8
20.0
19.3
18.6
17.8
16.9
16.0
15.1
14.1
13.1
10.8
8.1
4.9
0.9
⫺4.1
⫺12.0
—
33.5
32.9
32.4
31.8
31.2
30.5
29.9
29.2
28.9
28.5
28.2
27.8
27.5
27.1
26.7
26.3
26.0
25.6
25.2
24.8
24.3
23.9
23.5
23.0
22.6
22.1
21.7
21.2
20.7
20.2
19.2
18.1
17.0
15.9
14.6
13.3
12.0
33.5
33.0
32.4
31.8
31.3
30.7
30.1
29.4
29.1
28.8
28.5
28.1
27.8
27.4
27.1
26.7
26.4
26.0
25.6
25.3
24.9
24.5
24.1
23.7
23.3
22.9
22.4
22.0
21.6
21.1
20.2
19.3
18.3
17.2
16.2
15.1
13.9
33.5
32.9
32.4
31.8
31.2
30.6
29.9
29.3
28.9
28.6
28.2
27.9
27.5
27.2
26.8
26.4
26.0
25.6
25.2
24.8
24.4
24.0
23.6
23.2
22.7
22.3
21.8
21.3
20.9
20.4
19.4
18.3
17.2
16.1
14.9
13.6
12.3
33.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.20
92.38
88.55
84.70
80.84
76.96
73.06
71.11
69.15
67.19
65.22
63.25
61.27
59.29
57.31
55.32
53.33
51.33
49.33
47.33
45.32
43.30
41.28
39.26
37.23
35.20
33.17
31.13
29.08
24.98
20.86
16.73
12.57
8.40
4.21
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
33.63
32.28
30.94
29.59
28.25
26.90
25.56
24.21
23.54
22.87
22.19
21.52
20.85
20.18
19.50
18.83
18.16
17.49
16.81
16.14
15.47
14.80
14.12
13.45
12.78
12.11
11.43
10.76
10.09
9.416
8.071
6.726
5.380
4.035
2.690
1.345
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
119.9
116.4
113.0
109.5
106.1
102.6
99.19
95.74
94.02
92.29
90.57
88.85
87.12
85.40
83.68
81.95
80.23
78.51
76.78
75.06
73.34
71.61
69.89
68.17
66.45
64.72
63.00
61.28
59.55
57.83
54.38
50.94
47.49
44.04
40.60
37.15
33.70
Specific
volume, / (m3·kg⫺1)
0.9150
0.9132
0.9113
0.9095
0.9076
0.9057
0.9039
0.9020
0.9011
0.9002
0.8992
0.8983
0.8974
0.8964
0.8955
0.8946
0.8936
0.8927
0.8918
0.8909
0.8899
0.8890
0.8881
0.8871
0.8862
0.8853
0.8843
0.8834
0.8825
0.8815
0.8797
0.8778
0.8759
0.8741
0.8722
0.8703
0.8685
Properties of humid air
1-51
34 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.20
92.39
88.56
84.72
80.86
76.98
73.09
71.14
69.18
67.22
65.25
63.28
61.31
59.33
57.35
55.36
53.37
51.37
49.37
47.36
45.35
43.34
41.32
39.30
37.27
35.24
33.20
31.16
29.12
25.01
20.89
16.75
12.59
8.41
4.22
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
34.63
33.25
31.86
30.48
29.09
27.71
26.32
24.94
24.24
23.55
22.86
22.17
21.47
20.78
20.09
19.39
18.70
18.01
17.32
16.62
15.93
15.24
14.55
13.85
13.16
12.47
11.78
11.08
10.39
9.697
8.312
6.927
5.541
4.156
2.771
1.385
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
123.0
119.4
115.9
112.3
108.8
105.2
101.7
98.12
96.34
94.57
92.79
91.02
89.24
87.47
85.69
83.92
82.14
80.37
78.59
76.82
75.04
73.27
71.49
69.71
67.94
66.16
64.39
62.61
60.84
59.06
55.51
51.96
48.41
44.86
41.31
37.76
34.21
Specific
volume, / (m3·kg⫺1)
0.9179
0.9160
0.9141
0.9122
0.9102
0.9083
0.9064
0.9045
0.9035
0.9026
0.9016
0.9007
0.8997
0.8987
0.8978
0.8968
0.8959
0.8949
0.8939
0.8930
0.8920
0.8911
0.8901
0.8891
0.8882
0.8872
0.8863
0.8853
0.8843
0.8834
0.8814
0.8795
0.8776
0.8757
0.8737
0.8718
0.8699
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.319
5.117
4.914
4.710
4.506
4.301
4.094
3.887
3.784
3.679
3.575
3.470
3.366
3.261
3.155
3.050
2.944
2.838
2.732
2.626
2.519
2.412
2.305
2.198
2.090
1.982
1.874
1.766
1.657
1.549
1.330
1.111
0.8918
0.6705
0.4473
0.2241
0.0000
34.0
33.3
32.6
31.8
31.1
30.2
29.4
28.5
28.0
27.5
27.1
26.5
26.0
25.5
24.9
24.4
23.8
23.2
22.5
21.9
21.2
20.5
19.8
19.0
18.2
17.4
16.5
15.6
14.6
13.5
11.2
8.5
5.3
1.3
⫺3.7
⫺11.7
—
34.0
33.4
32.9
32.3
31.6
31.0
30.4
29.7
29.3
29.0
28.6
28.3
27.9
27.5
27.2
26.8
26.4
26.0
25.6
25.2
24.8
24.3
23.9
23.4
23.0
22.5
22.1
21.6
21.1
20.6
19.5
18.5
17.3
16.1
14.9
13.6
12.2
34.0
33.5
32.9
32.3
31.8
31.2
30.5
29.9
29.6
29.3
28.9
28.6
28.2
27.9
27.5
27.2
26.8
26.4
26.1
25.7
25.3
24.9
24.5
24.1
23.7
23.3
22.8
22.4
21.9
21.5
20.6
19.6
18.6
17.5
16.4
15.3
14.1
34.0
33.4
32.9
32.3
31.7
31.0
30.4
29.7
29.4
29.0
28.7
28.3
28.0
27.6
27.2
26.8
26.5
26.1
25.7
25.3
24.8
24.4
24.0
23.5
23.1
22.6
22.2
21.7
21.2
20.7
19.7
18.6
17.5
16.4
15.1
13.9
12.5
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.468
5.261
5.053
4.844
4.634
4.423
4.211
3.999
3.892
3.785
3.678
3.570
3.463
3.355
3.247
3.138
3.029
2.920
2.811
2.702
2.592
2.482
2.372
2.262
2.151
2.040
1.929
1.818
1.706
1.594
1.369
1.144
0.9181
0.6894
0.4606
0.2308
0.0000
34.5
33.8
33.1
32.3
31.5
30.7
29.9
29.0
28.5
28.0
27.5
27.0
26.5
26.0
25.4
24.8
24.3
23.7
23.0
22.4
21.7
21.0
20.2
19.5
18.7
17.8
16.9
16.0
15.0
14.0
11.6
9.0
5.7
1.7
⫺3.4
⫺11.3
—
34.5
33.9
33.3
32.7
32.1
31.5
30.8
30.2
29.8
29.5
29.1
28.7
28.4
28.0
27.6
27.2
26.8
26.4
26.0
25.6
25.2
24.7
24.3
23.8
23.4
22.9
22.4
22.0
21.5
20.9
19.9
18.8
17.6
16.4
15.2
13.8
12.4
34.5
34.0
33.4
32.8
32.2
31.6
31.0
30.4
30.0
29.7
29.4
29.0
28.7
28.3
28.0
27.6
27.2
26.9
26.5
26.1
25.7
25.3
24.9
24.5
24.1
23.6
23.2
22.8
22.3
21.8
20.9
19.9
18.9
17.8
16.7
15.5
14.3
34.5
33.9
33.4
32.8
32.1
31.5
30.9
30.2
29.9
29.5
29.1
28.8
28.4
28.1
27.7
27.3
26.9
26.5
26.1
25.7
25.3
24.8
24.4
24.0
23.5
23.0
22.6
22.1
21.6
21.1
20.1
19.0
17.8
16.7
15.4
14.1
12.7
34.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.21
92.40
88.58
84.74
80.89
77.01
73.12
71.17
69.21
67.25
65.29
63.32
61.35
59.37
57.39
55.40
53.41
51.41
49.41
47.40
45.39
43.38
41.36
39.34
37.31
35.28
33.24
31.20
29.15
25.04
20.92
16.77
12.61
8.42
4.22
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
35.67
34.24
32.81
31.39
29.96
28.53
27.11
25.68
24.97
24.25
23.54
22.83
22.11
21.40
20.69
19.97
19.26
18.55
17.83
17.12
16.41
15.69
14.98
14.27
13.55
12.84
12.13
11.41
10.70
9.986
8.560
7.133
5.707
4.280
2.853
1.427
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
126.2
122.5
118.8
115.2
111.5
107.9
104.2
100.6
98.72
96.89
95.07
93.24
91.41
89.58
87.75
85.92
84.09
82.26
80.43
78.61
76.78
74.95
73.12
71.29
69.46
67.63
65.80
63.97
62.15
60.32
56.66
53.00
49.34
45.69
42.03
38.37
34.71
Specific
volume, / (m3·kg⫺1)
0.9208
0.9189
0.9169
0.9149
0.9129
0.9110
0.9090
0.9070
0.9060
0.9050
0.9040
0.9030
0.9021
0.9011
0.9001
0.8991
0.8981
0.8971
0.8961
0.8951
0.8941
0.8931
0.8921
0.8912
0.8902
0.8892
0.8882
0.8872
0.8862
0.8852
0.8832
0.8812
0.8793
0.8773
0.8753
0.8733
0.713
1-52
Reference data
35 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.21
92.41
88.60
84.76
80.91
77.04
73.15
71.20
69.25
67.29
65.33
63.36
61.38
59.41
57.42
55.44
53.45
51.45
49.45
47.45
45.44
43.42
41.40
39.38
37.35
35.31
33.27
31.23
29.18
25.07
20.94
16.79
12.63
8.44
4.23
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
36.73
35.26
33.79
32.32
30.85
29.38
27.91
26.44
25.71
24.97
24.24
23.51
22.77
22.04
21.30
20.57
19.83
19.10
18.36
17.63
16.89
16.16
15.43
14.69
13.96
13.22
12.49
11.75
11.02
10.28
8.815
7.346
5.876
4.407
2.938
1.469
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
129.4
125.6
121.9
118.1
114.3
110.6
106.8
103.0
101.2
99.27
97.39
95.50
93.62
91.74
89.85
87.97
86.08
84.20
82.32
80.43
78.55
76.66
74.78
72.90
71.01
69.13
67.24
65.36
63.48
61.59
57.82
54.06
50.29
46.52
42.75
38.98
35.22
Specific
volume, / (m3·kg⫺1)
0.9238
0.9218
0.9197
0.9177
0.9157
0.9136
0.9116
0.9095
0.9085
0.9075
0.9065
0.9055
0.9044
0.9034
0.9024
0.9014
0.9004
0.8993
0.8983
0.8973
0.8963
0.8952
0.8942
0.8932
0.8922
0.8912
0.8901
0.8891
0.8881
0.8871
0.8850
0.8830
0.8809
0.8789
0.8768
0.8748
0.8727
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.622
5.409
5.196
4.981
4.765
4.549
4.331
4.113
4.003
3.893
3.783
3.673
3.562
3.451
3.340
3.228
3.117
3.005
2.893
2.780
2.667
2.554
2.441
2.328
2.214
2.100
1.985
1.871
1.756
1.641
1.410
1.177
0.9442
0.7098
0.4743
0.2377
0.0000
35.0
34.3
33.6
32.8
32.0
31.2
30.4
29.5
29.0
28.5
28.0
27.5
27.0
26.5
25.9
25.3
24.7
24.1
23.5
22.8
22.2
21.4
20.7
19.9
19.1
18.3
17.4
16.5
15.5
14.4
12.1
9.4
6.1
2.1
⫺3.0
⫺11.0
—
35.0
34.4
33.8
33.2
32.6
32.0
31.3
30.6
30.3
29.9
29.6
29.2
28.8
28.4
28.1
27.7
27.3
26.9
26.4
26.0
25.6
25.1
24.7
24.2
23.8
23.3
22.8
22.3
21.8
21.3
20.2
19.1
17.9
16.7
15.4
14.0
12.6
35.0
34.5
33.9
33.3
32.7
32.1
31.5
30.8
30.5
30.2
29.8
29.5
29.1
28.8
28.4
28.1
27.7
27.3
26.9
26.5
26.1
25.7
25.3
24.9
24.5
24.0
23.6
23.1
22.7
22.2
21.2
20.2
19.2
18.1
17.0
15.8
14.6
35.0
34.4
33.8
33.2
32.6
32.0
31.3
30.7
30.3
30.0
29.6
29.2
28.9
28.5
28.1
27.7
27.3
26.9
26.5
26.1
25.7
25.2
24.8
24.4
23.9
23.4
22.9
22.5
22.0
21.4
20.4
19.3
18.1
16.9
15.7
14.3
12.9
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.779
5.561
5.342
5.121
4.900
4.678
4.454
4.230
4.117
4.004
3.891
3.778
3.664
3.560
3.436
3.321
3.206
3.091
2.976
2.860
2.744
2.628
2.512
2.395
2.278
2.161
2.043
1.925
1.807
1.689
1.451
1.212
0.9719
0.7307
0.4883
0.2448
0.0000
35.5
34.8
34.1
33.3
32.5
31.7
30.9
29.9
29.5
29.0
28.5
28.0
27.5
26.9
26.4
25.8
25.2
24.6
24.0
23.3
22.6
21.9
21.2
20.4
19.6
18.7
17.8
16.9
15.9
14.9
12.5
9.8
6.6
2.5
⫺2.7
⫺10.7
—
35.5
34.9
34.3
33.7
33.1
32.4
31.8
31.1
30.7
30.4
30.0
29.6
29.3
28.9
28.5
28.1
27.7
27.3
26.9
26.4
26.0
25.6
25.1
24.6
24.2
23.7
23.2
22.7
22.2
21.7
20.6
19.4
18.3
17.0
15.7
14.3
12.8
35.5
34.9
34.4
33.8
33.2
32.6
32.0
31.3
31.0
30.6
30.3
29.9
29.6
29.2
28.9
28.5
28.1
27.7
27.3
26.9
26.5
26.1
25.7
25.3
24.9
24.4
24.0
23.5
23.0
22.6
21.6
20.6
19.5
18.4
17.2
16.0
14.8
35.5
34.9
34.3
33.7
33.1
32.5
31.8
31.1
30.8
30.4
30.1
29.7
29.3
28.9
28.6
28.2
27.8
27.4
26.9
26.5
26.1
25.7
25.2
24.8
24.3
23.8
23.3
22.8
22.3
21.8
20.7
19.6
18.5
17.2
15.9
14.6
13.1
35.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.22
92.43
88.61
84.78
80.94
77.07
73.19
71.24
69.28
67.33
65.36
63.40
61.42
59.45
57.47
55.48
53.49
51.49
49.49
47.49
45.48
43.46
41.44
39.42
37.39
35.35
33.31
31.27
29.22
25.10
20.97
16.82
12.64
8.45
4.24
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
37.82
36.31
34.79
33.28
31.77
30.26
28.74
27.23
26.47
25.72
24.96
24.20
23.45
22.69
21.93
21.18
20.42
19.67
18.91
18.15
17.40
16.64
15.88
15.13
14.37
13.62
12.86
12.10
11.35
10.59
9.076
7.564
6.051
4.538
3.026
1.513
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
132.8
128.9
125.0
121.1
117.2
113.3
109.5
105.6
103.6
101.7
99.76
97.82
95.88
93.94
92.00
90.06
88.12
86.18
84.23
82.29
80.35
78.41
76.47
74.53
72.59
70.65
68.71
66.77
64.83
62.89
59.01
55.13
51.24
47.36
43.48
39.60
35.72
Specific
volume, / (m3·kg⫺1)
0.9268
0.9247
0.9226
0.9205
0.9184
0.9163
0.9142
0.9121
0.9111
0.9100
0.9090
0.9079
0.9068
0.9058
0.9047
0.9037
0.9026
0.9016
0.9005
0.8995
0.8984
0.8974
0.8963
0.8953
0.8942
0.8932
0.8921
0.8910
0.8900
0.8889
0.8868
0.8847
0.8826
0.8805
0.8784
0.8763
0.8742
Properties of humid air
1-53
36 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.23
92.44
88.63
84.81
80.96
77.10
73.22
71.27
69.32
67.36
65.40
63.44
61.46
59.49
57.51
55.52
53.53
51.54
49.53
47.53
45.52
43.50
41.48
39.46
37.43
35.39
33.35
31.30
29.25
25.14
21.00
16.84
12.66
8.46
4.24
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
38.94
37.38
35.82
34.27
32.71
31.15
29.59
28.04
27.26
26.48
25.70
24.92
24.14
23.59
22.36
21.81
21.03
20.25
19.47
18.69
17.91
17.13
16.35
15.58
14.80
14.02
13.24
12.46
11.68
10.90
9.346
7.788
6.230
4.673
3.115
1.558
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
136.2
132.2
128.2
124.2
120.2
116.2
112.2
108.2
106.2
104.2
102.2
100.2
98.19
96.19
94.19
92.19
90.19
88.19
86.19
84.20
82.20
80.20
78.20
76.20
74.20
72.20
70.20
68.20
66.21
64.21
60.21
56.21
52.21
48.22
44.22
40.22
36.22
Specific
volume, / (m3·kg⫺1)
0.9299
0.9277
0.9256
0.9234
0.9212
0.9191
0.9169
0.9147
0.9136
0.9125
0.9115
0.9104
0.9093
0.9082
0.9071
0.9060
0.9049
0.9039
0.9028
0.9017
0.9006
0.8995
0.8984
0.8973
0.8963
0.8952
0.8941
0.8930
0.8919
0.8908
0.8886
0.8865
0.8843
0.8821
0.8799
0.8778
0.8756
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
5.940
5.716
5.491
5.265
5.038
4.810
4.580
4.350
4.234
4.118
4.002
3.885
3.768
3.651
3.534
3.416
3.298
3.180
3.061
2.943
2.823
2.704
2.584
2.464
2.344
2.223
2.102
1.981
1.860
1.738
1.493
1.248
1.000
0.7522
0.5027
0.2520
0.0000
36.0
35.3
34.6
33.8
33.0
32.2
31.3
30.4
30.0
29.5
29.0
28.5
28.0
27.4
26.9
26.3
25.7
25.1
24.4
23.8
23.1
22.4
21.6
20.9
20.0
19.2
18.3
17.4
16.4
15.3
13.0
10.2
7.0
2.9
⫺2.3
⫺10.4
—
36.0
35.4
34.8
34.2
33.6
32.9
32.3
31.6
31.2
30.8
30.5
30.1
29.7
29.3
28.9
28.5
28.1
27.7
27.3
26.9
26.4
26.0
25.5
25.1
24.6
24.1
23.6
23.1
22.6
22.0
20.9
19.8
18.6
17.3
15.9
14.5
13.0
36.0
35.4
34.9
34.3
33.7
33.1
32.4
31.8
31.4
31.1
30.5
30.4
30.0
29.7
29.3
28.9
28.5
28.2
27.8
27.4
27.0
26.5
26.1
25.7
25.3
24.8
24.3
23.9
23.4
22.9
21.9
20.9
19.8
18.7
17.5
16.3
15.0
36.0
35.4
34.8
34.2
33.6
33.0
32.3
31.6
31.2
30.9
30.5
30.2
29.8
29.4
29.0
28.6
28.2
27.8
27.4
26.9
26.5
26.1
25.6
25.2
24.7
24.2
23.7
23.2
22.7
22.2
21.1
20.0
18.8
17.5
16.2
14.8
13.3
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
6.106
5.876
5.645
5.412
5.179
4.945
4.709
4.472
4.354
4.235
4.115
3.996
3.876
3.755
3.635
3.514
3.392
3.271
3.149
3.027
2.905
2.782
2.659
2.535
3.412
2.288
2.163
2.039
1.914
1.788
1.537
1.284
1.030
0.7743
0.5175
0.2594
0.0000
36.5
35.8
35.1
34.3
33.5
32.7
31.8
30.9
30.5
30.0
29.5
29.0
28.4
27.9
27.3
26.8
26.2
25.5
24.9
24.2
23.6
22.8
22.1
21.3
20.5
19.7
18.8
17.8
16.8
15.8
13.4
10.7
7.4
3.3
⫺2.0
⫺10.0
—
36.5
35.9
35.3
34.7
34.1
33.4
32.7
32.0
31.7
31.3
30.9
30.6
30.2
29.8
29.4
29.0
28.6
28.2
27.7
27.3
26.8
26.4
25.9
25.5
25.0
24.5
24.0
23.5
22.9
22.4
21.3
20.1
18.9
17.6
16.2
14.7
13.2
36.5
35.9
35.4
34.8
34.2
33.5
32.9
32.2
31.9
31.6
31.2
30.8
30.5
30.1
29.7
29.4
29.0
28.6
28.2
27.8
27.4
27.0
26.5
26.1
25.6
25.2
24.7
24.3
23.8
23.3
22.3
21.2
20.1
19.0
17.8
16.5
15.2
36.5
35.9
35.3
34.7
34.1
33.4
32.8
32.1
31.7
31.4
31.0
30.6
30.2
29.8
29.5
29.1
28.6
28.2
27.8
27.4
26.9
26.5
26.0
25.6
25.1
24.6
24.1
23.6
23.1
22.5
21.4
20.3
19.1
17.8
16.5
15.0
13.5
36.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.23
92.45
88.65
84.83
80.99
77.13
73.25
71.31
69.36
67.40
65.44
63.48
61.51
59.53
57.55
55.56
53.57
51.58
49.58
47.57
45.56
43.55
41.53
39.50
37.47
35.43
33.39
31.34
29.29
25.17
21.03
16.87
12.68
8.48
4.25
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
40.09
38.49
36.88
35.28
33.68
32.07
30.47
28.87
28.06
27.26
26.46
25.66
24.86
24.06
23.25
22.45
21.65
20.85
20.05
19.24
18.44
17.64
16.84
16.04
15.24
14.43
13.63
12.83
12.03
11.23
9.622
8.018
6.415
4.811
3.207
1.604
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
139.7
135.5
131.4
127.3
123.2
119.1
115.0
110.8
108.8
106.7
104.7
102.6
100.6
98.49
96.43
94.37
92.31
90.25
88.19
86.14
84.08
82.02
79.96
77.90
75.84
73.78
71.72
69.67
67.61
65.55
61.43
57.31
53.20
49.08
44.96
40.84
36.73
Specific
volume, / (m3·kg⫺1)
0.9330
0.9308
0.9285
0.9263
0.9241
0.9218
0.9196
0.9174
0.9162
0.9151
0.9140
0.9129
0.9118
0.9106
0.9095
0.9084
0.9073
0.9062
0.9050
0.9039
0.9028
0.9017
0.9006
0.8994
0.8983
0.8972
0.8961
0.8950
0.8938
0.8927
0.8905
0.8882
0.8860
0.8837
0.8815
0.8792
0.8770
1-54
Reference data
37 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.24
92.46
88.67
84.85
81.02
77.16
73.29
71.34
69.40
67.44
65.48
63.52
61.55
59.57
57.59
55.61
53.62
51.62
49.62
47.62
45.61
43.59
41.57
39.54
37.51
35.47
33.43
31.38
29.33
25.20
21.06
16.89
12.70
8.49
4.26
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
41.28
39.62
37.97
36.32
34.67
33.02
31.37
29.72
28.89
28.07
27.24
26.42
25.59
24.77
23.94
23.11
22.29
21.46
20.64
19.81
18.99
18.16
17.34
16.51
15.68
14.86
14.03
13.21
12.38
11.56
9.906
8.255
6.604
4.953
3.302
1.651
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
143.2
139.0
134.8
130.5
126.3
122.0
117.8
113.6
111.4
109.3
107.2
105.1
103.0
100.8
98.72
96.60
94.48
92.36
90.24
88.12
86.00
83.88
81.75
79.63
77.51
75.39
73.27
71.15
69.03
66.91
62.67
58.43
54.19
49.95
45.71
41.47
37.23
Specific
volume, / (m3·kg⫺1)
0.9362
0.9339
0.9316
0.9293
0.9270
0.9246
0.9223
0.9200
0.9189
0.9177
0.9166
0.9154
0.9143
0.9131
0.9120
0.9108
0.9096
0.9085
0.9073
0.9062
0.9050
0.9039
0.9027
0.9016
0.9004
0.8992
0.8981
0.8969
0.8958
0.8946
0.8923
0.8900
0.8877
0.8854
0.8830
0.8807
0.8784
Vapour
pressure,
pv / kPa
6.274
6.038
5.802
5.563
5.324
5.083
4.842
4.598
4.476
4.354
4.232
4.109
3.985
3.862
3.738
3.614
3.489
3.364
3.239
3.114
2.988
2.862
2.735
2.608
2.481
2.354
2.226
2.098
1.969
1.840
1.581
1.321
1.060
0.7970
0.5327
0.2671
0.0000
Dew point
temperature,
θd / ⬚C
37.0
36.3
35.6
34.8
34.0
33.2
32.3
31.4
30.9
30.5
30.0
29.4
28.9
28.4
27.8
27.2
26.6
26.0
25.4
24.7
24.0
23.3
22.6
21.8
21.0
20.1
19.2
18.3
17.3
16.2
13.8
11.1
7.8
3.7
⫺1.6
⫺9.7
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
37.0
36.4
35.8
35.2
34.5
33.9
33.2
32.5
32.1
31.8
31.4
31.0
30.6
30.2
29.8
29.4
29.0
28.6
28.2
27.7
27.3
26.8
26.3
25.9
25.4
24.9
24.4
23.8
23.3
22.8
21.6
20.4
19.2
17.9
16.5
15.0
13.4
37.0
36.4
35.9
35.3
34.6
34.0
33.4
32.7
32.4
32.0
31.7
31.3
30.9
30.6
30.2
29.8
29.4
29.0
28.6
28.2
27.8
27.4
26.9
26.5
26.0
25.6
25.1
24.6
24.1
23.7
22.6
21.6
20.4
19.3
18.0
16.8
15.4
37.0
36.4
35.8
35.2
34.6
33.9
33.2
32.5
32.2
31.8
31.4
31.1
30.7
30.3
29.9
29.5
29.1
28.7
28.2
27.8
27.4
26.9
26.4
26.0
25.5
25.0
24.5
24.0
23.4
22.9
21.8
20.6
19.4
18.1
16.7
15.3
13.7
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
37.5
36.9
36.3
35.7
35.0
34.4
33.7
33.0
32.6
32.2
31.9
31.5
31.1
30.7
30.3
29.9
29.4
29.0
28.6
28.1
27.7
27.2
26.7
26.3
25.8
25.3
24.7
24.2
23.7
23.1
22.0
20.8
19.5
18.1
16.7
15.2
13.6
37.5
36.9
36.3
35.8
35.1
34.5
33.8
33.2
32.8
32.5
32.1
31.8
31.4
31.0
30.6
30.2
29.9
29.5
29.0
28.6
28.2
27.8
27.3
26.9
26.4
26.0
25.5
25.0
24.5
24.0
23.0
21.9
20.7
19.6
18.3
17.0
15.6
37.5
36.9
36.3
35.7
35.0
34.4
33.7
33.0
32.6
32.3
31.9
31.5
31.1
30.7
30.3
29.9
29.5
29.1
28.7
28.2
27.8
27.3
26.8
26.4
25.9
25.4
24.9
24.3
23.8
23.3
22.1
20.9
19.7
18.4
17.0
15.5
13.9
37.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.25
92.48
88.69
84.87
81.04
77.19
73.32
71.38
69.43
67.48
65.52
63.56
61.59
59.62
57.64
55.65
53.66
51.67
49.67
47.66
45.65
43.64
41.61
39.59
37.55
35.52
33.47
31.42
29.37
25.24
21.09
16.92
12.72
8.50
4.26
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
42.49
40.79
39.09
37.39
35.69
33.99
32.29
30.59
29.74
28.89
28.04
27.20
26.35
25.50
24.65
23.80
22.95
22.10
21.25
20.40
19.55
18.70
17.85
17.00
16.15
15.30
14.45
13.60
12.75
11.90
10.20
8.498
6.799
5.099
3.399
1.700
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
146.9
142.5
138.2
133.8
129.4
125.1
120.7
116.3
114.2
112.0
109.8
107.6
105.4
103.2
101.1
98.87
96.69
94.50
92.32
90.14
87.95
85.77
83.59
81.40
79.22
77.04
74.85
72.67
70.49
68.30
63.93
59.57
55.20
50.83
46.47
42.10
37.73
Specific
volume, / (m3·kg⫺1)
0.9394
0.9370
0.9346
0.9323
0.9299
0.9275
0.9251
0.9227
0.9216
0.9204
0.9192
0.9180
0.9168
0.9156
0.9144
0.9132
0.9120
0.9108
0.9097
0.9085
0.9073
0.9061
0.9049
0.9037
0.9025
0.9013
0.9001
0.8989
0.8977
0.8965
0.8942
0.8918
0.8894
0.8870
0.8846
0.8822
0.8798
Vapour
pressure,
pv / kPa
6.447
6.205
5.962
5.718
5.472
5.225
4.977
4.727
4.602
4.477
4.351
4.225
4.098
3.971
3.844
3.716
3.588
3.460
3.331
3.202
3.073
2.943
2.813
2.683
2.552
2.421
2.290
2.158
2.026
1.893
1.627
1.360
1.091
0.8202
0.5483
0.2749
0.0000
Dew point
temperature,
θd / ⬚C
37.5
36.8
36.1
35.3
34.5
33.7
32.8
31.9
31.4
30.9
30.4
29.9
29.4
28.9
28.3
27.7
27.1
26.5
25.9
25.2
24.5
23.8
23.0
22.2
21.4
20.6
19.7
18.7
17.7
16.6
14.3
11.5
8.3
4.1
⫺1.3
⫺9.4
—
Properties of humid air
1-55
38 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.25
92.49
88.70
84.90
81.07
77.23
73.36
71.42
69.47
67.52
65.57
63.60
61.64
59.66
57.68
55.70
53.71
51.72
49.72
47.71
45.70
43.68
41.66
39.63
37.60
35.56
33.51
31.46
29.41
25.27
21.12
16.94
12.74
8.52
4.27
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
43.74
41.99
40.24
38.49
36.74
34.99
33.24
31.49
30.62
29.74
28.87
28.00
27.12
26.25
25.37
24.50
23.62
22.75
21.87
21.00
20.12
19.25
18.37
17.50
16.62
15.75
14.87
14.00
13.12
12.25
10.50
8.748
6.999
5.249
3.499
1.750
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
150.7
146.2
141.7
137.2
132.7
128.2
123.7
119.2
116.9
114.7
112.4
110.2
107.9
105.7
103.4
101.2
98.95
96.70
94.45
92.20
89.95
87.70
85.46
83.21
80.96
78.71
76.46
74.21
71.96
69.72
65.22
60.72
56.22
51.73
47.23
42.73
38.24
Specific
volume, / (m3·kg⫺1)
0.9427
0.9402
0.9378
0.9353
0.9329
0.9304
0.9279
0.9255
0.9243
0.9230
0.9218
0.9206
0.9194
0.9181
0.9169
0.9157
0.9145
0.9132
0.9120
0.9108
0.9095
0.9083
0.9071
0.9059
0.9046
0.9034
0.9022
0.9009
0.8997
0.8985
0.8960
0.8936
0.8911
0.8886
0.8862
0.8837
0.8813
Vapour
pressure,
pv / kPa
6.624
6.376
6.127
5.876
5.624
5.371
5.116
4.860
4.731
4.602
4.473
4.343
4.213
4.083
3.952
3.821
3.690
3.558
3.426
3.293
3.161
3.027
2.894
2.760
2.625
2.491
2.356
2.220
2.084
1.948
1.674
1.399
1.122
0.8442
0.5644
0.2830
0.0000
Dew point
temperature,
θd / ⬚C
38.0
37.3
36.6
35.8
35.0
34.2
33.3
32.4
31.9
31.4
30.9
30.4
29.9
29.3
28.8
28.2
27.6
27.0
26.3
25.7
25.0
24.2
23.5
22.7
21.9
21.0
20.1
19.2
18.2
17.1
14.7
12.0
8.7
4.5
⫺0.9
⫺9.0
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
38.0
37.4
36.8
36.2
35.5
34.8
34.2
33.4
33.1
32.7
32.3
31.9
31.5
31.1
30.7
30.3
29.9
29.5
29.0
28.6
28.1
27.6
27.2
26.7
26.2
25.7
25.1
24.6
24.0
23.5
22.3
21.1
19.8
18.4
17.0
15.4
13.8
38.0
37.4
36.8
36.2
35.6
35.0
34.3
33.6
33.3
32.9
32.6
32.2
31.8
31.5
31.1
30.7
30.3
29.9
29.5
29.1
28.6
28.2
27.7
27.3
26.8
26.4
25.9
25.4
24.9
24.4
23.3
22.2
21.1
19.8
18.6
17.2
15.8
38.0
37.4
36.8
36.2
35.5
34.9
34.2
33.5
33.1
32.7
32.4
32.0
31.6
31.2
30.8
30.4
30.0
29.5
29.1
28.7
28.2
27.7
27.3
26.8
26.3
25.8
25.3
24.7
24.2
23.6
22.5
21.3
20.0
18.7
17.2
15.7
14.1
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
38.5
37.9
37.3
36.7
36.0
35.3
34.6
33.9
33.5
33.2
32.8
32.4
32.0
31.6
31.2
30.8
30.3
29.9
29.4
29.0
28.5
28.1
27.6
27.1
26.6
26.1
25.5
25.0
24.4
23.9
22.7
21.4
20.1
18.7
17.2
15.7
14.0
38.5
37.9
37.3
36.7
36.1
35.5
34.8
34.1
33.8
33.4
33.0
32.7
32.3
31.9
31.5
31.1
30.7
30.3
29.9
29.5
29.0
28.6
28.2
27.7
27.2
26.8
26.3
25.8
25.3
24.7
23.7
22.5
21.4
20.1
18.8
17.5
16.0
38.5
37.9
37.3
36.7
36.0
35.4
34.7
33.9
33.6
33.2
32.8
32.4
32.0
31.6
31.2
30.8
30.4
30.0
29.5
29.1
28.6
28.1
27.7
27.2
26.7
26.2
25.6
25.1
24.6
24.0
22.8
21.6
20.3
18.9
17.5
16.0
14.3
38.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.26
92.50
88.72
84.92
81.10
77.26
73.40
71.46
69.52
67.57
65.61
63.65
61.68
59.71
57.73
55.75
53.76
51.76
49.76
47.76
45.75
43.73
41.71
39.68
37.64
35.60
33.56
31.50
29.45
25.31
21.15
16.97
12.77
8.53
4.28
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
45.03
43.23
41.42
39.62
37.82
36.02
34.22
32.42
31.52
30.62
29.72
28.82
27.92
27.02
26.12
25.22
24.31
23.41
22.51
21.61
20.71
19.81
18.91
18.01
17.11
16.21
15.31
14.41
13.51
12.61
10.81
9.005
7.204
5.403
3.602
1.801
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
154.5
149.9
145.2
140.6
136.0
131.4
126.7
122.1
119.8
117.5
115.2
112.8
110.5
108.2
105.9
103.6
101.3
98.94
96.62
94.31
91.99
89.68
87.36
85.05
82.73
80.42
78.10
75.79
73.47
71.15
66.52
61.89
57.26
52.63
48.00
43.37
38.74
Specific
volume, / (m3·kg⫺1)
0.9460
0.9434
0.9409
0.9384
0.9359
0.9333
0.9308
0.9283
0.9270
0.9258
0.9245
0.9232
0.9220
0.9207
0.9194
0.9182
0.9169
0.9156
0.9144
0.9131
0.9118
0.9106
0.9093
0.9080
0.9068
0.9055
0.9042
0.9030
0.9017
0.9004
0.8979
0.8954
0.8928
0.8903
0.8878
0.8852
0.8827
Vapour
pressure,
pv / kPa
6.806
6.551
6.295
6.038
5.780
5.520
5.258
4.995
4.863
4.731
4.598
4.465
4.332
4.198
4.064
3.929
3.794
3.659
3.523
3.387
3.250
3.113
2.976
2.838
2.700
2.562
2.423
2.284
2.144
2.004
1.723
1.440
1.155
0.8688
0.5809
0.2913
0.0000
Dew point
temperature,
θd / ⬚C
38.5
37.8
37.1
36.3
35.5
34.7
33.8
32.9
32.4
31.9
31.4
30.9
30.4
29.8
29.3
28.7
28.1
27.4
26.8
26.1
25.4
24.7
24.0
23.2
22.4
21.5
20.6
19.6
18.6
17.5
15.2
12.4
9.1
4.9
⫺0.6
⫺8.7
—
1-56
Reference data
39 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.27
92.52
88.74
84.95
81.13
77.30
73.44
71.50
69.56
67.61
65.65
63.69
61.73
59.76
57.78
55.80
53.81
51.81
49.81
47.81
45.80
43.78
41.76
39.73
37.69
35.65
33.60
31.55
29.49
25.35
21.19
17.00
12.79
8.55
4.29
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
46.35
44.49
42.64
40.79
38.93
37.08
35.22
33.37
32.44
31.52
30.59
29.66
28.74
27.81
26.88
25.95
25.03
24.10
23.17
22.25
21.32
20.39
19.47
18.54
17.61
16.68
15.76
14.83
13.90
12.98
11.12
9.269
7.416
5.562
3.708
1.854
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
158.4
153.7
148.9
144.1
139.4
134.6
129.8
125.1
122.7
120.3
117.9
115.3
113.1
110.8
108.4
106.0
103.6
101.2
98.84
94.46
94.08
91.69
89.31
86.92
84.54
82.16
79.77
77.39
75.00
72.62
67.85
63.08
58.32
53.55
48.78
44.01
39.24
Specific
volume, / (m3·kg⫺1)
0.9494
0.9467
0.9441
0.9415
0.9389
0.9363
0.9337
0.9311
0.9298
0.9285
0.9272
0.9259
0.9246
0.9233
0.9220
0.9207
0.9194
0.9181
0.9168
0.9155
0.9142
0.9129
0.9116
0.9102
0.9089
0.9076
0.9063
0.9050
0.9037
0.9024
0.8998
0.8972
0.8946
0.8919
0.8893
0.8867
0.8841
Vapour
pressure,
pv / kPa
6.991
6.730
6.468
6.204
5.939
5.672
5.404
5.134
4.999
4.863
4.727
4.590
4.453
4.316
4.178
4.040
3.901
3.762
3.622
3.483
3.342
3.202
3.061
2.919
2.777
2.635
2.492
2.349
2.206
2.062
1.772
1.481
1.188
0.8940
0.5978
0.2998
0.0000
Dew point
temperature,
θd / ⬚C
39.0
38.3
37.6
36.8
36.0
35.2
34.3
33.4
32.9
32.4
31.9
31.4
30.8
30.3
29.7
29.2
28.5
27.9
27.3
26.6
25.9
25.2
24.4
23.6
22.8
22.0
21.0
20.1
19.1
18.0
15.6
12.8
9.5
5.4
⫺0.3
⫺8.4
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
39.0
38.4
37.8
37.1
36.5
35.8
35.1
34.4
34.0
33.6
33.2
32.8
32.4
32.0
31.6
31.2
30.8
30.3
29.9
29.4
29.0
28.5
28.0
27.5
27.0
26.4
25.9
25.4
24.8
24.2
23.0
21.8
20.4
19.0
17.5
15.9
14.2
39.0
38.4
37.8
37.2
36.6
35.9
35.3
34.6
34.2
33.9
33.5
33.1
32.7
32.4
32.0
31.6
31.2
30.8
30.3
29.9
29.5
29.0
28.6
28.1
27.6
27.1
26.7
26.1
25.6
25.1
24.0
22.9
21.7
20.4
19.1
17.7
16.2
39.0
38.4
37.8
37.2
36.5
35.8
35.1
34.4
34.0
33.7
33.3
32.9
32.5
32.1
31.7
31.3
30.8
30.4
30.0
29.5
29.0
28.6
28.1
27.6
27.1
26.6
26.0
25.5
24.9
24.4
23.2
21.9
20.6
19.2
17.8
16.2
14.5
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
39.5
38.9
38.3
37.6
37.0
36.3
35.6
34.9
34.5
34.1
33.7
33.3
32.9
32.5
32.1
31.6
31.2
30.8
30.3
29.9
29.4
28.9
28.4
27.9
27.4
26.8
26.3
25.7
25.2
24.6
23.4
22.1
20.7
19.3
17.8
16.1
14.4
39.5
38.9
38.3
37.7
37.1
35.4
35.7
35.0
34.7
34.3
34.0
33.6
33.2
32.8
32.4
32.0
31.6
31.2
30.8
30.3
29.9
29.4
29.0
28.5
28.0
27.5
27.0
26.5
26.0
25.5
24.4
23.2
22.0
20.7
19.4
17.9
16.4
39.5
38.9
38.3
37.6
37.0
36.3
35.6
34.9
34.5
34.1
33.8
33.4
33.0
32.6
32.1
31.7
31.3
30.8
30.4
29.9
29.5
29.0
28.5
28.0
27.5
27.0
26.4
25.9
25.3
24.7
23.5
22.3
20.9
19.5
18.0
16.4
14.7
39.5 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.27
92.53
88.76
84.98
81.16
77.33
73.48
71.54
69.60
67.65
65.70
63.74
61.78
59.81
57.83
55.85
53.86
51.86
49.87
47.86
45.85
43.83
41.80
39.77
37.74
35.70
33.65
31.59
29.53
25.39
21.22
17.03
12.81
8.57
4.30
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
47.70
45.80
43.89
41.98
40.07
38.16
36.25
34.35
33.39
32.44
31.48
30.53
29.58
28.62
27.67
26.71
25.76
24.81
23.85
22.90
21.94
20.99
20.04
19.08
18.13
17.17
16.22
15.27
14.31
13.36
11.45
9.541
7.632
5.724
3.816
1.908
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
162.5
157.6
152.7
147.8
142.8
137.9
133.0
128.1
125.7
123.2
120.8
118.3
115.8
113.4
110.9
108.5
106.0
103.6
101.1
98.66
96.20
93.75
91.30
88.84
86.39
83.93
81.48
79.02
76.57
74.11
69.20
64.29
59.38
54.47
49.56
44.66
39.74
Specific
volume, / (m3·kg⫺1)
0.9528
0.9501
0.9474
0.9447
0.9420
0.9394
0.9367
0.9340
0.9326
0.9313
0.9300
0.9286
0.9273
0.9259
0.9246
0.9232
0.9219
0.9205
0.9192
0.9179
0.9165
0.9152
0.9138
0.9125
0.9111
0.9098
0.9084
0.9071
0.9057
0.9044
0.9017
0.8990
0.8963
0.8936
0.8909
0.8882
0.8855
Vapour
pressure,
pv / kPa
7.181
6.914
6.645
6.374
6.102
5.829
5.553
5.276
5.138
4.948
4.858
4.718
4.577
4.436
4.295
4.153
4.010
3.868
3.724
3.581
3.437
3.292
3.147
3.002
2.856
2.710
2.563
2.416
2.269
2.121
1.823
1.524
1.223
0.9199
0.6152
0.3085
0.0000
Dew point
temperature,
θd / ⬚C
39.5
38.8
38.1
37.3
36.5
35.7
34.8
33.9
33.4
32.9
32.4
31.9
31.3
30.8
30.2
29.6
29.0
28.4
27.8
27.1
26.4
25.7
24.9
24.1
23.3
22.4
21.5
20.5
19.5
18.4
16.1
13.3
9.9
5.8
0.1
⫺8.1
—
Properties of humid air
1-57
40 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.28
92.54
88.78
85.00
81.20
77.37
73.52
71.58
69.64
67.70
65.75
63.79
61.83
59.86
57.88
55.90
53.91
51.92
49.92
47.91
45.90
43.88
41.86
39.82
37.79
35.74
33.69
31.64
29.57
25.43
21.26
17.06
12.83
8.58
4.31
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
49.10
47.13
45.17
43.21
41.24
39.28
37.31
35.35
34.37
33.39
32.40
31.42
30.44
29.46
28.48
27.49
26.51
25.53
24.55
23.57
22.58
21.60
20.62
19.64
18.66
17.67
16.69
15.71
14.73
13.75
11.78
9.819
7.856
5.892
3.928
1.964
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
166.6
161.6
156.5
151.5
146.4
141.3
136.3
131.2
128.7
126.2
123.7
121.1
118.6
116.1
113.5
111.0
108.5
106.0
103.4
100.9
98.38
95.85
93.32
90.80
88.27
85.74
83.21
80.69
78.16
75.63
70.58
65.52
60.47
55.41
50.36
45.30
40.25
Specific
volume, / (m3·kg⫺1)
0.9563
0.9535
0.9507
0.9480
0.9452
0.9424
0.9397
0.9369
0.9355
0.9341
0.9327
0.9314
0.9300
0.9286
0.9272
0.9258
0.9244
0.9230
0.9217
0.9203
0.9189
0.9175
0.9161
0.9147
0.9133
0.9119
0.9106
0.9092
0.9078
0.9064
0.9036
0.9008
0.8981
0.8953
0.8925
0.8897
0.8869
Vapour
pressure,
pv / kPa
7.375
7.101
6.826
6.548
6.269
5.989
5.706
5.422
5.280
5.137
4.993
4.849
4.705
4.560
4.415
4.269
4.123
3.976
3.829
3.682
3.534
3.385
3.236
3.087
2.937
2.787
2.636
2.485
2.333
2.181
1.875
1.568
1.258
0.9466
0.6330
0.3175
0.0000
Dew point
temperature,
θd / ⬚C
40.0
39.3
38.6
37.8
37.0
36.1
35.3
34.3
33.9
33.4
32.9
32.4
31.8
31.3
30.7
30.1
29.5
28.9
28.2
27.6
26.9
26.1
25.4
24.6
23.7
22.9
22.0
21.0
20.0
18.9
16.5
13.7
10.4
6.2
0.5
⫺7.7
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
40.0
39.4
38.8
38.1
37.5
36.8
36.1
35.3
34.9
34.6
34.2
33.8
33.4
32.9
32.5
32.1
31.7
31.2
30.7
30.3
29.8
29.3
28.8
28.3
27.8
27.2
26.7
26.1
25.6
25.0
23.7
22.4
21.0
19.6
18.0
16.3
14.6
40.0
39.4
38.8
38.2
37.6
36.9
36.2
35.5
35.2
34.8
34.4
34.0
33.7
33.3
32.9
32.5
32.0
31.6
31.2
30.8
30.3
29.9
29.4
28.9
28.4
27.9
27.4
26.9
26.4
25.8
24.7
23.5
22.3
21.0
19.6
18.2
16.6
40.0
39.4
38.8
38.1
37.5
36.8
36.1
35.4
35.0
34.6
34.2
33.8
33.4
33.0
32.6
32.2
31.7
31.3
30.8
30.4
29.9
29.4
28.9
28.4
27.9
27.4
26.8
26.3
25.7
25.1
23.9
22.6
21.2
19.8
18.3
16.6
14.9
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
41.0
40.3
39.8
39.1
38.4
37.7
37.0
36.3
35.9
35.5
35.1
34.7
34.3
33.9
33.4
33.0
32.5
32.1
31.6
31.1
30.7
30.2
29.6
29.1
28.6
28.0
27.5
26.9
26.3
25.7
24.4
23.1
21.7
20.2
18.5
16.8
14.9
41.0
40.4
39.8
39.2
38.5
37.9
37.2
36.5
36.1
35.7
35.3
35.0
34.6
34.2
33.8
33.4
32.9
32.5
32.1
31.6
31.2
30.7
30.2
29.7
29.2
28.7
28.2
27.7
27.1
26.6
25.4
24.2
22.9
21.6
20.1
18.6
17.0
41.0
40.4
39.8
39.1
38.5
37.8
37.0
36.3
35.9
35.5
35.1
34.7
34.3
33.9
33.5
33.1
32.6
32.2
31.7
31.2
30.7
30.3
29.7
29.2
28.7
28.2
27.6
27.0
26.4
25.8
24.6
23.3
21.9
20.4
18.8
17.1
15.3
41 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.30
92.57
88.83
85.06
81.26
77.44
73.60
71.67
69.74
67.79
65.84
63.89
61.93
59.96
57.99
56.01
54.02
52.03
50.03
48.02
46.01
43.99
41.96
39.93
37.89
35.84
33.79
31.73
29.66
25.51
21.33
17.12
12.88
8.62
4.32
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
52.00
49.92
47.84
45.76
43.68
41.60
39.52
37.44
36.40
35.36
34.32
33.28
32.24
31.20
30.16
29.12
28.08
27.04
26.00
24.96
23.92
22.88
21.84
20.80
19.76
18.72
17.68
16.64
15.60
14.56
12.48
10.40
8.320
6.240
4.160
2.080
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
175.2
169.8
164.5
159.1
153.8
148.4
143.0
137.7
135.0
132.3
129.7
127.0
124.3
121.6
118.9
116.3
113.6
110.9
108.2
105.5
102.9
100.2
97.51
94.83
92.15
89.47
86.79
84.12
81.44
78.76
73.40
68.04
62.69
57.33
51.97
46.61
41.26
Specific
volume, / (m3·kg⫺1)
0.9634
0.9605
0.9576
0.9546
0.9517
0.9487
0.9458
0.9429
0.9414
0.9399
0.9384
0.9370
0.9355
0.9340
0.9326
0.9311
0.9296
0.9281
0.9267
0.9252
0.9237
0.9222
0.9208
0.9193
0.9178
0.9163
0.9149
0.9134
0.9119
0.9104
0.9075
0.9045
0.9016
0.8986
0.8957
0.8927
0.8898
Vapour
pressure,
pv / kPa
7.778
7.490
7.200
6.909
6.616
6.320
6.023
5.725
5.575
5.424
5.273
5.121
4.969
4.817
4.664
4.510
4.356
4.201
4.046
3.891
3.735
3.578
3.421
3.264
3.106
2.947
2.788
2.628
2.468
2.307
1.984
1.659
1.332
1.002
0.6702
0.3362
0.0000
Dew point
temperature,
θd / ⬚C
41.0
40.3
39.5
38.8
38.0
37.1
36.3
35.3
34.8
34.4
33.8
33.3
32.8
32.2
31.7
31.1
30.5
29.8
29.2
28.5
37.8
27.1
26.3
25.5
24.7
23.8
22.9
21.9
20.9
19.8
17.4
14.6
11.2
7.0
1.3
⫺7.1
—
1-58
Reference data
42 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.31
92.61
88.87
85.11
81.33
77.52
73.69
71.76
69.83
67.89
65.95
63.99
62.03
60.07
58.10
56.12
54.13
52.14
50.14
48.13
46.12
44.10
42.07
40.04
38.00
35.95
33.89
31.83
29.76
25.60
21.41
17.18
12.93
8.65
4.34
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
55.07
52.87
50.66
48.46
46.26
44.06
41.85
39.65
38.55
37.45
36.35
35.24
34.14
33.04
31.94
30.84
29.74
28.64
27.53
26.43
25.33
24.23
23.13
22.03
20.93
19.82
18.72
17.62
16.52
15.42
13.22
11.01
8.811
6.608
4.406
2.203
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
184.2
178.5
172.8
167.2
161.5
155.8
150.1
144.5
141.6
138.8
135.9
133.1
130.3
127.4
124.6
121.7
118.9
116.1
113.2
110.4
107.6
104.7
101.9
99.03
96.20
93.36
90.52
87.68
84.84
82.00
76.33
70.65
64.97
59.40
53.62
47.94
42.26
Specific
volume, / (m3·kg⫺1)
0.9709
0.9677
0.9646
0.9615
0.9584
0.9553
0.9521
0.9490
0.9474
0.9459
0.9443
0.9428
0.9412
0.9396
0.9381
0.9365
0.9349
0.9334
0.9318
0.9302
0.9287
0.9271
0.9255
0.9240
0.9224
0.9208
0.9193
0.9177
0.9161
0.9146
0.9114
0.9083
0.9052
0.9020
0.8989
0.8957
0.8926
Vapour
pressure,
pv / kPa
8.199
7.897
7.593
7.287
6.978
6.668
6.356
6.042
5.884
5.726
5.566
5.407
5.247
5.086
4.925
4.763
4.601
4.438
4.275
4.111
3.946
3.781
3.616
3.449
3.283
3.115
2.947
2.779
2.610
2.440
2.099
1.755
1.409
1.060
0.7095
0.3560
0.0000
Dew point
temperature,
θd / ⬚C
42.0
41.3
40.5
39.8
39.0
38.1
37.2
36.3
35.8
35.3
34.8
34.3
33.8
33.2
32.6
32.0
31.4
30.8
30.1
29.5
28.7
28.0
27.2
26.4
25.6
24.7
23.8
22.8
21.8
20.7
18.3
15.5
12.1
7.8
2.1
⫺6.4
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
42.0
41.3
40.7
40.0
39.4
38.7
38.0
37.2
36.8
36.4
36.0
35.6
35.2
34.8
34.3
33.9
33.4
33.0
32.5
32.0
31.5
31.0
30.5
29.9
29.4
28.8
28.3
27.7
27.1
26.4
25.1
23.8
22.3
20.7
19.1
17.2
15.3
42.0
41.4
40.8
40.2
39.5
38.8
38.1
37.4
37.0
36.7
36.3
35.9
35.5
35.1
34.7
34.2
33.8
33.4
32.9
32.5
32.0
31.5
31.0
30.5
30.0
29.5
29.0
28.4
27.9
27.3
26.1
24.9
23.5
22.2
20.7
19.1
17.4
42.0
41.4
40.8
40.1
39.4
38.7
38.0
37.3
36.9
36.5
36.1
35.7
35.3
34.8
34.4
34.0
33.5
33.0
32.6
32.1
31.6
31.1
30.6
30.1
29.5
29.0
28.4
27.8
27.2
26.6
25.3
23.9
22.5
21.0
19.3
17.6
15.7
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
43.0
42.3
41.6
40.9
40.2
39.7
38.9
38.2
37.8
37.4
37.0
36.5
36.1
35.7
35.2
34.8
34.3
33.9
33.4
32.9
32.4
31.9
31.3
30.8
30.2
29.6
29.1
28.5
27.8
27.2
25.9
24.4
22.9
21.3
19.6
17.7
15.7
43.0
42.4
41.8
41.1
40.5
39.8
39.1
38.4
38.0
37.6
37.2
36.8
36.4
36.0
35.6
35.1
34.7
34.3
33.8
33.3
32.9
32.4
31.9
31.4
30.8
30.3
29.8
29.2
28.6
28.1
26.8
25.5
24.2
22.7
21.2
19.6
17.8
43.0
42.4
41.7
41.1
40.4
39.7
39.0
38.2
37.8
37.4
37.0
36.6
36.2
35.7
35.3
34.9
34.4
33.9
33.5
33.0
32.5
31.9
31.4
30.9
30.3
29.8
29.2
28.6
28.0
27.3
26.0
24.6
23.1
21.5
19.8
18.3
16.0
43 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.33
92.64
88.92
85.18
81.40
77.61
73.78
71.86
69.93
68.00
66.05
64.10
62.15
60.18
58.21
56.24
54.25
52.26
50.26
48.25
46.24
44.22
42.19
40.15
38.11
36.06
34.00
31.93
29.86
25.69
21.49
17.25
12.99
8.69
4.36
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
58.30
55.98
53.64
51.31
48.98
46.65
44.31
41.98
40.82
39.65
38.48
37.32
36.15
34.98
33.82
32.65
31.49
30.32
29.15
27.99
26.82
25.66
24.49
23.32
22.16
20.99
19.82
18.66
17.49
16.33
13.99
11.66
9.329
6.997
4.665
2.332
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
193.7
187.6
181.6
175.6
169.6
163.6
157.6
151.6
148.5
145.5
142.5
139.5
136.5
133.5
130.5
127.5
124.5
121.5
118.5
115.5
112.4
109.4
106.4
103.4
100.4
97.40
94.40
91.39
88.39
85.38
79.36
73.34
67.33
61.31
55.30
49.29
43.27
Specific
volume, / (m3·kg⫺1)
0.9786
0.9752
0.9719
0.9686
0.9653
0.9620
0.9587
0.9553
0.9537
0.9520
0.9504
0.9487
0.9470
0.9454
0.9437
0.9421
0.9404
0.9387
0.9371
0.9354
0.9337
0.9321
0.9304
0.9288
0.9271
0.9254
0.9238
0.9221
0.9204
0.9188
0.9154
0.9121
0.9088
0.9055
0.9021
0.8988
0.8954
Vapour
pressure,
pv / kPa
8.640
8.322
8.004
7.682
7.359
7.033
6.705
6.375
6.209
6.042
5.875
5.707
5.538
5.369
5.200
5.029
4.858
4.687
4.515
4.342
4.169
3.995
3.820
3.645
3.469
3.292
3.115
2.937
2.759
2.580
2.219
1.856
1.491
1.122
0.7509
0.3769
0.0000
Dew point
temperature,
θd / ⬚C
43.0
42.3
41.5
40.8
40.0
39.1
38.2
37.3
36.8
36.3
35.8
35.3
34.7
34.2
33.6
33.0
32.4
31.7
31.1
30.4
29.7
29.0
28.2
27.4
26.5
25.7
24.7
23.7
22.7
21.6
19.2
16.3
12.9
8.7
2.9
⫺5.7
—
Properties of humid air
1-59
44 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.35
92.67
88.97
85.24
81.48
77.69
73.88
71.96
70.04
68.11
66.17
64.22
62.27
60.30
58.34
56.36
54.38
52.38
50.38
48.38
46.36
44.34
42.31
40.27
38.23
36.17
34.11
32.04
29.97
25.78
21.57
17.33
13.05
8.73
4.38
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
61.73
59.26
56.79
54.32
51.85
49.38
46.91
44.45
43.21
41.98
40.74
39.51
38.27
37.04
35.80
34.57
33.33
32.10
30.87
29.63
28.40
27.16
25.93
24.69
23.46
22.22
20.99
19.75
18.52
17.28
14.82
12.35
9.877
7.408
4.938
2.469
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
203.6
197.2
190.9
184.5
178.1
171.7
165.4
159.0
155.8
152.6
149.4
146.2
143.1
139.9
136.7
133.5
130.3
127.1
123.9
120.8
117.6
114.4
111.2
108.0
104.8
101.6
98.45
95.26
92.07
88.89
82.51
76.14
69.77
63.40
57.02
50.65
44.28
Specific
volume, / (m3·kg⫺1)
0.9865
0.9830
0.9795
0.9760
0.9725
0.9689
0.9654
0.9619
0.9601
0.9584
0.9566
0.9548
0.9531
0.9513
0.9495
0.9478
0.9460
0.9443
0.9425
0.9407
0.9390
0.9372
0.9354
0.9337
0.9319
0.9301
0.9284
0.9266
0.9248
0.9231
0.9195
0.9160
0.9125
0.9089
0.9054
0.9018
0.8983
Vapour
pressure,
pv / kPa
9.100
8.768
8.434
8.097
7.757
7.415
7.071
6.723
6.549
6.374
6.198
6.022
5.844
5.666
5.488
5.309
5.129
4.949
4.767
4.585
4.403
4.219
4.035
3.851
3.665
3.479
3.292
3.104
2.916
2.727
2.347
1.963
1.577
1.187
0.7946
0.3989
0.0000
Dew point
temperature,
θd / ⬚C
44.0
43.3
42.5
41.8
40.9
40.1
39.2
38.3
37.8
37.3
36.8
36.2
35.7
35.1
34.6
34.0
33.3
32.7
32.0
31.4
30.6
29.9
29.1
28.3
27.5
26.6
25.7
24.7
23.6
22.5
20.1
17.2
13.8
9.5
3.7
⫺5.1
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
44.0
43.3
42.6
41.9
41.2
40.4
39.9
39.1
38.7
38.3
37.9
37.5
37.0
36.6
36.2
35.7
35.2
34.7
34.3
33.8
33.2
32.7
32.2
31.6
31.0
30.5
29.9
29.2
28.6
28.0
26.6
25.1
23.6
21.9
20.1
18.1
16.0
44.0
43.4
42.8
42.1
41.4
40.8
40.0
39.3
38.9
38.5
38.1
37.7
37.3
36.9
36.5
36.0
35.6
35.1
34.7
34.2
33.7
33.2
32.7
32.2
31.7
31.1
30.6
30.0
29.4
28.8
27.5
26.2
24.8
23.3
21.7
20.0
18.2
44.0
43.4
42.7
42.1
41.4
40.7
39.9
39.2
38.8
38.4
37.9
37.5
37.1
36.7
36.2
35.8
35.3
34.8
34.3
33.8
33.3
32.8
32.3
31.7
31.2
30.6
30.0
29.4
28.7
28.1
26.7
25.3
23.8
22.1
20.4
18.5
16.4
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
45.0
44.3
43.6
42.9
42.2
41.4
40.6
40.0
39.7
39.3
38.8
38.4
38.0
37.5
37.1
36.6
36.1
35.6
35.1
34.6
34.1
33.6
33.0
32.5
31.9
31.3
30.7
30.0
29.4
28.7
27.3
25.8
24.2
22.5
20.6
18.6
16.4
45.0
44.4
43.8
43.1
42.4
41.7
41.0
40.2
39.9
39.5
39.1
38.7
38.2
37.8
37.4
36.9
36.5
36.0
35.6
35.1
34.6
34.1
33.6
33.0
32.5
31.9
31.4
30.8
30.2
29.5
28.3
26.9
25.4
23.9
22.2
20.5
18.6
45.0
44.4
43.7
43.0
42.4
41.6
40.9
40.1
39.7
39.3
38.9
38.5
38.0
37.6
37.1
36.7
36.2
35.7
35.2
34.7
34.2
33.7
33.1
32.6
32.0
31.4
30.8
30.2
29.5
28.9
27.5
26.0
24.4
22.7
20.9
18.9
16.8
45 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.37
92.71
89.02
85.31
81.56
77.79
73.98
72.07
70.15
68.22
66.28
64.34
62.39
60.43
58.46
56.49
54.51
52.52
50.52
48.51
46.49
44.47
42.44
40.40
38.35
36.30
34.23
32.16
30.08
25.89
21.66
17.40
13.11
8.77
4.41
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
65.34
62.73
60.12
57.50
54.89
52.28
49.66
47.05
45.74
44.44
43.13
41.82
40.51
39.21
37.90
36.59
35.29
33.98
32.67
31.37
30.06
28.75
27.45
26.14
24.83
23.52
22.22
20.91
19.60
18.30
15.68
13.07
10.46
7.842
5.228
2.614
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
214.1
207.3
200.6
193.8
187.0
180.3
173.6
166.8
163.4
160.0
156.7
153.3
149.9
146.5
143.2
139.8
136.4
133.0
129.7
126.3
122.9
119.5
116.2
112.8
109.4
106.0
102.7
99.29
95.91
92.54
85.79
79.04
72.29
65.54
58.79
52.04
45.28
Specific
volume, / (m3·kg⫺1)
0.9948
0.9911
0.9874
0.9836
0.9799
0.9761
0.9724
0.9687
0.9668
0.9649
0.9630
0.9612
0.9593
0.9574
0.9556
0.9537
0.9518
0.9499
0.9481
0.9462
0.9443
0.9424
0.9406
0.9387
0.9368
0.9349
0.9331
0.9312
0.9293
0.9274
0.9237
0.9199
0.9162
0.9124
0.9086
0.9049
0.9011
Vapour
pressure,
pv / kPa
9.582
9.234
8.884
8.530
8.174
7.815
7.454
7.089
6.906
6.722
6.537
6.352
6.165
5.978
5.791
5.602
5.413
5.223
5.032
4.841
4.648
4.455
4.261
4.067
3.871
3.675
3.478
3.280
3.082
2.882
2.481
2.076
1.668
1.256
0.8417
0.4221
0.0000
Dew point
temperature,
θd / ⬚C
45.0
44.3
43.5
42.8
41.9
41.1
40.2
39.3
38.8
38.3
37.8
37.2
36.7
36.1
35.5
34.9
34.3
33.7
33.0
32.3
31.6
30.9
30.1
29.3
28.4
27.5
26.6
25.6
24.5
23.4
21.0
18.1
14.7
10.3
4.5
⫺4.4
—
1-60
Reference data
46 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.39
92.75
89.08
85.37
81.64
77.88
74.09
72.18
70.27
68.34
66.41
64.47
62.52
60.56
58.60
56.63
54.64
52.65
50.66
48.65
46.63
44.61
42.58
40.53
38.48
36.43
34.36
32.28
30.19
25.99
21.76
17.48
13.17
8.82
4.43
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
69.17
66.40
63.63
60.87
58.10
55.33
52.57
49.80
48.42
47.03
45.65
44.27
42.88
41.50
40.12
38.73
37.35
35.97
34.58
33.20
31.82
30.43
29.05
27.67
26.28
24.90
23.52
22.13
20.75
19.37
16.60
13.83
11.07
8.300
5.533
2.767
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
225.0
217.9
210.8
203.6
196.4
189.3
182.1
175.0
171.4
167.8
164.3
160.7
157.1
153.5
150.0
146.4
142.8
139.2
135.7
132.1
128.5
124.9
121.4
117.8
114.2
110.6
107.1
103.5
99.92
96.34
89.19
82.04
74.89
67.74
60.59
53.44
46.29
Specific
volume, / (m3·kg⫺1)
1.003
0.9995
0.9955
0.9915
0.9876
0.9836
0.9796
0.9757
0.9737
0.9717
0.9697
0.9677
0.9657
0.9637
0.9618
0.9598
0.9578
0.9558
0.9538
0.9518
0.9498
0.9478
0.9458
0.9438
0.9419
0.9399
0.9379
0.9359
0.9339
0.9319
0.9279
0.9239
0.9199
0.9159
0.9120
0.9080
0.9040
Vapour
pressure,
pv / kPa
10.09
9.722
9.354
8.984
8.611
8.235
7.855
7.473
7.280
7.087
6.893
6.698
6.502
6.306
6.108
5.910
5.711
5.511
5.311
5.109
4.907
4.703
4.499
4.294
4.088
3.882
3.674
3.465
3.256
3.045
2.622
2.194
1.763
1.328
0.8895
0.4467
0.0000
Dew point
temperature,
θd / ⬚C
46.0
45.3
44.5
43.8
42.9
42.1
41.2
40.2
39.8
39.3
38.7
38.2
37.7
37.1
36.5
35.9
35.3
34.6
34.0
33.3
32.6
31.8
31.0
30.2
29.4
28.5
27.5
26.5
25.5
24.3
21.9
19.0
15.5
11.2
5.3
⫺3.7
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
46.0
45.3
44.6
43.9
43.1
42.3
41.5
40.7
40.2
40.0
39.8
39.3
38.9
38.5
38.0
37.5
37.0
36.5
36.0
35.5
35.0
34.4
33.9
33.3
32.7
32.1
31.5
30.8
30.2
29.5
28.0
26.5
24.8
23.1
21.1
19.0
16.7
46.0
45.4
44.7
44.1
43.4
42.7
42.0
41.2
40.8
40.4
40.0
39.6
39.2
38.7
38.3
37.8
37.4
36.9
36.4
35.9
35.4
34.9
34.4
33.9
33.3
32.7
32.2
31.6
30.9
30.3
29.0
27.6
26.1
24.5
22.8
20.9
19.0
46.0
45.4
44.7
44.0
43.3
42.6
41.9
41.1
40.7
40.3
39.8
39.4
39.0
38.5
38.1
37.6
37.1
36.6
36.1
35.6
35.1
34.5
34.0
33.4
32.8
32.2
31.6
31.0
30.3
29.6
28.2
26.7
25.1
23.3
21.4
19.4
17.1
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
47.0
46.3
45.6
44.9
44.1
43.3
42.5
41.6
41.2
40.7
40.3
40.0
39.8
39.4
38.9
38.4
37.9
37.4
36.9
36.4
35.9
35.3
34.7
34.1
33.5
32.9
32.3
31.6
30.9
30.2
28.8
27.2
25.5
23.7
21.7
19.5
17.1
47.0
46.4
45.7
45.1
44.4
43.7
42.9
42.2
41.8
41.4
40.9
40.5
40.1
39.7
39.2
38.8
38.3
37.8
37.3
36.8
36.3
35.8
35.3
34.7
34.1
33.6
33.0
32.3
31.7
31.1
29.7
28.3
26.7
25.1
23.3
21.4
19.3
47.0
46.4
45.7
45.0
44.3
43.6
42.8
42.0
41.6
41.2
40.8
40.3
39.9
39.4
39.0
38.5
38.0
37.5
37.0
36.5
35.9
35.4
34.8
34.3
33.7
33.0
32.4
31.8
31.1
30.4
28.9
27.4
25.7
23.9
21.9
19.8
17.5
47 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.41
92.78
89.13
85.45
81.73
77.98
74.20
72.30
70.39
68.47
66.54
64.60
62.66
60.70
58.74
56.77
54.79
52.80
50.80
48.79
46.78
44.75
42.72
40.68
38.62
36.56
34.49
32.41
30.32
26.11
21.86
17.57
13.24
8.87
4.45
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
73.20
70.27
67.35
64.42
61.49
58.56
55.63
52.71
51.24
49.78
48.31
46.85
45.39
43.92
42.46
40.99
39.53
38.07
36.60
35.14
33.67
32.21
30.75
29.28
27.82
26.35
24.89
23.43
21.96
20.50
17.57
14.64
11.71
8.784
5.856
2.928
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
236.6
229.0
221.5
213.9
206.3
198.8
191.2
183.6
179.8
176.0
172.2
168.5
164.7
160.9
157.1
153.3
149.5
145.7
142.0
138.2
134.4
130.6
126.8
123.0
119.2
115.4
111.7
107.9
104.1
100.3
92.74
85.16
77.59
70.02
62.44
54.87
47.30
Specific
volume, / (m3·kg⫺1)
1.012
1.008
1.004
0.9998
0.9956
0.9913
0.9871
0.9829
0.9808
0.9787
0.9766
0.9745
0.9724
0.9703
0.9681
0.9660
0.9639
0.9618
0.9597
0.9576
0.9555
0.9534
0.9513
0.9491
0.9470
0.9449
0.9428
0.9407
0.9386
0.9365
0.9322
0.9280
0.9238
0.9195
0.9153
0.9110
0.9068
Vapour
pressure,
pv / kPa
10.61
10.23
9.847
9.459
9.068
8.674
8.276
7.875
7.673
7.470
7.266
7.061
6.856
6.649
6.442
6.234
6.025
5.814
5.603
5.391
5.178
4.964
4.749
4.534
4.317
4.099
3.880
3.660
3.439
3.217
2.770
2.319
1.864
1.405
0.9409
0.4727
0.0000
Dew point
temperature,
θd / ⬚C
47.0
46.3
45.5
44.7
43.9
43.1
42.2
41.2
40.7
40.2
39.7
39.2
38.6
38.1
37.5
36.9
36.3
35.6
34.9
34.2
33.5
32.8
32.0
31.2
30.3
29.4
28.5
27.5
26.4
25.3
22.8
19.9
16.4
12.0
6.1
⫺3.1
—
Properties of humid air
1-61
48 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.43
92.83
89.19
85.52
81.82
78.09
74.32
72.42
70.51
68.60
66.68
64.74
62.80
60.85
58.89
56.92
54.94
52.95
50.95
48.95
46.93
44.90
42.87
40.82
38.77
36.70
34.63
32.54
30.45
26.22
21.96
17.66
13.31
8.92
4.48
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
77.47
74.37
71.27
68.17
65.08
61.98
58.88
55.78
54.23
52.68
51.13
49.58
48.03
46.48
44.93
43.38
41.83
40.28
38.74
37.19
35.64
34.09
32.54
30.99
29.44
27.89
26.34
24.79
23.24
21.69
18.59
15.49
12.40
9.296
6.198
3.099
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
248.8
240.8
232.8
224.7
216.7
208.7
200.7
192.7
188.7
184.6
180.6
176.6
172.6
168.6
164.6
160.6
156.6
152.6
148.6
144.5
140.5
136.5
132.5
128.5
124.5
120.5
116.5
112.5
108.5
104.4
96.42
88.40
80.38
72.36
64.35
56.33
48.31
Specific
volume, / (m3·kg⫺1)
1.022
1.017
1.013
1.008
1.004
0.9994
0.9949
0.9904
0.9882
0.9860
0.9837
0.9815
0.9792
0.9770
0.9748
0.9725
0.9703
0.9680
0.9658
0.9636
0.9613
0.9591
0.9568
0.9546
0.9523
0.9501
0.9479
0.9456
0.9434
0.9411
0.9366
0.9321
0.9276
0.9231
0.9186
0.9141
0.9096
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
11.16
10.76
10.36
9.956
9.546
9.133
8.716
8.295
8.084
7.871
7.657
7.442
7.227
7.010
6.792
6.573
6.353
6.133
5.911
5.688
5.464
5.239
5.012
4.785
4.557
4.327
4.097
3.865
3.632
3.398
2.927
2.451
1.971
1.485
0.9952
0.5000
0.0000
48.0
47.3
46.5
45.7
44.9
44.1
43.2
42.2
41.7
41.2
40.7
40.2
39.6
39.0
38.5
37.9
37.2
36.6
35.9
35.2
34.5
33.7
32.9
32.1
31.3
30.3
29.4
28.4
27.3
26.2
23.7
20.8
17.3
12.9
6.9
⫺2.4
—
48.0
47.4
46.7
46.0
45.3
44.5
43.8
42.9
42.5
42.1
41.7
41.2
40.8
40.3
39.8
39.4
38.9
38.3
37.8
37.3
36.7
36.2
35.6
35.0
34.4
33.8
33.1
32.4
31.7
31.0
29.5
27.9
26.1
24.3
22.2
19.9
17.4
48.0
47.4
46.7
46.1
45.4
44.6
43.9
43.1
42.7
42.3
41.9
41.5
41.0
40.6
40.1
39.7
39.2
38.7
38.2
37.7
37.2
36.7
36.1
35.5
35.0
34.4
33.8
33.1
32.5
31.8
30.4
29.0
27.4
25.7
23.8
21.8
19.7
48.0
47.4
46.7
46.0
45.3
44.6
43.8
43.0
42.6
42.2
41.7
41.3
40.8
40.4
39.9
39.4
38.9
38.4
37.9
37.4
36.8
36.3
35.7
35.1
34.5
33.9
33.2
32.6
31.9
31.2
29.7
28.1
26.4
24.5
22.5
20.2
17.8
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
49.0
48.3
47.7
47.0
46.3
45.5
44.7
43.9
43.5
43.1
42.6
42.2
41.7
41.2
40.8
40.3
39.8
39.3
38.7
38.2
37.6
37.1
36.5
35.9
35.2
34.6
33.9
33.2
32.5
31.8
30.3
28.6
26.8
24.9
22.7
20.4
17.8
49.0
48.4
47.7
47.0
46.3
45.6
44.9
44.1
43.7
43.3
42.8
42.4
42.0
41.5
41.1
40.6
40.1
39.6
39.1
38.6
38.1
37.5
37.0
36.4
35.8
35.2
34.6
33.9
33.3
32.6
31.2
29.6
28.0
26.3
24.4
22.3
20.0
49.0
48.4
47.7
47.0
46.3
45.5
44.8
44.0
43.5
43.1
42.7
42.2
41.8
41.3
40.8
40.3
39.8
39.3
38.8
38.3
37.7
37.2
36.6
36.0
35.3
34.7
34.1
33.4
32.7
31.9
30.4
28.8
27.0
25.1
23.0
20.7
18.1
49 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.45
92.87
89.25
85.60
81.92
78.20
74.44
72.55
70.65
68.74
66.82
64.89
62.95
61.00
59.04
57.08
55.10
53.11
51.12
49.11
47.09
45.06
43.03
40.98
38.92
36.85
34.77
32.68
30.58
26.35
22.07
17.75
13.38
8.97
4.51
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
81.98
78.70
75.43
72.15
68.87
65.59
62.31
59.03
57.39
55.75
54.11
52.47
50.83
49.19
47.55
45.91
44.27
42.63
40.99
39.35
37.71
36.07
34.43
32.79
31.15
29.51
27.88
26.24
24.60
22.96
19.68
16.40
13.12
9.838
6.559
3.279
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
261.6
253.1
244.6
236.2
227.7
219.2
210.7
202.2
197.9
193.7
189.4
185.2
181.0
176.7
172.5
168.2
164.0
159.7
155.5
151.2
147.0
142.7
138.5
134.2
130.0
125.7
121.5
117.3
113.0
108.8
100.3
91.78
83.78
74.79
66.30
57.81
49.31
Specific
volume, / (m3·kg⫺1)
1.0315
1.0267
1.0220
1.0172
1.0125
1.0077
1.0030
0.9982
0.9959
0.9935
0.9911
0.9887
0.9864
0.9840
0.9816
0.9792
0.9768
0.9745
0.9721
0.9697
0.9673
0.9649
0.9626
0.9602
0.9578
0.9554
0.9530
0.9507
0.9483
0.9459
0.9411
0.9364
0.9316
0.9268
0.9220
0.9173
0.9125
11.74
11.32
10.90
10.48
10.05
9.614
9.177
8.736
8.515
8.291
8.067
7.842
7.616
7.388
7.159
6.930
6.699
6.467
6.233
5.999
5.764
5.527
5.289
5.050
4.809
4.568
4.325
4.081
3.836
3.589
3.092
2.590
2.083
1.571
1.053
0.5290
0.0000
49.0
48.3
47.5
46.7
45.9
45.1
44.2
43.2
42.7
42.2
41.7
41.2
40.6
40.0
39.4
38.8
38.2
37.6
36.9
36.2
35.4
34.7
33.9
33.1
32.2
31.3
30.3
29.3
28.3
27.1
24.6
21.7
18.2
13.7
7.7
⫺1.7
—
1-62
Reference data
50 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.47
92.91
89.32
85.69
82.02
78.31
74.57
72.68
70.79
68.88
66.97
65.04
63.11
61.16
59.21
57.24
55.27
53.28
51.28
49.28
47.26
45.23
43.19
41.14
39.08
37.01
34.93
32.83
30.73
26.48
22.19
17.85
13.46
9.02
4.54
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
86.76
83.29
79.82
76.35
72.88
69.41
65.94
62.47
60.73
59.00
57.26
55.53
53.79
52.06
50.32
48.58
46.85
45.11
43.38
41.64
39.91
38.17
36.44
34.70
32.97
31.23
29.50
27.76
26.03
24.29
20.82
17.35
13.88
10.41
6.941
3.470
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
275.2
266.2
257.2
248.2
239.2
230.2
221.2
212.2
207.7
203.2
198.7
194.2
189.7
185.2
180.7
176.2
171.7
167.2
162.7
158.2
153.7
149.2
144.8
140.3
135.8
131.3
126.8
122.3
117.8
113.3
104.3
95.29
86.29
77.30
68.31
59.31
50.32
Specific
volume, / (m3·kg⫺1)
1.042
1.037
1.032
1.026
1.022
1.016
1.011
1.006
1.004
1.001
0.9988
0.9963
0.9937
0.9912
0.9887
0.9862
0.9836
0.9811
0.9786
0.9761
0.9735
0.9710
0.9685
0.9660
0.9634
0.9609
0.9584
0.9558
0.9533
0.9508
0.9457
0.9407
0.9356
0.9305
0.9255
0.9204
0.9153
Vapour
pressure,
pv / kPa
12.34
11.90
11.46
11.02
10.57
10.12
9.660
9.198
8.966
8.732
8.497
8.261
8.023
7.785
7.545
7.304
7.061
6.817
6.572
6.326
6.079
5.830
5.580
5.328
5.075
4.821
4.565
4.308
4.050
3.790
3.266
2.737
2.202
1.660
1.113
0.5597
0.0000
Dew point
temperature,
θd / ⬚C
50.0
49.3
48.5
47.7
46.9
46.1
45.2
44.2
43.7
43.2
42.7
42.1
41.6
41.0
40.4
39.8
39.2
38.5
37.9
37.2
36.4
35.7
34.9
34.0
33.2
32.2
31.3
30.3
29.2
28.1
25.5
22.6
19.0
14.6
8.6
⫺1.0
—
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
50.0
49.3
48.7
48.0
47.2
46.5
45.7
44.9
44.4
44.0
43.6
43.1
42.7
42.2
41.7
41.2
40.7
40.2
39.6
39.1
38.5
37.9
37.3
36.7
36.1
35.4
34.8
34.1
33.3
32.6
31.0
29.3
27.5
25.5
23.3
20.8
18.1
50.0
49.4
48.7
48.0
47.3
46.6
45.8
45.0
44.6
44.2
43.8
43.4
42.9
42.5
42.0
41.5
41.0
40.5
40.0
39.5
39.0
38.4
37.8
37.2
36.7
36.0
35.4
34.7
34.1
33.4
31.9
30.3
28.7
26.9
24.9
22.7
20.4
50.0
49.4
48.7
48.0
47.3
46.5
45.7
44.9
44.5
44.1
43.6
43.2
42.7
42.3
41.8
41.3
40.8
40.3
39.7
39.2
38.6
38.0
37.4
36.8
36.2
35.6
34.9
34.2
33.5
32.7
31.2
29.5
27.7
25.7
23.5
21.1
18.5
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
51.0
50.3
49.7
49.0
48.2
47.5
46.7
45.8
45.4
45.0
44.5
44.1
43.6
43.1
42.6
42.1
41.6
41.1
40.5
40.0
39.4
38.8
38.2
37.6
36.9
36.3
35.6
34.9
34.1
33.4
31.8
30.0
28.1
26.1
23.8
21.3
18.4
51.0
50.4
49.7
49.0
48.3
47.6
46.8
46.0
45.6
45.2
44.7
44.3
43.8
43.4
42.9
42.4
41.9
41.4
40.9
40.4
39.8
39.3
38.7
38.1
37.5
36.9
36.2
35.6
34.9
34.2
32.7
31.1
29.3
27.5
25.4
23.2
20.8
51.0
50.3
49.7
49.0
48.2
47.5
46.7
45.9
45.5
45.0
44.6
44.1
43.7
43.2
42.7
42.2
41.7
41.2
40.6
40.1
39.5
38.9
38.3
37.7
37.1
36.4
35.7
35.0
34.3
33.5
31.9
30.2
28.3
26.3
24.1
21.6
18.8
51 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.50
92.96
89.38
85.77
82.12
78.43
74.70
72.83
70.94
69.04
67.13
65.20
63.27
61.33
59.38
57.42
55.44
53.46
51.46
49.46
47.44
45.41
43.37
41.32
39.25
37.18
35.09
32.99
30.88
26.62
22.31
17.95
13.54
9.08
4.57
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
91.81
88.14
84.46
80.79
77.12
73.45
69.78
66.10
64.27
62.43
60.59
58.76
56.92
55.09
53.25
51.41
49.58
47.74
45.90
44.07
42.23
40.40
38.56
36.72
34.89
33.05
31.22
29.38
27.54
25.71
22.03
18.36
14.69
11.02
7.345
3.672
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
289.4
279.9
270.4
260.8
251.3
241.8
232.3
222.8
218.0
213.2
208.5
203.7
198.9
194.2
189.4
184.7
179.9
175.1
170.4
165.6
160.8
156.1
151.3
146.6
141.8
137.0
132.3
127.5
122.8
118.0
108.5
98.94
89.42
79.90
70.37
60.85
51.33
Specific
volume, / (m3·kg⫺1)
1.052
1.047
1.042
1.036
1.031
1.026
1.020
1.015
1.012
1.009
1.007
1.004
1.001
0.9987
0.9960
0.9933
0.9907
0.9880
0.9853
0.9826
0.9799
0.9773
0.9746
0.9719
0.9692
0.9665
0.9639
0.9612
0.9585
0.9558
0.9504
0.9451
0.9397
0.9343
0.9289
0.9235
0.9182
Vapour
pressure,
pv / kPa
12.96
12.51
12.05
11.58
11.12
10.64
10.16
9.682
9.439
9.194
8.948
8.700
8.451
8.201
7.949
7.696
7.442
7.186
6.929
6.670
6.410
6.148
5.885
5.621
5.355
5.087
4.818
4.548
4.276
4.002
3.450
2.892
2.327
1.755
1.177
0.5920
0.0000
Dew point
temperature,
θd / ⬚C
51.0
50.3
49.5
48.7
47.9
47.1
46.2
45.2
44.7
44.2
43.7
43.1
42.6
42.0
41.4
40.8
40.2
39.5
38.8
38.1
37.4
36.6
35.8
35.0
34.1
33.2
32.2
31.2
30.1
29.0
26.4
23.5
19.9
15.5
9.4
⫺0.4
—
Properties of humid air
1-63
52 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.52
93.01
89.46
85.86
82.23
78.56
74.84
72.97
71.09
69.19
67.29
65.37
63.45
61.51
59.56
57.60
55.63
53.64
51.65
49.64
47.62
45.59
43.55
41.50
39.43
37.35
35.26
33.16
31.04
26.77
22.44
18.06
13.63
9.14
4.60
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
97.16
93.27
89.38
85.50
81.61
77.72
73.84
69.95
68.01
66.07
64.12
62.18
60.24
58.29
56.35
54.41
52.46
50.52
48.58
46.63
44.69
42.75
40.81
38.86
36.92
34.98
33.03
31.09
29.15
27.20
23.32
19.43
15.54
11.66
7.772
3.886
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
304.5
294.4
284.3
274.2
264.1
254.0
243.9
233.9
228.8
223.8
218.7
213.7
208.7
203.6
198.6
193.5
188.5
183.4
178.4
173.4
168.3
163.3
158.2
153.2
148.1
143.1
138.1
133.0
128.0
122.9
112.8
102.8
92.68
82.59
72.51
62.42
52.34
Specific
volume, / (m3·kg⫺1)
1.063
1.058
1.052
1.046
1.041
1.035
1.029
1.024
1.021
1.018
1.015
1.012
1.009
1.007
1.004
1.001
0.9980
0.9951
0.9923
0.9894
0.9866
0.9837
0.9809
0.9780
0.9752
0.9723
0.9695
0.9667
0.9638
0.9610
0.9553
0.9495
0.9438
0.9381
0.9324
0.9267
0.9210
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
13.61
13.14
12.66
12.18
11.69
11.19
10.69
10.19
9.934
9.677
9.420
9.160
8.899
8.637
8.373
8.108
7.841
7.573
7.303
7.031
6.758
6.483
6.207
5.929
5.649
5.368
5.085
4.800
4.513
4.225
3.644
3.056
2.459
1.856
1.245
0.6263
0.0000
52.0
51.3
50.5
49.7
48.9
48.1
47.2
46.2
45.7
45.2
44.7
44.1
43.6
43.0
42.4
41.8
41.2
40.5
39.8
39.1
38.4
37.6
36.8
36.0
35.1
34.2
33.2
32.2
31.1
29.9
27.4
24.4
20.8
16.3
10.2
0.3
—
52.0
51.3
50.7
49.9
49.2
48.4
47.6
46.8
46.4
45.9
45.5
45.0
44.6
44.1
43.6
43.1
42.5
42.0
41.5
40.9
40.3
39.7
39.1
38.5
37.8
37.1
36.4
35.7
35.0
34.2
32.5
30.8
28.8
26.7
24.3
21.7
18.8
52.0
51.4
50.7
50.0
49.3
48.5
47.8
47.0
46.6
46.1
45.7
45.3
44.8
44.3
43.9
43.4
42.9
42.4
41.8
41.3
40.7
40.2
39.6
39.0
38.4
37.7
37.1
36.4
35.7
34.9
33.4
31.8
30.0
28.1
26.0
23.7
21.1
52.0
51.3
50.7
50.0
49.2
48.5
47.7
46.9
46.4
46.0
45.5
45.1
44.6
44.1
43.6
43.1
42.6
42.1
41.6
41.0
40.4
39.8
39.2
38.6
37.9
37.3
36.6
35.8
35.1
34.3
32.7
30.9
29.0
26.9
24.6
22.0
19.2
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
14.29
13.80
13.30
12.80
12.29
11.77
11.25
10.72
10.45
10.18
9.914
9.642
9.369
9.095
8.818
8.540
8.260
7.979
7.695
7.410
7.124
6.835
6.545
6.252
5.958
5.663
5.365
5.065
4.764
4.460
3.848
3.227
2.599
1.962
1.316
0.6625
0.0000
53.0
52.3
51.5
50.7
49.9
49.1
48.2
47.2
46.7
46.2
45.7
45.1
44.6
44.0
43.4
42.8
42.1
41.5
40.8
40.1
39.3
38.6
37.8
36.9
36.1
35.1
34.2
33.1
32.0
30.9
28.3
25.3
21.7
17.2
11.1
1.1
—
53.0
52.3
51.7
50.9
50.2
49.4
48.6
47.8
47.4
46.9
46.5
46.0
45.5
45.0
44.5
44.0
43.5
42.9
42.4
41.8
41.2
40.6
40.0
39.3
38.7
38.0
37.3
36.5
35.8
35.0
33.3
31.5
29.5
27.3
24.9
22.2
19.1
53.0
52.4
51.7
51.0
50.3
49.5
48.8
47.9
47.5
47.1
46.7
46.2
45.7
45.3
44.8
44.3
43.8
43.3
42.7
42.2
41.6
41.1
40.5
39.9
39.2
38.6
37.9
37.2
36.5
35.7
34.2
32.5
30.7
28.7
26.5
24.1
21.4
53.0
52.3
51.7
51.0
50.2
49.5
48.7
47.8
47.4
47.0
46.5
46.0
45.6
45.1
44.6
44.1
43.6
43.0
42.5
41.9
41.3
40.7
40.1
39.5
38.8
38.1
37.4
36.7
35.9
35.1
33.5
31.7
29.7
27.5
25.2
22.5
19.5
53 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.55
93.06
89.53
85.96
82.35
78.69
74.99
73.13
71.25
69.36
67.46
65.55
63.63
61.69
59.75
57.79
55.82
53.84
51.85
49.84
47.82
45.79
43.74
41.69
39.62
37.53
35.44
33.33
31.21
26.92
22.58
18.18
13.72
9.21
4.64
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
102.87
98.70
94.59
90.48
86.37
82.25
78.14
74.03
71.97
69.92
67.86
65.80
63.75
61.69
59.63
57.58
55.52
53.46
51.41
49.35
47.30
45.24
43.18
41.13
39.07
37.01
34.96
32.90
30.85
28.79
24.68
20.56
16.45
12.34
8.225
4.112
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
320.3
309.7
299.0
288.3
277.6
266.9
256.3
245.6
240.2
234.9
229.6
224.2
218.9
213.5
208.2
202.9
197.5
192.2
186.8
181.5
176.2
170.8
165.5
160.1
154.8
149.5
144.1
138.8
133.4
128.1
117.4
106.7
96.06
85.38
74.70
64.02
53.34
Specific
volume, / (m3·kg⫺1)
1.075
1.069
1.063
1.057
1.051
1.045
1.039
1.033
1.030
1.027
1.024
1.021
1.018
1.015
1.012
1.009
1.006
1.003
0.9995
0.9965
0.9934
0.9904
0.9874
0.9844
0.9814
0.9783
0.9753
0.9723
0.9693
0.9662
0.9602
0.9541
0.9481
0.9420
0.9360
0.9299
0.9238
1-64
Reference data
54 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.58
93.11
89.61
86.06
82.47
78.83
75.15
73.29
71.42
69.54
67.64
65.74
63.82
61.89
59.95
57.99
56.02
54.04
52.05
50.05
48.03
45.99
43.95
41.89
39.82
37.73
35.63
33.51
31.38
27.08
22.72
18.30
13.82
9.28
4.67
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
108.8
104.5
100.1
95.76
91.40
87.05
82.70
78.35
76.17
73.99
71.82
69.64
67.47
65.29
63.11
60.94
58.76
56.58
54.41
52.23
50.06
47.88
45.70
43.53
41.35
39.17
37.00
34.82
32.64
30.47
26.12
21.76
17.41
13.06
8.705
4.353
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
337.1
325.8
314.5
303.2
291.9
280.6
269.2
257.9
252.3
246.6
241.0
235.3
229.7
224.0
218.4
212.7
207.0
201.4
195.7
190.1
184.4
178.8
173.1
167.5
161.8
156.1
150.5
144.8
139.2
133.5
122.2
110.9
99.59
88.28
76.97
65.66
54.35
Specific
volume, / (m3·kg⫺1)
1.0869
1.0805
1.0741
1.0678
1.0614
1.0550
1.0486
1.0422
1.0390
1.0358
1.0326
1.0294
1.0262
1.0230
1.0198
1.0166
1.0134
1.0102
1.0070
1.0038
1.0006
0.9974
0.9942
0.9909
0.9877
0.9845
0.9813
0.9781
0.9749
0.9717
0.9653
0.9588
0.9524
0.9460
0.9396
0.9331
0.9267
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
15.00
14.49
13.97
13.44
12.91
12.37
11.83
11.27
10.99
10.71
10.43
10.16
9.862
9.574
9.285
8.993
8.700
8.405
8.108
7.809
7.508
7.205
6.900
6.593
6.284
5.973
5.660
5.345
5.028
4.708
4.063
3.409
2.746
2.074
1.392
0.7009
0.0000
54.0
53.3
52.5
51.7
50.9
50.1
49.2
48.2
47.7
47.2
46.7
46.1
45.6
45.0
44.4
43.8
43.1
42.5
41.8
41.1
40.3
39.6
38.8
37.9
37.0
36.1
35.1
34.1
33.0
31.8
29.3
26.2
22.6
18.1
11.9
1.9
—
54.0
53.3
52.6
51.9
51.2
50.4
49.6
48.8
48.3
47.9
47.4
47.0
46.5
46.0
45.5
45.0
44.4
43.9
43.3
42.7
42.1
41.5
40.9
40.2
39.6
38.9
38.1
37.4
36.6
35.8
34.1
32.2
30.2
27.9
25.4
22.6
19.4
54.0
53.4
52.7
52.0
51.3
50.5
49.7
48.9
48.5
48.1
47.6
47.2
46.7
46.2
45.7
45.2
44.7
44.2
43.7
43.1
42.5
42.0
41.4
40.7
40.1
39.4
38.7
38.0
37.3
36.5
34.9
33.2
31.3
29.3
27.0
24.6
21.8
54.0
53.3
52.7
52.0
51.2
50.4
49.6
48.8
48.4
47.9
47.5
47.0
46.5
46.0
45.5
45.0
44.5
44.0
43.4
42.8
42.2
41.6
41.0
40.4
39.7
39.0
38.3
37.5
36.8
36.0
34.3
32.4
30.4
28.2
25.7
22.9
19.8
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
15.74
15.21
14.67
14.12
13.56
13.00
12.43
11.85
11.56
11.2
10.97
10.68
10.38
10.08
9.774
9.479
9.161
8.852
8.541
8.237
7.911
7.593
7.273
6.951
6.636
6.300
5.971
5.640
5.305
4.979
4.290
3.600
2.901
2.192
1.472
0.7416
0.0000
55.0
54.3
53.5
52.7
51.9
51.1
50.2
49.2
48.7
48.2
47.7
47.1
46.6
46.0
45.4
44.8
44.1
43.5
42.8
42.1
41.3
40.5
39.7
38.9
38.0
37.1
36.1
35.1
34.0
32.8
30.2
27.2
23.5
19.0
12.7
2.7
—
55.0
54.3
53.6
52.9
52.2
51.4
50.6
49.7
49.3
48.9
48.4
47.9
47.4
46.9
46.4
45.9
45.4
44.8
44.2
43.7
43.1
42.4
41.8
41.1
40.4
39.7
39.0
38.2
37.4
36.6
34.9
33.0
30.9
28.6
26.0
23.1
19.7
55.0
54.4
53.7
53.0
52.3
51.5
50.7
49.9
49.5
49.0
48.6
48.1
47.7
47.2
46.7
46.2
45.7
45.1
44.6
44.0
43.5
42.9
42.2
41.6
41.0
40.3
39.6
38.9
38.1
37.4
35.7
34.0
32.0
29.9
27.6
25.0
22.1
55.0
54.3
53.7
52.9
52.2
51.4
50.6
49.8
49.4
48.9
48.4
48.0
47.5
47.0
46.5
46.0
45.4
44.9
44.3
43.8
43.2
42.5
41.9
41.2
40.6
39.9
39.1
38.4
37.6
36.8
35.0
33.2
31.1
28.8
26.3
23.4
20.1
55 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.60
93.17
89.69
86.16
82.59
78.97
75.31
73.46
71.60
69.72
67.83
65.93
64.02
62.09
60.16
58.20
56.24
54.26
52.27
50.26
48.24
46.21
44.16
42.10
40.02
37.93
35.83
33.71
31.57
27.25
22.88
18.43
13.93
9.35
4.71
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
115.2
110.6
106.0
101.4
96.74
92.14
87.53
82.92
80.62
78.32
76.01
73.71
71.41
69.10
66.80
64.50
62.19
59.89
57.59
55.28
52.98
50.68
48.37
46.07
43.76
41.46
39.16
36.86
34.55
32.25
27.64
23.03
18.43
13.82
9.214
4.607
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
354.8
342.9
330.9
318.9
306.9
294.9
283.0
271.0
265.0
259.0
253.0
247.0
241.0
235.0
229.1
223.1
217.1
211.1
205.1
199.1
193.1
187.1
181.1
175.2
169.2
163.2
157.2
151.2
145.2
139.2
127.2
115.3
103.3
91.30
79.32
67.34
55.36
Specific
volume, / (m3·kg⫺1)
1.100
1.093
1.086
1.079
1.072
1.066
1.059
1.052
1.049
1.045
1.042
1.038
1.035
1.032
1.028
1.025
1.022
1.018
1.015
1.011
1.008
1.004
1.001
0.9977
0.9943
0.9909
0.9875
0.9841
0.9807
0.9773
0.9705
0.9637
0.9568
0.9500
0.9432
0.9363
0.9295
Properties of humid air
1-65
56 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.63
93.23
89.77
86.27
82.72
79.12
75.48
73.64
71.78
69.91
68.03
66.14
64.23
62.31
60.37
58.42
56.46
54.49
52.49
50.49
48.47
46.44
44.39
42.32
40.24
38.15
36.04
33.91
31.77
27.44
23.04
18.57
14.04
9.43
4.75
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
121.9
117.0
112.2
107.3
102.4
97.53
92.65
87.78
85.34
82.90
80.46
78.03
75.59
73.15
70.71
68.27
65.83
63.40
60.96
58.52
56.08
53.64
51.20
48.77
46.33
43.89
41.45
39.01
36.57
34.14
29.26
24.38
19.51
14.63
9.753
4.877
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
373.6
360.9
348.2
335.5
322.8
310.2
297.5
284.8
278.4
272.1
265.7
259.4
253.0
246.7
240.4
234.0
227.7
221.3
215.0
208.6
202.3
195.9
189.6
183.3
176.9
170.6
164.2
157.9
151.5
145.2
132.5
119.9
107.1
94.43
81.74
69.06
56.37
Specific
volume, / (m3·kg⫺1)
1.113
1.106
1.099
1.091
1.084
1.077
1.070
1.062
1.059
1.055
1.052
1.048
1.044
1.041
1.037
1.034
1.030
1.026
1.023
1.019
1.016
1.012
1.008
1.005
1.001
0.9976
0.9939
0.9903
0.9867
0.9831
0.9759
0.9686
0.9614
0.9541
0.9469
0.9396
0.9323
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
16.51
15.96
15.39
14.82
14.24
13.66
13.06
12.46
12.16
11.85
11.54
11.23
10.92
10.60
10.29
9.968
9.646
9.322
8.996
8.667
8.336
8.003
7.667
7.329
6.988
6.644
6.298
5.950
5.599
5.245
4.530
3.804
3.066
2.317
1.557
0.7847
0.0000
56.0
55.3
54.5
53.7
52.9
52.1
51.2
50.2
49.7
49.2
48.7
48.1
47.6
47.0
46.4
45.8
45.1
44.5
43.8
43.1
42.3
41.5
40.7
39.9
39.0
38.1
37.1
36.0
34.9
33.8
31.1
28.1
24.5
19.9
13.6
3.5
—
56.0
55.3
54.6
53.9
53.2
52.4
51.6
50.7
50.3
49.8
49.4
48.9
48.4
47.9
47.4
46.9
46.3
45.8
45.2
44.6
44.0
43.4
42.7
42.0
41.3
40.6
39.9
39.1
38.3
37.5
35.7
33.7
31.6
29.2
26.5
23.5
20.0
56.0
55.4
54.7
54.0
53.2
52.5
51.7
50.9
50.4
50.0
49.6
49.1
48.6
48.1
47.6
47.1
46.6
46.1
45.5
45.0
44.4
43.8
43.1
42.5
41.8
41.2
40.5
39.7
39.0
38.2
36.5
34.7
32.7
30.6
28.1
25.5
22.5
56.0
55.3
54.7
53.9
53.2
52.4
51.6
50.8
50.3
49.9
49.4
49.0
48.5
48.0
47.5
46.9
46.4
45.8
45.3
44.7
44.1
43.5
42.8
42.1
41.5
40.7
40.0
39.2
38.4
37.6
35.8
33.9
31.8
29.4
26.8
23.8
20.4
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
17.31
16.74
16.15
15.56
14.96
14.34
13.73
13.10
12.78
12.46
12.14
11.81
11.49
11.16
10.83
10.49
10.16
9.816
9.474
9.130
8.783
8.433
8.080
7.725
7.368
7.007
6.644
6.277
5.908
5.536
4.783
4.018
3.240
2.450
1.647
0.8303
0.0000
57.0
56.3
55.5
54.8
53.9
53.1
52.2
51.2
50.7
50.2
49.7
49.1
48.6
48.0
47.4
46.8
46.1
45.5
44.8
44.1
43.3
42.5
41.7
40.9
40.0
39.0
38.1
37.0
35.9
34.7
32.1
29.1
25.4
20.8
14.5
4.3
—
57.0
56.3
55.6
54.9
54.2
53.4
52.6
51.7
51.3
50.8
50.3
49.9
49.4
48.9
48.4
47.8
47.3
46.7
46.1
45.5
44.9
44.3
43.6
42.9
42.2
41.5
40.7
40.0
39.1
38.3
36.5
34.5
32.3
29.9
27.1
24.0
20.3
57.0
56.3
55.7
55.0
54.2
53.5
52.7
51.9
51.4
51.0
50.5
50.1
49.6
49.1
48.6
48.1
47.6
47.0
46.5
45.9
45.3
44.7
44.1
43.4
42.7
42.0
41.3
40.6
39.8
39.0
37.3
35.4
33.4
31.2
28.7
25.9
22.8
57.0
56.3
55.7
54.9
54.2
53.4
52.6
51.8
51.3
50.9
50.4
49.9
49.4
48.9
48.4
47.9
47.4
46.8
46.2
45.6
45.0
44.4
43.7
43.1
42.4
41.6
40.9
40.1
39.3
38.5
36.7
34.7
32.5
30.1
27.4
24.3
20.7
57 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.66
93.29
89.86
86.38
82.86
79.28
75.65
73.82
71.97
70.11
68.24
66.35
64.45
62.53
60.60
58.66
56.70
54.72
52.73
50.73
48.71
46.67
44.62
42.56
40.47
38.37
36.26
34.13
31.98
27.63
23.21
18.72
14.15
9.51
4.80
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
129.1
123.9
118.7
113.6
108.4
103.3
98.09
92.93
90.35
87.77
85.19
82.60
80.02
77.44
74.86
72.28
69.70
67.12
64.53
61.95
59.37
56.79
54.21
51.63
49.05
46.46
43.88
41.30
38.72
36.14
30.98
25.81
20.65
15.49
10.33
5.163
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
393.4
380.0
366.6
353.1
339.7
326.2
312.8
299.3
292.6
285.9
279.2
272.5
265.7
259.0
252.3
245.6
238.9
232.1
225.4
218.7
212.0
205.2
198.5
191.8
185.1
178.4
171.6
164.9
158.2
151.5
138.0
124.6
111.1
97.70
84.26
70.82
57.37
Specific
volume, / (m3·kg⫺1)
1.127
1.119
1.112
1.104
1.096
1.089
1.081
1.073
1.070
1.066
1.062
1.058
1.054
1.050
1.047
1.043
1.039
1.035
1.031
1.027
1.024
1.020
1.016
1.012
1.008
1.004
1.001
0.9967
0.9929
0.9891
0.9814
0.9737
0.9660
0.9583
0.9506
0.9429
0.9352
1-66
Reference data
58 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.70
93.35
89.95
86.50
83.00
79.45
75.84
74.02
72.18
70.32
68.46
66.58
64.68
62.77
60.84
58.90
56.94
54.97
52.98
50.98
48.96
46.92
44.87
42.80
40.72
38.61
36.49
34.35
32.20
27.83
23.39
18.87
14.28
9.60
4.84
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
136.70
131.20
125.70
120.30
114.80
109.30
103.70
98.40
95.67
92.93
90.20
87.47
84.73
82.00
79.27
76.53
73.80
71.07
68.33
65.60
62.87
60.13
57.40
54.67
51.93
49.20
46.47
43.73
41.00
38.27
32.80
27.33
21.87
16.40
10.93
5.467
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
414.5
400.2
386.0
371.7
357.5
343.3
329.0
314.8
307.6
300.5
293.4
286.3
279.2
272.0
264.9
257.8
250.7
243.6
236.4
229.3
222.2
215.1
207.9
200.8
193.7
186.6
179.5
172.3
165.2
158.1
143.8
129.6
115.4
101.1
86.87
72.62
58.38
Specific
volume, / (m3·kg⫺1)
1.141
1.134
1.125
1.117
1.109
1.101
1.093
1.085
1.081
1.077
1.073
1.068
1.064
1.060
1.056
1.052
1.048
1.044
1.040
1.036
1.032
1.028
1.024
1.020
1.016
1.012
1.008
1.003
0.9993
0.9952
0.9871
0.9789
0.9707
0.9626
0.9544
0.9462
0.9380
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
18.15
17.55
16.94
16.32
15.70
15.06
14.42
13.76
13.43
13.10
12.76
12.42
12.08
11.74
11.39
11.04
10.69
10.33
9.976
9.615
9.252
8.885
8.516
8.143
7.767
7.389
7.007
6.622
6.234
5.843
5.050
4.244
3.424
2.590
1.742
0.8788
0.0000
58.0
57.3
56.5
55.8
54.9
54.1
53.2
52.2
51.7
51.2
50.7
50.1
49.6
49.0
48.4
47.8
47.1
46.5
45.8
45.1
44.3
43.5
42.7
41.9
41.0
40.0
39.0
38.0
36.9
35.7
33.1
30.0
26.3
21.7
15.3
5.1
—
58.0
57.3
56.6
55.9
55.2
54.4
53.6
52.7
52.3
51.8
51.3
50.8
50.3
49.8
49.3
48.8
48.2
47.7
47.1
46.5
45.9
45.2
44.5
43.9
43.1
42.4
41.6
40.8
40.0
39.1
37.3
35.3
33.0
30.5
27.7
24.4
20.6
58.0
57.3
56.7
56.0
55.2
54.5
53.7
52.8
52.4
52.0
51.5
51.0
50.6
50.1
49.6
49.1
48.5
48.0
47.4
46.8
46.2
45.6
45.0
44.3
43.6
42.9
42.2
41.4
40.7
39.8
38.1
36.2
34.1
31.8
29.3
26.4
23.1
58.0
57.3
56.7
55.9
55.2
54.4
53.6
52.7
52.3
51.8
51.4
50.9
50.4
49.9
49.4
48.9
48.3
47.8
47.2
46.6
46.0
45.3
44.7
44.0
43.3
42.5
41.8
41.0
40.2
39.3
37.5
35.5
33.2
30.8
28.0
24.8
21.1
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
19.02
18.39
17.76
17.12
16.47
15.81
15.14
14.46
14.11
13.77
13.41
13.06
12.70
12.35
11.98
11.62
11.25
10.88
10.50
10.13
9.745
9.361
8.973
8.583
8.189
7.791
7.390
6.986
6.578
6.167
5.332
4.484
3.619
2.739
1.843
0.9302
0.0000
59.0
58.3
57.5
56.8
56.0
55.1
54.2
53.2
52.7
52.2
51.7
51.2
50.6
50.0
49.4
48.8
48.2
47.5
46.8
46.1
45.3
44.5
43.7
42.9
42.0
41.0
40.0
39.0
37.9
36.7
34.0
31.0
27.3
22.6
16.2
5.9
—
59.0
58.3
57.6
56.9
56.2
55.4
54.6
53.7
53.2
52.8
52.3
51.8
51.3
50.8
50.3
49.8
49.2
48.6
48.0
47.4
46.8
46.1
45.5
44.8
44.1
43.3
42.5
41.7
40.9
40.0
38.1
36.0
33.7
31.2
28.3
24.9
20.9
59.0
58.3
57.7
57.0
56.2
55.5
54.7
53.8
53.4
52.9
52.5
52.0
51.5
51.0
50.5
50.0
49.5
48.9
48.4
47.8
47.2
46.5
45.9
45.2
44.5
43.8
43.1
42.3
41.5
40.7
38.9
37.0
34.8
32.5
29.8
26.9
23.4
59.0
58.3
57.7
56.9
56.2
55.4
54.6
53.7
53.3
52.8
52.4
51.9
51.4
50.9
50.4
49.8
49.3
48.7
48.1
47.5
46.9
46.3
45.6
44.9
44.2
43.4
42.7
41.9
41.0
40.2
38.3
36.2
34.0
31.4
28.5
25.2
21.4
59 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.73
93.41
90.05
86.62
83.15
79.62
76.03
74.22
72.39
70.54
68.69
66.81
64.92
63.02
61.09
59.16
57.20
55.23
53.25
51.25
49.23
47.19
45.13
43.06
40.97
38.86
36.74
34.59
32.43
28.04
23.58
19.03
14.41
9.69
4.89
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
144.7
138.9
133.2
127.4
121.6
115.8
110.0
104.2
101.3
98.42
95.53
92.63
89.74
86.84
83.95
81.05
78.16
75.26
72.37
69.47
66.58
63.68
60.79
57.90
55.00
52.11
49.21
46.32
43.42
40.53
34.74
28.95
23.16
17.37
11.58
5.790
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
436.8
421.7
406.6
391.5
376.4
361.3
346.2
331.1
323.6
316.0
308.5
300.9
293.4
285.8
278.3
270.7
263.2
255.6
248.1
240.5
233.0
225.4
217.9
210.3
202.8
195.2
187.7
180.2
172.6
165.1
150.0
134.9
119.8
104.7
89.58
74.48
59.39
Specific
volume, / (m3·kg⫺1)
1.157
1.149
1.140
1.131
1.123
1.114
1.105
1.097
1.092
1.088
1.084
1.080
1.075
1.071
1.066
1.062
1.058
1.054
1.049
1.045
1.041
1.036
1.032
1.028
1.023
1.019
1.015
1.010
1.006
1.002
0.9930
0.9843
0.9756
0.9669
0.9583
0.9496
0.9409
Properties of humid air
1-67
60 °C DRY-BULB
Percentage
saturation,
μ/%
Relative
humidity,
φ /%
100
96
92
88
84
80
76
72
70
68
66
64
62
60
58
56
54
52
50
48
46
44
42
40
38
36
34
32
30
28
24
20
16
12
8
4
0
100.00
96.77
93.48
90.14
86.75
83.30
79.80
76.23
74.43
72.61
70.78
68.92
67.06
65.17
63.28
61.36
59.43
57.48
55.51
53.53
51.52
49.50
47.47
45.41
43.34
41.24
39.13
37.00
34.84
32.67
28.27
23.78
19.21
14.54
9.79
4.94
0.00
Value of stated parameter per kg dry air
Moisture
content, g
/ (g·kg⫺1)
153.3
147.2
141.1
134.9
128.8
122.7
116.5
110.4
107.3
104.3
101.2
98.14
95.06
91.99
88.93
85.86
82.79
79.73
76.66
73.60
70.53
67.46
64.40
61.33
58.26
55.20
52.13
49.06
46.00
42.93
36.80
30.66
24.53
18.40
12.27
6.133
0.000
Specific
enthalpy, h
/ (kJ·kg⫺1)
460.4
444.4
428.4
412.4
396.4
380.4
364.4
348.4
340.4
332.4
324.4
316.4
308.4
300.4
292.4
284.4
276.4
268.4
260.4
252.4
244.4
236.4
228.4
220.4
212.4
204.4
196.4
188.4
180.4
172.4
156.4
140.4
124.4
108.4
92.40
76.40
60.40
Specific
volume, / (m3·kg⫺1)
1.173
1.164
1.155
1.146
1.137
1.128
1.118
1.109
1.105
1.100
1.096
1.091
1.086
1.082
1.077
1.073
1.068
1.063
1.059
1.054
1.050
1.045
1.041
1.036
1.031
1.027
1.022
1.018
1.013
1.008
0.9991
0.9899
0.9806
0.9714
0.9622
0.9529
0.9437
Vapour
pressure,
pv / kPa
Dew point
temperature,
θd / ⬚C
Adiabatic
saturation
temperature,
θ * / ⬚C
Wet bulb temperature
Screen,
θ ⬘sc / ⬚C
Sling,
θ ⬘sl / ⬚C
19.92
19.28
18.62
17.96
17.28
16.59
15.90
15.19
14.83
14.46
14.10
13.73
13.36
12.98
12.60
12.22
11.84
11.45
11.06
10.66
10.26
9.861
9.455
9.046
8.632
8.215
7.795
7.370
6.941
6.508
5.631
4.737
3.826
2.897
1.950
0.9848
0.0000
60.0
59.3
58.6
57.8
57.0
56.1
55.2
54.3
53.8
53.2
52.7
52.2
51.6
51.0
50.4
49.8
49.2
48.5
47.8
47.1
46.3
45.6
44.7
43.9
43.0
42.0
41.0
40.0
38.9
37.7
35.0
31.9
28.2
23.5
17.1
6.8
—
60.0
59.3
58.6
57.9
57.2
56.4
55.6
54.7
54.2
53.8
53.3
52.8
52.3
51.8
51.3
50.7
50.2
49.6
49.0
48.4
47.8
47.1
46.4
45.7
45.0
44.2
43.4
42.6
41.8
40.9
38.9
36.8
34.5
31.8
28.8
25.3
21.2
60.0
59.3
58.7
58.0
57.2
56.5
55.7
54.8
54.4
53.9
53.5
53.0
52.5
52.0
51.5
51.0
50.4
49.9
49.3
48.7
48.1
47.5
46.8
46.2
45.5
44.7
44.0
43.2
42.4
41.5
39.7
37.8
35.6
33.1
30.4
27.3
23.7
60.0
59.3
58.7
57.9
57.2
56.4
55.6
54.7
54.3
53.8
53.4
52.9
52.4
51.9
51.4
50.8
50.3
49.7
49.1
48.5
47.9
47.2
46.5
45.8
45.1
44.4
43.6
42.8
41.9
41.0
39.1
37.0
34.7
32.1
29.1
25.7
21.7
2-1
2
2.1
Properties of water and steam
Introduction
References
Tables of data
2.1
Introduction
The data presented in Tables 2.1, 2.2, and 2.3 are based
upon the tables prepared by the National Engineering
Laboratory(1), augmented as necessary by further values
obtained by interpolation from the tables of Mayhew and
Rogers(2).
Other data have been published, e.g. UK Steam Tables in SI
Units(3). These tables differ slightly from the NEL Steam
Tables. For building services applications, these variations
are not significant. However, for critical applications the
latest internationally agreed tables should be consulted.
The units and symbols used are as follows:
The values quoted were in all cases derived from NEL
Table 2, except for Prandtl numbers, which were obtained
by Lagrangian interpolation from Mayhew and Rogers,
page 10.
Table 2.2 lists values of the saturation vapour pressure,
specific heat capacity, dynamic viscosity, density (specific
mass) and of the specific enthalpy and Prandtl numbers of
the saturated liquid and vapour at round values of temperature.
The values quoted were derived as follows:
—
vapour pressure, density (as reciprocal of volume)
and specific enthalpy from NEL Table 1.
—
specific heat capacity, dynamic viscosity and
Prandtl numbers (all by Lagrangian interpolation)
from Mayhew and Rogers, page 10.
cf
Specific heat capacity (kJ·kg–1·K–1)
hf
Specific enthalpy (saturated liquid) (kJ·kg–1)
hg
Specific enthalpy (saturated vapour) (kJ·kg–1)
hfg
Specific latent heat of evaporation (kJ·kg–1)
p
Absolute pressure (kPa)
ps
Absolute saturation pressure (kPa)
v
Specific volume (m3·kg–1)
(Pr)f
Prandtl number (saturated liquid)
(Pr)g
Prandtl number (saturated vapour)
θ
Temperature (°C)
θs
Temperature (saturation) (°C)
References
μf
Dynamic viscosity (saturated liquid) (μPa·s)
1
ρ
Density (specific mass) (kg·m–3)
Steam Tables 1964 (Edinburgh: National Engineering
Laboratory/Her Majesty’s Stationery Office) (1964)
2
Mayhew Y R and Rogers G F C Thermodynamics and transport
properties of fluids (Oxford: Blackwell) (1989)
3
UK Steam Tables in SI units (Oxford: Butterworth-Heinemann)
(1970)
Table 2.1 lists values of saturation temperature, specific
volume, specific enthalpies of saturated liquid and vapour
and the specific latent heat of evaporation at round values
of absolute pressure.
Table 2.3 lists values of specific enthalpy for superheated
steam at round values of absolute pressure for a restricted
range of final temperatures.
The values quoted were in all cases derived from NEL
Table 3.
2-2
Reference data
Table 2.1 Properties of saturated steam
Absolute
pressure,
p / kPa
Temperature,
θs / ⬚C
Specific enthalpy
In saturated
liquid, hf
/ (kJ·kg⫺1)
Latent heat
of evaporation,
hfg / (kJ·kg⫺1)
In saturated
vapour, hg
/ (kJ·kg⫺1)
Specific
volume, v
/ (m3·kg⫺1)
Specific
heat capacity
of vapour, cf
/ (kJ·kg⫺1·K⫺1)
Prandtl
number,
(Pr)g
Absolute
pressure,
p / kPa
1
2
4
6
8
6.98
17.51
28.98
36.18
41.53
29.3
73.5
121.4
151.5
173.9
2484.3
2459.5
2432.4
2415.3
2402.5
2513.6
2533.0
2553.9
2566.8
2576.4
129.205
67.010
34.805
23.742
18.104
1.86
1.87
1.88
1.88
1.89
1.03
1.03
1.02
1.02
1.02
1
2
4
6
8
10
20
30
40
50
45.83
60.09
69.13
75.89
81.35
191.8
251.5
289.3
317.7
340.6
2392.2
2357.7
2335.4
2318.6
2304.9
2584.1
2609.1
2624.8
2636.3
2645.4
14.673
7.648
5.228
3.992
3.239
1.89
1.91
1.93
1.94
1.95
1.03
1.03
1.03
1.03
1.04
10
20
30
40
50
60
70
80
90
100
85.95
89.96
83.51
96.71
99.63
359.9
376.8
391.7
405.2
417.5
2293.2
2282.9
2273.7
2265.4
2257.7
2653.1
2659.7
2665.4
2670.6
2675.2
2.731
2.364
2.087
1.869
1.694
1.96
1.97
1.98
1.99
2.01
1.04
1.04
1.04
1.04
1.04
60
70
80
90
100
110
120
130
140
150
102.32
104.81
107.13
109.32
111.37
428.8
439.3
449.2
458.4
367.5
2250.6
2244.0
2237.8
2231.9
2226.3
2679.5
2683.3
2686.9
2690.3
2693.4
1.549
1.428
1.325
1.237
1.159
2.02
2.03
2.04
2.05
2.05
1.05
1.05
1.05
1.05
1.05
110
120
130
140
150
160
170
180
190
200
113.32
115.17
116.93
118.62
120.23
475.4
483.2
490.7
497.9
504.7
2221.0
2215.9
2211.1
2206.4
2201.9
2696.4
2699.1
2701.8
2704.2
2706.6
1.091
1.031
0.977
0.929
0.886
2.06
2.07
2.07
2.08
2.09
1.06
1.06
1.06
1.06
1.06
160
170
180
190
200
210
220
230
240
250
121.78
123.27
124.71
126.09
127.43
511.3
517.6
523.7
529.6
535.4
2197.6
2193.4
2189.3
2185.4
2181.6
2708.9
2711.0
2713.1
2715.0
2716.9
0.846
0.810
0.777
0.747
0.719
2.10
2.11
2.12
2.13
2.13
1.06
1.07
1.07
1.07
1.07
210
220
230
240
250
260
270
280
290
300
128.73
129.99
131.21
132.39
133.54
540.9
546.2
551.5
556.5
561.4
2177.8
2174.2
2170.7
2167.3
2163.9
2718.7
2720.5
2722.2
2723.8
2725.4
0.693
0.669
0.646
0.625
0.606
2.14
2.15
2.16
2.16
2.17
1.07
1.08
1.08
1.08
1.08
260
270
280
290
300
310
320
330
340
350
134.66
135.76
136.82
137.86
138.88
566.2
570.9
575.5
579.9
584.3
2160.6
2157.4
2154.3
2151.2
2148.2
2726.9
2728.4
2729.8
2731.1
2732.5
0.587
0.570
0.554
0.539
0.524
2.18
2.19
2.20
2.20
2.21
1.09
1.09
1.09
1.09
1.10
310
320
330
340
350
360
370
380
390
400
139.87
140.84
141.79
142.72
143.63
588.5
592.7
596.8
600.8
604.7
2145.2
2142.3
2139.5
2136.7
2133.9
2733.8
2735.0
2736.3
2737.5
2738.6
0.510
0.497
0.485
0.473
0.462
2.21
2.22
2.22
2.23
2.24
1.10
1.10
1.10
1.11
1.11
360
370
380
390
400
410
420
430
440
450
144.52
145.39
146.25
147.09
147.92
608.5
612.3
616.0
619.6
623.2
2131.2
2128.6
2125.9
2123.4
2120.8
2739.8
2740.9
2741.9
2743.0
2744.0
0.452
0.442
0.432
0.423
0.414
2.24
2.25
2.26
2.27
2.28
1.11
1.11
1.11
1.12
1.12
410
420
430
440
450
460
470
480
490
500
148.73
149.53
150.31
151.09
151.85
626.7
630.1
633.5
636.8
640.1
2118.2
2115.8
2113.4
2111.0
2108.6
2745.0
2746.0
2746.9
2747.8
2748.7
0.405
0.397
0.389
0.382
0.375
2.28
2.29
2.29
2.30
2.31
1.12
1.13
1.13
1.13
1.13
460
470
480
490
500
Properties of water and steam
2-3
Table 2.1 Properties of saturated steam — continued
Absolute
pressure,
p / kPa
Temperature,
θs / ⬚C
Specific enthalpy
In saturated
liquid, hf
/ (kJ·kg⫺1)
Latent heat
of evaporation,
hfg / (kJ·kg⫺1)
In saturated
vapour, hg
/ (kJ·kg⫺1)
Specific
volume, v
/ (m3·kg⫺1)
Specific
heat capacity
of vapour, cf
/ (kJ·kg⫺1·K⫺1)
Prandtl
number,
(Pr)g
Absolute
pressure,
p / kPa
520
540
560
580
600
153.33
154.77
156.16
157.52
158.84
646.5
652.8
658.8
664.7
670.4
2104.0
2099.4
2095.0
2090.7
2086.4
2750.5
2752.2
2753.8
2755.4
2756.8
0.361
0.349
0.337
0.326
0.316
2.32
2.33
2.34
2.35
2.37
1.13
1.14
1.14
1.14
1.14
520
540
560
580
600
620
640
660
680
700
160.12
161.38
162.60
163.79
164.96
676.0
681.5
686.8
692.0
697.1
2082.3
2078.2
2074.2
2070.3
2066.4
2758.3
2759.9
2761.0
2762.3
2763.5
0.306
0.297
0.288
0.280
0.273
2.38
2.39
2.40
2.41
2.43
1.15
1.15
1.16
1.16
1.16
620
640
660
680
700
720
740
760
780
800
166.10
167.21
168.30
169.37
170.41
702.0
706.9
711.7
716.4
720.9
2062.7
2058.9
2055.3
2051.7
2048.2
2764.7
2765.8
2767.0
2768.0
2769.1
0.266
0.259
0.252
0.246
0.240
2.44
2.45
2.47
2.48
2.49
1.17
1.17
1.17
1.18
1.18
720
740
760
780
800
820
840
860
880
900
171.44
172.45
173.43
174.40
175.36
725.4
729.8
734.2
738.4
742.6
2044.7
2041.2
2037.8
2034.5
2031.2
2770.1
2771.1
2772.0
2772.9
2773.8
0.235
0.229
0.224
0.220
0.215
2.51
2.52
2.53
2.55
2.56
1.18
1.19
1.19
1.20
1.21
820
840
860
880
900
920
940
960
980
1000
176.29
177.21
178.12
179.01
179.88
746.8
750.8
754.8
758.7
762.6
2028.0
2024.7
2021.6
2018.4
2015.3
2774.7
2775.6
2776.4
2777.2
2777.9
0.210
0.206
0.202
0.198
0.194
2.57
2.58
2.60
2.61
2.62
1.21
1.21
1.22
1.22
1.23
920
940
960
980
1000
1100
1200
1300
1400
1500
184.06
187.96
191.60
195.04
198.28
781.1
798.4
814.7
830.0
844.6
2000.4
1986.2
1972.6
1959.6
1947.1
2781.5
2784.6
2787.3
2789.7
2791.8
0.177
0.163
0.151
0.141
0.132
2.67
2.71
2.76
2.81
2.86
1.25
1.26
1.27
1.29
1.30
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
201.37
204.30
207.10
209.79
212.37
858.5
871.8
884.5
896.8
908.6
1935.1
1923.4
1912.1
1901.1
1890.4
2793.6
2795.2
2796.6
2797.8
2798.9
0.124
0.117
0.110
0.105
0.100
2.91
2.96
3.01
3.07
3.13
1.31
1.33
1.35
1.36
1.37
1600
1700
1800
1900
2000
2200
2400
2600
2800
3000
217.24
221.78
226.03
230.04
233.84
930.0
951.9
971.7
990.5
1008.3
1869.7
1850.0
1831.0
1812.7
1795.0
2800.6
2801.9
2802.7
2903.2
2803.4
0.091
0.083
0.077
0.071
0.067
3.19
3.25
3.36
3.45
3.53
1.39
1.41
1.43
1.44
1.46
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
237.44
240.88
244.16
247.31
250.33
1025.4
1041.8
1057.6
1072.7
1087.4
1777.9
1761.2
1744.9
1728.9
1713.4
2803.3
2803.0
2802.4
2802.1
2801.7
0.062
0.059
0.055
0.052
0.050
3.60
3.68
3.77
3.86
3.94
1.49
1.53
1.57
1.59
1.60
3200
3400
3600
3800
4000
2-4
Reference data
Table 2.2 Properties of water at saturation
Temperature,
θs / ⬚C
Absolute vapour
pressure, ps
/ kPa
Specific heat
capacity, cf
/ (kJ·kg⫺1·K⫺1)
Dynamic
viscosity,
lf /(lPa·s)
Density,
/ (kg·m⫺3)
Specific enthalpy
of liquid, hf
/ (kJ·kg⫺1)
Prandtl
number,
(Pr)g
Temperature,
θs / ⬚C
0.01
1
2
3
4
0.61
0.66
0.71
0.76
0.81
4.2100
4.2096
4.2088
4.2075
4.2059
1782
1724
1669
1616
1565
999.8
999.8
999.9
999.9
999.9
0.00
4.17
8.39
12.60
16.80
13.61
13.11
12.64
12.18
11.75
0.01
1
2
3
4
5
6
7
8
9
0.87
0.93
1.00
1.07
1.15
4.2040
4.2019
4.1997
4.1974
4.1952
1517
1471
1427
1385
1344
999.9
999.9
999.9
999.8
999.7
21.01
25.21
29.41
33.61
37.81
11.33
10.93
10.55
10.19
9.85
5
6
7
8
9
10
11
12
13
14
1.23
1.31
1.40
1.50
1.60
4.1930
4.1913
4.1897
4.1883
4.1871
1306
1269
1234
1201
1169
999.7
999.6
999.4
999.3
999.2
42.00
46.19
50.38
54.57
58.75
9.52
9.21
8.92
8.64
8.37
10
11
12
13
14
15
16
17
18
19
1.70
1.82
1.94
2.06
2.20
4.1860
4.1852
4.1845
4.1839
4.1834
1138
1108
1080
1053
1027
999.0
998.9
998.7
998.6
998.4
62.94
67.13
71.31
75.49
79.68
8.12
7.88
7.64
7.42
7.20
15
16
17
18
19
20
21
22
23
24
2.34
2.49
2.64
2.81
2.98
4.1830
4.1826
4.1821
4.1817
4.1814
1002
978
955
932
911
998.2
997.9
997.7
997.5
997.2
83.86
88.04
92.23
96.41
100.59
7.00
6.81
6.62
6.44
6.27
20
21
22
23
24
25
26
27
28
29
3.17
3.36
3.56
3.78
4.00
4.1810
4.1806
4.1801
4.1797
4.1794
890
870
851
833
815
997.0
996.7
996.5
996.2
995.9
104.77
108.95
113.13
117.31
121.49
6.11
5.95
5.80
5.66
5.52
25
26
27
28
29
30
31
32
33
34
4.24
4.49
4.75
5.01
5.32
4.1790
4.1787
4.1784
4.1782
4.1781
798
781
765
749
734
995.6
995.3
995.0
994.6
994.3
125.67
129.85
134.03
138.20
142.38
5.39
5.26
5.14
5.02
4.91
30
31
32
33
34
35
36
37
38
39
5.62
5.94
6.27
6.62
6.99
4.1780
4.1781
4.1782
4.1784
4.1787
719
705
692
678
666
994.0
993.6
993.3
993.0
992.6
146.56
150.74
154.92
159.09
163.27
4.80
4.69
4.59
4.49
4.39
35
36
37
38
39
40
41
42
43
44
7.38
7.78
8.20
8.64
9.10
4.1790
4.1794
4.1798
4.1802
4.1806
653
641
629
618
606
992.2
991.8
991.4
991.0
990.6
167.45
171.63
175.81
179.99
184.17
4.30
4.21
4.13
4.05
3.97
40
41
42
43
44
45
46
47
48
49
9.58
10.09
10.61
11.16
11.74
4.1810
4.1812
4.1815
4.1817
4.1818
596
586
576
566
556
990.2
989.8
989.3
988.9
988.5
188.35
192.53
196.71
200.90
205.08
3.89
3.81
3.74
3.67
3.60
45
46
47
48
49
50
51
52
53
54
12.33
12.96
13.61
14.29
15.00
4.1820
4.1822
4.1823
4.1825
4.1828
547
538
529
521
512
988.0
987.6
987.2
986.7
986.2
209.26
213.44
217.62
221.81
225.99
3.53
3.47
3.40
3.35
3.29
50
51
52
53
54
Properties of water and steam
2-5
Table 2.2 Properties of water at saturation — continued
Temperature,
θs / ⬚C
Absolute vapour
pressure, ps
/ kPa
Specific heat
capacity, cf
/ (kJ·kg⫺1·K⫺1)
Dynamic
viscosity,
lf /(lPa·s)
Density,
/ (kg·m⫺3)
Specific enthalpy
of liquid, hf
/ (kJ·kg⫺1)
Prandtl
number,
(Pr)g
Temperature,
θs / ⬚C
55
56
57
58
59
15.74
16.51
17.31
18.15
19.02
4.1830
4.1833
4.1837
4.1841
4.1845
504
496
489
481
474
985.7
985.2
984.7
984.3
983.7
230.17
234.35
238.54
242.72
246.81
3.23
3.17
3.12
3.06
3.01
55
56
57
58
59
60
61
62
63
64
19.92
20.86
21.84
22.85
23.91
4.1850
4.1856
4.1861
4.1867
4.1874
467
460
453
447
440
983.2
982.7
982.1
981.6
981.1
251.09
255.27
259.46
263.65
267.83
2.96
2.91
2.87
2.82
2.78
60
61
62
63
64
65
66
67
68
69
25.01
26.15
27.33
28.56
29.84
4.1880
4.1886
4.1892
4.1898
4.1904
434
428
422
416
410
980.5
979.9
979.4
978.9
978.3
272.02
276.21
280.40
284.59
288.78
2.74
2.70
2.66
2.62
2.58
65
66
67
68
69
70
71
72
73
74
31.16
32.53
33.96
35.43
36.96
4.1910
4.1916
4.1921
4.1927
4.1934
404
399
394
388
383
977.7
977.1
976.6
976.0
975.4
292.97
297.16
301.35
305.54
309.74
2.54
2.50
2.47
2.43
2.39
70
71
72
73
74
75
76
77
78
79
38.55
40.19
41.89
43.65
45.47
4.1940
4.1947
4.1955
4.1962
4.1971
378
373
369
364
359
974.9
974.3
973.6
973.1
972.5
313.93
318.12
322.32
326.52
330.71
2.36
2.33
2.30
2.27
2.24
75
76
77
78
79
80
81
82
83
84
47.36
49.31
51.33
53.42
55.57
4.1980
4.1990
4.1999
4.2009
4.2020
355
350
346
342
338
971.8
971.2
970.6
969.9
969.3
334.91
339.11
343.31
347.51
351.71
2.21
2.18
2.15
2.12
2.10
80
81
82
83
84
85
86
87
88
89
57.80
60.11
62.49
64.95
67.49
4.2030
4.2040
4.2050
4.2060
4.2070
334
330
326
322
318
968.6
968.0
967.3
966.7
966.0
355.91
360.11
364.32
368.52
372.73
2.07
2.05
2.02
2.00
1.97
85
86
87
88
89
90
91
92
93
94
70.11
72.82
75.61
78.49
81.46
4.2080
4.2090
4.2099
4.2109
4.2120
314
311
307
304
300
965.3
964.7
964.0
963.3
962.7
376.94
381.15
385.36
389.57
393.78
1.95
1.93
1.90
1.88
1.85
90
91
92
93
94
95
96
97
98
99
84.53
87.69
90.94
94.30
97.76
4.2130
4.2141
4.2153
4.2165
4.2177
297
294
291
287
284
961.9
961.2
960.5
959.8
959.1
397.99
402.30
406.42
410.63
414.84
1.83
1.81
1.79
1.77
1.76
95
96
97
98
99
100
102
104
106
108
101.33
108.78
116.68
125.04
133.90
4.2190
4.2217
4.2246
4.2274
4.2302
281
275
269
264
259
958.3
956.9
955.5
954.0
952.6
419.06
427.50
435.95
444.40
452.86
1.74
1.70
1.67
1.63
1.60
100
102
104
106
108
110
112
114
116
118
143.26
153.16
163.61
174.64
186.28
4.2330
4.2357
4.2386
4.2414
4.2445
253
248
243
239
234
951.0
949.5
948.0
946.3
944.7
461.32
469.79
478.26
486.74
495.20
1.57
1.54
1.51
1.48
1.45
110
112
114
116
118
2-6
Table 2.2
Reference data
Properties of water at saturation — continued
Temperature,
θs / ⬚C
Absolute vapour
pressure, ps
/ kPa
Specific heat
capacity, cf
/ (kJ·kg⫺1·K⫺1)
Dynamic
viscosity,
lf /(lPa·s)
Density,
/ (kg·m⫺3)
Specific enthalpy
of liquid, hf
/ (kJ·kg⫺1)
Prandtl
number,
(Pr)g
Temperature,
θs / ⬚C
120
122
124
126
128
198.53
211.44
225.03
239.32
254.34
4.2480
4.2527
4.2576
4.2621
4.2661
230
226
223
219
216
943.1
941.5
939.9
938.3
936.5
503.70
512.20
520.70
529.20
537.80
1.42
1.40
1.38
1.36
1.34
120
122
124
126
128
130
132
134
136
138
270.12
286.68
304.05
322.27
341.36
4.2700
4.2740
4.2780
4.2820
4.2860
212
209
206
202
199
934.8
933.1
931.4
929.6
927.9
546.30
554.90
563.40
572.00
580.50
1.32
1.30
1.28
1.26
1.25
130
132
134
136
138
140
142
144
146
148
361.36
382.28
404.18
427.07
450.99
4.2900
4.2934
4.2975
4.3029
4.3102
196
193
191
189
187
926.1
924.3
922.5
920.6
918.8
589.10
597.70
606.30
614.90
623.50
1.23
1.21
1.20
1.18
1.17
140
142
144
146
148
150
152
154
156
158
475.97
502.05
529.26
557.64
587.23
4.3200
4.3250
4.3320
4.3380
4.3440
185
183
181
178
176
916.9
915.1
913.2
911.2
909.3
632.20
640.80
649.40
658.10
666.80
1.17
1.16
1.15
1.13
1.12
150
152
154
156
158
160
162
164
166
168
618.05
650.14
683.55
718.31
754.45
4.3500
4.3557
4.3614
4.3674
4.3735
174
172
170
167
165
907.4
905.4
903.4
901.5
899.4
675.50
684.20
692.90
701.60
710.40
1.11
1.10
1.09
1.07
1.06
160
162
164
166
168
170
172
174
176
178
792.03
831.07
871.61
913.71
957.39
4.3800
4.3875
4.3954
4.4034
4.4117
163
161
159
157
155
897.3
895.3
893.3
891.2
889.1
719.1
727.9
736.7
745.5
754.3
1.05
1.04
1.03
1.02
1.01
170
172
174
176
178
180
182
184
186
188
1002.7
1049.7
1098.4
1148.9
1201.1
4.4200
4.4277
4.4354
4.4434
4.4515
153
151
150
148
146
886.9
884.8
882.6
880.4
879.7
763.1
772.0
780.8
789.7
798.6
1.00
0.99
0.99
0.98
0.98
180
182
184
186
188
190
192
194
196
198
1255.2
1311.2
1369.2
1429.1
1491.0
4.4600
4.4695
4.4794
4.4894
4.4997
145
144
142
141
139
876.0
873.8
781.5
869.3
867.0
807.5
816.4
825.4
834.4
843.4
0.97
0.96
0.96
0.95
0.95
190
192
194
196
198
200
205
210
215
220
1555.1
1724.5
1908.0
2106.3
2320.1
4.5100
4.5337
4.5600
4.5937
4.6300
138
134
131
128
125
864.7
858.8
852.8
846.6
840.3
852.4
875.0
897.7
920.6
943.7
0.94
0.92
0.91
0.90
0.90
200
205
210
215
220
225
230
235
240
245
2550.4
2797.0
3063.5
3348.0
3652.4
4.6644
4.7000
4.7387
4.7800
4.8231
122
120
118
115
112
833.9
827.3
820.6
813.6
806.5
966.9
990.3
1013.8
1037.6
1061.6
0.90
0.89
0.89
0.88
0.87
225
230
235
240
245
250
3977.6
4.8700
110
799.2
1085.8
0.87
250
Properties of water and steam
2-7
Table 2.3 Enthalpy of superheated steam
Absolute
pressure,
p / kPa
Saturation
temperature,
θs / ⬚C
Enthalpy of superheated steam (/ kJ·kg⫺1) for stated final steam temperature / ⬚C
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
2676
2717
2715
2713
2711
2708
2757
2755
2754
2752
2751
2797
2796
2794
2793
2792
2836
2835
2834
2833
2832
2876
2875
2874
2873
2872
2915
2914
2914
2913
2912
2955
2954
2953
2953
2952
2995
2994
2993
2993
2992
3034
3034
3033
3033
3032
3075
3074
3074
3073
3073
3115
3114
3114
3114
3113
3155
3155
3155
3154
3154
3196
3196
3195
3195
3195
3237
3237
3236
3236
3236
3278
3278
3278
3277
3277
100
120
140
160
180
99.6
104.8
109.3
113.3
116.9
200
220
240
260
280
120.2
123.3
126.1
128.7
131.2
2749
2747
2745
2743
2742
2790
2789
2787
2786
2785
2831
2830
2829
2827
2826
2871
2870
2969
2868
2867
2911
2911
2910
2909
2908
2951
2951
2950
2949
2949
2992
2991
2990
2990
2989
3032
3031
3031
3030
3030
3072
3072
3071
3071
3070
3113
3112
3112
3111
3111
3153
3153
3153
3152
3152
3194
3194
3194
3193
3193
3235
3235
3235
3234
3234
3277
3276
3276
3276
3275
300
340
380
420
460
133.5
137.9
141.8
145.4
148.7
2740
2736
2783
2780
2777
2774
2771
2825
2823
2820
2818
2816
2866
2865
2863
2861
2859
2907
2906
2904
2902
2901
2948
2947
2945
2944
2942
2988
2987
2986
2985
2984
3029
3028
3027
3026
3025
3070
3069
3068
3067
3066
3110
3110
3109
3108
3107
3151
3151
3150
3149
3148
3192
3192
3191
3190
3189
3234
3233
3232
3232
3231
3275
3274
3274
3273
3273
500
600
700
800
900
151.8
158.8
165.0
170.4
175.4
2768
2759
2813
2807
2800
2793
2785
2857
2851
2846
2840
2835
2899
2895
2890
2886
2881
2941
2937
2933
2930
2926
2982
2979
2976
2973
2969
3024
3021
3018
3015
3012
3065
3062
3060
3057
3055
3106
3104
3102
3099
3097
3147
3145
3143
3141
3139
3189
3187
3185
3183
3181
3230
3229
3227
3225
3223
3272
3270
3269
3267
3266
1000
1200
1400
1600
1800
179.9
188.0
195.0
201.4
207.1
2778
2829
2817
2803
2876
2867
2856
2846
2834
2922
2914
2905
2897
2888
2966
2959
2952
2945
2937
3009
3003
2997
2991
2985
3052
3047
3042
3036
3031
3095
3090
3085
3081
3076
3137
3133
3129
3124
3120
3179
3176
3172
3168
3164
3222
3218
3215
3211
3207
3264
3261
3257
3254
3251
2000
2500
3000
3500
4000
212.4
223.9
233.8
242.5
250.3
2822
2878
2853
2825
2930
2909
2888
2864
2838
2978
2961
2943
2925
2904
3025
3011
2995
2980
2963
3071
3058
3045
3031
3017
3116
3105
3093
3081
3069
3160
3150
3140
3129
3118
3204
3195
3185
3176
3166
3248
3239
3231
3222
3214
4500
5000
6000
7000
8000
257.4
263.9
275.6
285.8
295.0
2809
2883
2859
2806
2946
2927
2887
2841
2787
3003
2988
2955
2919
2880
3056
3043
3016
2987
2955
3107
3096
3072
3048
3021
3156
3146
3126
3104
3082
3205
3196
3177
3158
3139
9000
10000
303.3
311.0
2835
2784
2921
2884
2993
2964
3058
3033
3118
3097
3-1
3
Heat transfer
3.1
Introduction
3.2
Heat transfer principles
3.3
Heat transfer practice
3.1
Introduction
This chapter of CIBSE Guide C is concerned with heat
transfer. It is divided into a theoretical part and a practical
part. The theoretical part provides a number of basic
equations and discussion for convection, conduction and
radiation together with a brief review of mass transfer.
This part is not exhaustive and for a detailed treatment of
the subject, the references cited at the end of the section
should be consulted.
The practical part is intended for reference in dealing with
common heat transfer problems related to the built environment. This is structured as: external environment;
internal environment; human body. This part concludes
with a treatment of components and equipment. For
particular products, the manufacturer’s data should be
consulted. Example calculations are provided where
appropriate to aid understanding and application.
In view of the number of equations, the notation is given at
the start so as to provide a point of reference for the section.
3.1.1
Notation
D
Characteristic plate dimension (m)
E
Emissivity factor (dimensionless)
Eb i
Emissive power for surface i (W·m–2)
F
View factor (or form factor or angle factor)
Fi j
View factor of surface j with respect to surface i
Fp–N
Mean view factor between a person and a room
surface (see Figures 3.3–3.7)
Fr
Radiation exchange factor for two surfaces
(dimensionless)
F12
View factor of surface 2 with respect to surface 1
Gr
Grashof number (= γ g ρ2 D3 Δθ / μ2 )
H
Height of vertical rectangular enclosure (m)
I
Intensity of solar radiation (W·m–2)
Iclo
Thermal resistance of clothing (clo)
Ji , Jj
Radiosity for surfaces i and j respectively (W·m–2)
L
Length of cylinder, pipe, etc. (m)
M
Mass flow rate (kg·s–1)
A
Area (m2)
N
Number of surfaces within the enclosure
Ac
Cross-sectional area (m2)
NTU
Number of exchanger heat transfer units
Nu
Nusselt number (= h D/ λ)
Ai , Aj Area for surface i or j (m2)
As
Heated or cooled surface area (m2)
P
Perimeter (m)
Asi
Inside surface area (m2)
Pr
Prandtl number (= cp μ / λ)
Aso
Outside surface area (m2)
R
Thermal resistance (m2·K·W–1)
A1
Area of surface 1, etc. (m2)
Ra
Thermal resistance of air gap (m2·K·W–1)
C
A constant (specified in text)
Cmax
Cmin
Ra
Rayleigh number (= Gr·Pr)
Fluid heat capacity rate (greater)
(W·K–1)
Re
Thermal resistance of earth (m2·K·W–1)
Fluid heat capacity rate (smaller)
(W·K–1)
Re
Reynolds number (= ρ v D/ μ)
3-2
Rn
Reference data
Thermal resistance of insulation (m2·K·W–1)
hcn
Convective heat transfer coefficient for natural
convection at internal surfaces (W·m–2·K–1)
hco
Outside surface convective heat transfer coefficient
(W·m–2·K–1)
hfg
Latent heat of evaporation of water (kJ·kg–1)
(= 2450 kJ·kg–1at 20 °C)
(m2·K·W–1)
Rse
External surface resistance
R1
Thermal resistance of element 1, etc. (m2·K·W–1)
T
Absolute temperature (K)
Ta
Absolute temperature of air (K)
Tfs
Absolute temperature of fictitious surface (given
by an area and emissivity-weighted average of
other surfaces) (K)
hr
Radiative heat transfer coefficient (W·m–2·K–1)
hsi
Inside surface heat transfer coefficient (or film
coefficient) (W·m–2·K–1)
Ti
Absolute surface temperature for surface i (K)
hso
Tr
Absolute mean radiant temperature (K)
Outside surface heat transfer coefficient (or film
coefficient) (W·m–2·K–1)
Trs
Absolute mean radiant temperature of the sky (K)
(= 253 + θa)
l
Length (m)
m
Burial depth (m)
Ts
Absolute temperature of heat emitting/absorbing
surface (K)
n
An index (specified in text)
Tsw
Absolute temperature of water surface (K)
psw
Saturated vapour pressure at water surface (kPa)
T1
Absolute temperature of surface 1, etc. (K)
pv
Vapour pressure of moisture in air remote from
water surface (kPa)
U
Overall thermal transmittance (W·m–2·K–1)
qv
Volume flow rate (m3·s–1)
Uc
Thermal transmittance
(W·m–2·K–1)
r
Radius (m)
Ut
Thermal transmittance of water tank (W·m–2·K–1)
ri
Inside radius (m)
W
Rate of water evaporation (kg·m–2·s–1)
ro
Outside radius (m)
Z
Heat capacity rate ratio
r1
Radius of surface 1, etc. (m)
a
Length (m)
x
Thickness (m)
a1
Length of side 1, etc. (m)
xn
Thickness of insulation (m)
b
Width (m)
xw
Wall thickness (m)
c
Velocity (m·s–1)
xzi
Inside fouling substance thickness (m)
cas
Air velocity at water surface (m·s–1)
xzo
Outside fouling substance thickness (m)
car
Air velocity in room (m·s–1)
x1
Thickness of element 1, etc. (m)
cp
Specific heat capacity at constant pressure
(kJ·kg–1·K–1)
Δθ
Temperature difference (K)
Δθca
Difference between clothing and air temperatures
(K)
Δθl
Logarithmic mean temperature difference (K)
Δθm
Change in temperature per unit length (K·m–1)
Δθtg
Greatest terminal temperature difference (K)
of
clean
surfaces
(m·s–1)
cs
Surface wind speed
d
Diameter (m)
dh
Hydraulic mean (equivalent) diameter (m)
di
Inside diameter (m)
dic
Inside diameter of casing (m)
Δθsa
Surface to air temperature difference (K)
di1
Inside diameter of element 1, etc. (m)
Δθts
Smallest terminal temperature difference (K)
do
Outside diameter (m)
Δθλ
Temperature difference between opposite surfaces
of a solid with thermal conductivity λ (K)
don
Outside diameter of insulation (m)
Outside diameter of pipe (m)
Φ
dop
Actual rate of heat transfer (for a heat exchanger)
(W)
do1
Outside diameter of element 1, etc. (m)
Φc
f
A function (specified in text)
Rate of convective heat transfer by a heated or
cooled surface (W)
fcl
Clothing area factor (ratio of clothed to unclothed
body surface area)
Φi
Net rate of heat transfer by radiation to surface i
(W)
g
Acceleration due to gravity (m·s–2) (= 9.81 m·s–2)
Φmax
Maximum possible rate of heat transfer (for a heat
exchanger) (W)
h
Heat transfer coefficient (W·m–2·K–1)
hc
Convective heat transfer coefficient (W·m–2·K–1)
Φr
Rate of radiant heat transfer by a heated or cooled
surface (W)
hci
Inside surface convective heat transfer coefficient
(W·m–2·K–1)
Φt
Total rate of heat transfer by a heated or cooled
surface (W)
Heat transfer
α
3-3
Angle (degrees)
λ*
Pipe friction coefficient (see chapter 4)
μ
Dynamic viscosity (Pa·s)
γ
Coefficient of cubical expansion
ε
Emissivity
ν
Kinematic viscosity (m2·s–1)
εi
Emissivity of surface i
ξ
Layer thickness (m)
εw
Emissivity of water
ρ
Density (kg·m–3)
ε1
Emissivity of surface 1, etc.
σ
η
Heat exchanger effectiveness
Stefan-Boltzmann constant (W·m–2·K–4)
(= 5.67 × 10–8 W·m–2·K–4)
θ
Celsius temperature (°C)
φ
Heat exchange per unit area (W·m–2)
θa
Air temperature (°C)
φc
Convective heat exchange per unit area (W·m–2)
θc
Casing temperature (°C)
φcd
Conductive heat exchange per unit area (W·m–2)
θcfi
Cold fluid inlet temperature (°C)
φe
Evaporative heat exchange per unit area (W·m–2)
θcfo
Cold fluid outlet temperature (°C)
φhb
θcl
Clothing surface temperature (°C)
Heat loss by convection per unit area of the human
body (W·m–2)
θd
Temperature at down stream end of pipe or duct
section (°C)
φr
Radiative heat exchange per unit area (W·m–2)
θe
Ground temperature (°C)
θf
Free stream fluid temperature (°C)
θfs
Area weighted
temperature (°C)
θhfi
Hot fluid inlet temperature (°C)
θhfo
Hot fluid outlet temperature (°C)
θhi
Shell inlet temperature (°C)
θho
Shell outlet temperature (°C)
θi
Inside temperature (°C)
θj
Surface temperature of each of the surfaces
comprising the fictitious surface (°C)
θm
Mean of the inlet and outlet fluid temperatures in
a tube (°C)
θn
Insulation temperature (°C)
θo
Outside temperature (°C)
θs
Surface temperature (°C)
θsi
Inside surface temperature (°C)
Convection is a mode of heat transfer between a moving
fluid and a solid, liquid or gas. Convection can be free or
forced. Free convection is the movement of a fluid primarily due to buoyancy forces. Forced convection is the
movement of a fluid due primarily to external means, i.e. a
mechanical pump or a pressure difference induced by a
fan, for example. Many complications can arise due to the
following reasons:
θso
Outside surface temperature (°C)
(a)
θs1
Temperature of surface 1, etc. (°C)
θti
Tube inlet temperature (°C)
θto
Tube outlet temperature (°C)
θu
Temperature at upstream end of pipe or duct
section (°C)
The flow can be laminar (having smooth and
orderly streamlines) or turbulent (having irregularly interwoven streamlines) or separated (having
a reversed flow along the fluid boundary, as with
cylinders in cross flow with vortex shedding).
There is a transitional state between laminar and
turbulent flow.
θw
Water temperature (°C)
(b)
There is a boundary layer between the fluid and
the other medium.
θsw
Water surface temperature (°C)
(c)
λ
Thermal conductivity (W·m–1·K–1)
λe
Thermal conductivity of earth (W·m–1·K–1)
At the base of the boundary layer the fluid is
stationary with respect to the other medium. This
means that there is a thin layer in which only
conduction and mass transfer can take place.
λn
Thermal conductivity of insulation (W·m–1·K–1)
(d)
λw
Thermal conductivity of wall (W·m–1·K–1)
λzi
Inside surface thermal conductivity of fouling
substance (W·m–1·K–1)
For heat to be transferred within any substance, a
temperature gradient must exist. In a fluid,
therefore, there are density gradients which cause
buoyancy forces.
λzo
Outside surface thermal conductivity of fouling
substance (W·m–1·K–1)
average
(K–1)
fictitious
3.2
surface
Heat transfer principles
The mechanisms of heat transfer are convection,
conduction, radiation and mass transfer. Theoretical and
experimental work has led to the development of many
equations that express the magnitude of heat transfer by
these modes. Some of the commonly used equations are
given in this chapter of CIBSE Guide C, but a wider range
of heat transfer equations, especially those for particular
applications, may be found in some of the many references
given at the end of the chapter.
3.2.1
Convection
The remainder of this section is structured as follows.
Empirical correlations (in the form of dimensionless
3-4
Reference data
numbers) are presented for the conditions of free and
forced convection and for a range of common situations.
These situations are classified as being either external
flows (over surfaces) or internal flows (inside enclosures).
In both cases the flow regimes can be either laminar or
turbulent. For each situation, guidance is given regarding
its particular characteristics and the use of the appropriate
equation.
The following equations can be used for heating or
cooling applications provided that no phase change (e.g.
condensation or evaporation) occurs since, for most
practical purposes, the theoretical differences between
heating and cooling are usually negligible. The equations
are valid (strictly) only for ideal fluids, i.e. with nonvariable property values, and for incompressible flow.
Table 3.1(1) gives typical values of the convection coefficients for various situations.
If the fluid property values change significantly over the
temperature range investigated, account can be taken of
them by using values at some mean temperature(2).
Table 3.1 Typical convection coefficients, hc , for different modes of
convection (reproduced from Engineering Thermodynamics, Work and Heat
Transfer by G F C Rogers and Y R Mayhew by permission of Pearson
Education Ltd. ©Longman Group UK Ltd.)
Mode
Coefficient / W·m–2·K–1
Forced convection:
— gases and dry vapours
— liquids
— liquid metals
10 to 103
102 to 104
5 × 103 to 4 × 104
Free convection:
— gases and dry vapours
— liquids
0.5 to 103
50 to 3 × 103
Condensation:
— filmwise
— dropwise
5 × 102 to 3 × 104
2 × 104 to 5 × 105
Boiling
5 × 102 to 2 × 104
3.2.1.1
Free convection over surfaces
Table 3.2 presents correlations for the average Nu number
for free convection over various geometries for a range of
Ra numbers.The appropriate characteristic length is also
given. The flow regime is determined by calculating the
Ra number for a particular situation; note that the power
of the Ra number is usually 0.25 for laminar flow and 0.33
for turbulent flow. All fluid properties are evaluated at the
average of the surface temperature (θs) and the free stream
fluid temperature (θf ).
3.2.1.2
Free convection inside enclosures
Table 3.3 presents correlations for the average Nu number
for free convection within enclosures of various
geometries for a range of Ra numbers. Here, the term
‘enclosures’ refers to cavities such as those found in walls,
double glazed windows or solar collectors etc. The
characteristic length is the distance between the hot and
cold surfaces. All fluid properties are evaluated at the
average of the hot and cold surface temperatures.
3.2.1.3
Forced convection over flat plates
For laminar flow over an entire horizontal flat surface, the
average Nu number, based on plate length D, over the
entire plate is given by:
NuD = 0.664 ReD1/2 Pr1/3
(3.27)
for Pr ≥ 0.6 and ReD < 5 × 105.
For turbulent flow over an entire horizontal flat surface,
the average Nu number, based on plate length D, over the
entire plate is given by:
NuD = 0.037 ReD4/5 Pr1/3
(3.28)
for 0.6 ≤ Pr ≤ 60 and 5 × 105 ≤ ReD ≤ 107.
Equations 3.27 and 3.28 are restricted to the condition of
uniform surface temperature over a smooth plate(3).
However, for other conditions, including uniform heat
flux over a plate, unheated sections, combinations of
laminar and turbulent flows, entry region effects and
evaluation of local Nu numbers, the reader should consult
references 3 and 4. Note that fluid properties are evaluated
at the average of the surface temperature (θs ) and the free
stream fluid temperature (θf ).
3.2.1.4
Cross flow
Table 3.4 presents correlations for the average Nu number
for forced convection over circular and non-circular
smooth cylinders and surfaces in cross flow for a range of
Re numbers. The characteristic length is also shown. All
fluid properties are evaluated at the average of the surface
temperature (θs) and the free stream fluid temperature (θf ).
3.2.1.5
Forced convection inside enclosures
(tubes)
Table 3.5 presents correlations for the average Nu number
for forced convection, fully developed, laminar flow inside
tubes of circular and non-circular cross-sections. Laminar
flow in tubes occurs for ReD < 2300. Values of Nu numbers
are given for the following thermal conditions at the
surface of the tube:
(a)
Constant surface temperature: a typical situation for
which this condition is applicable would be when
a phase change process takes place at the outer
surface of the tube (such as condensation or
evaporation).
(b)
Constant heat flux: a typical example would be
when the tube is subjected to uniform heating
such as from an electric element.
For turbulent flow within circular and non-circular tubes
and ducts, the following correlation can be used:
NuD = 0.023 ReD4/5 Prn
(3.41)
where n = 0.4 for heating (θs > θm) and 0.3 for cooling
(θs < θm), where θm is the mean fluid temperature,
evaluated as the average of the inlet and outlet fluid
temperatures of the tube:
θm = (θti + θto) / 2
(3.42)
Heat transfer
3-5
Table 3.2 Empirical correlations for the average Nusselt number for free convection over surfaces (adapted from Introduction to Thermodynamics and
Heat Transfer by Y A Cengel (1997) by permission of The McGraw-Hill Companies)
Geometry
Characteristic
length
Ra range
Nusselt number, Nu
Vertical plate
D
104–109
109–1013
Nu = 0.59 Ra1/4
Nu = 0.1 Ra1/3
Entire range
0.387 Ra1/6
Nu = 0.825 + ——————————–
8/27
[1 + (0.492 / Pr) 9/16]
θs
D
(3.1)
(3.2)
(
)
2
(3.3)
(complex but more accurate)
Inclined plate
Use vertical plate equations as a first degree of approximation
D
Replace g with g cos h in the formula for Gr, see page 3-1, for
Ra < 109
α
D
Horizontal plate (surface
area = A and perimeter = P)
(a)
Upper surface of a hot
plate or lower surface of
a cold plate
Lower surface of a hot
plate or upper surface of
a cold plate
θs
104–107
107–1011
Nu 0.54 Ra1/4
Nu 0.15 Ra1/3
(3.4)
(3.5)
105–1011
Nu 0.27 Ra1/4
(3.6)
θs
Hot surface
(b)
A/ P
Hot surface
Vertical cylinder
A vertical cylinder can be treated as a vertical plate when:
D
35 D
d ≥ ——
Gr1/4
θs
(3.7)
D
d
Horizontal cylinder
θs
d
105–1012
(
)
0.387 Ra1/6
Nu = 0.6 + —————————–
8/27
[1 + (0.559 / Pr) 9/16]
2
(3.8)
d
π d/2
Sphere
d
Ra ≤ 1011
Pr ≥ 0.7
0.589 Ra1/4
Nu = 2 + —————————–
4/9
[1 + (0.469 / Pr) 9/16]
(3.9)
3-6
Reference data
Table 3.3 Empirical correlations for the average Nusselt number for free convection in enclosures (the characteristic length D is as indicated on the
respective diagram) (adapted from Introduction to Thermodynamics and Heat Transfer by Y A Cengel (1997) by permission of The McGraw-Hill
Companies)
Geometry
Fluid
H/D
Pr range
Ra range
Nusselt number, Nu
Vertical rectangular
or cylindrical enclosure
Gas or
liquid
—
—
< 2000
Nu 1
Gas
11–42
11–42
0.5–2
(2 × 103)–(2 × 105)
0.5–2
(2 × 105)–107
1–20 000
104–107
1–20
106–109
H
Liquid
D
10–40
1–40
Inclined rectangular
enclosure
Nu 0.197 Ra1/ 4
Nu 0.073 Ra1/ 3
(3.10)
1/9
( )
( )
H
D
H
D
Nu 0.42 Pr0.012 Ra1/ 4
Nu 0.046 Ra1/3
(3.11)
1/9
(3.12)
( )
H
D
0.3
(3.13)
(3.14)
Use the correlations for vertical enclosures
as a first degree approximation for a 20º
by replacing g with g cos h in the formula for
Ra, see page 3-1.
Cold
D
α
Hot
Horizontal rectangular
enclosure (hot surface
at the top)
Gas or
liquid
—
—
—
Nu 1
(3.15)
Horizontal rectangular
enclosure (hot surface
at the bottom)
Gas or
liquid
—
—
< 1700
Nu 1
(3.16)
Gas
—
0.5–2
(1.7 × 103)–(7 × 103)
Nu 0.059 Ra0.4
(3.17)
—
0.5–2
(7 × 103)–(3.2 × 105)
Nu 0.212 Ra1/4
(3.18)
—
0.5–2
3.2 × 105
Nu 0.061 Ra1/3
(3.19)
—
1–5000
(1.7 × 103)–(6 × 103)
Nu 0.012 Ra0.6
(3.20)
—
1–5000
(6 × 103)–(3.7 × 104)
Nu 0.375 Ra0.2
(3.21)
—
1–20
(3.7 × 104)–108
Nu 0.13 Ra0.3
(3.22)
—
1–20
108
Nu 0.057 Ra1/3
(3.23)
Cold
D
Liquid
Hot
Concentric horizontal
cylinders
D
Gas or
liquid
—
—
1–5000
1–5000
(6.3 × 103)–106
106–108
Nu 0.11 Ra0.29
Nu 0.40 Ra0.20
(3.24)
(3.25)
Concentric spheres
Gas or
liquid
—
0.7–4000
102–109
Nu 0.228 Ra0.226
(3.26)
D
Heat transfer
3-7
Table 3.4 Empirical correlations for the average Nusselt number for forced convection over circular and non-circular cylinders in cross flow(5,6)
(adapted from Introduction to Thermodynamics and Heat Transfer by Y A Cengel (1997) by permission of The McGraw-Hill Companies)
Cross section
Fluid
Re range
Nusselt number, Nu
Circle
Gas or liquid
0.4–4
4–40
40–4000
4000–40 000
40 000–400 000
Nu = 0.989 Re0.33 Pr1/3
Nu = 0.911 Re0.385 Pr1/3
Nu = 0.683 Re0.466 Pr1/3
Nu = 0.193 Re0.618 Pr1/3
Nu = 0.027 Re0.805 Pr1/3
(3.29)
(3.30)
(3.31)
(3.32)
(3.33)
Gas
5000–100 000
Nu = 0.102 Re0.675 Pr1/3
(3.34)
Gas
5000–100 000
Nu = 0.246 Re0.588 Pr1/3
(3.35)
Gas
5000–100 000
Nu = 0.153 Re0.638 Pr1/3
(3.36)
Gas
5000–19 500
19 500–100 000
Nu = 0.160 Re0.638 Pr1/3
Nu = 0.0385 Re0.782 Pr1/3
(3.37)
(3.38)
Gas
4000–15 000
Nu = 0.228 Re0.731 Pr1/3
(3.39)
Gas
2500–15 000
Nu = 0.248 Re0.612 Pr1/3
(3.40)
D
Square
D
Square (tilted 45)
D
Hexagon
D
Hexagon (tilted 45)
D
Vertical plate
D
Ellipse
D
3-8
Reference data
Table 3.5 Nusselt numbers for fully developed laminar flow in tubes of various cross sections
(hydraulic diameter dh = 4 Ac / P) (adapted from Introduction to Thermodynamics and Heat Transfer
by Y A Cengel (1997) by permission of The McGraw-Hill Companies)
a/b or a
Cross section of tube
Circle
Nusselt number, Nu
θs = const.
Φt = const.
—
3.66
4.36
—
3.35
4.00
1
2.98
3.61
1
2
3
4
6
8
2.98
3.39
3.96
4.44
5.14
5.60
7.54
3.61
4.12
4.79
5.33
6.05
6.49
8.24
1
2
4
8
16
3.66
3.74
3.79
3.72
3.65
4.36
4.56
4.88
5.09
5.18
10
30
60
90
120
1.61
2.26
2.47
2.34
2.00
2.45
2.91
3.11
2.98
2.68
d
Hexagon
Square
a
a
Rectangle
b
a
Ellipse
b
a
Triangle
α
Equation 3.41 is known as the Dittus-Boelter equation,
and has been confirmed by experiment(4) to be valid for
the range 0.7 ≤ Pr ≤ 160, and for ReD > 10000.
Friction coefficients may be obtained from chapter 4,
equation 4.5.
Flow in tubes is considered to be turbulent for Re > 3000
and laminar for Re < 2000.
3.2.2
Conduction
(3.43)
Conduction is the transfer of heat within substances from
positions of higher temperature to positions of lower
temperature. Within all substances, except metals,
conduction is primarily due to molecular movements
although internal radiation can be significant. Within
metals, most heat is transferred by free electrons(1).
Equation 3.43 is valid for the range 0.5 < Pr < 2000, and
2300 < ReD < 5 × 106.
The following equations assume that heat is transferred
steadily, one dimensionally, and that materials are
homogeneous and isotropic. These equations can be used
for heating or cooling applications and are based on
Fourier’s Law:
Another expression has been proposed(7) to cover the
range of ReD for the transitional and turbulent regimes:
(λ∗ /8) (ReD – 1000) Pr
NuD = —————————–——
1 + 12.7 (λ∗ /8)1/2 (Pr2/3 – 1)
where λ∗ is the friction coefficient.
Heat transfer
3-9
dθ
= –λ A —
—
dx
(3.44)
where λ is the thermal conductivity (W·m–1·K–1).
In practice, it is usually necessary to consider heat
transfer by conduction in two or three dimensions in
order to obtain the temperature distribution throughout
the medium of interest. To do this, it is necessary to
solve the Fourier conduction equation in its two- or
three-dimensional form. This can be achieved either
analytically (using the method of separation of variables), graphically (using the flux plotting method), or
numerically (using the finite difference technique). For
details of these methods see reference 4.
Non-steady state or transient heat transfer occurs in
situations where the boundary conditions are varying with
respect to time. In these instances, the methods stated
above can be used to solve the transient or non-steady
state conduction equation in one, two or three dimensions
as required(4). References 8 and 9 also contain methods for
solving such heat transfer problems. The availability of
powerful computers together with software for simulating
the dynamic thermal behaviour of buildings and systems
has meant that the numerical method is the most commonly used for producing practical solutions.
Chapter 5 of CIBSE Guide A(10) describes a number of
procedures that can be used for structural problems.
Complications arise when heat is conducted through
porous materials; this is because they are rarely dry, so
that there are transient periods at the end and beginning
of heat transfer during which moisture is also transferred.
Eventually, equilibrium states are reached, though
sometimes only after many months. Chapter 3 of CIBSE
Guide A(10) deals with the problem of moisture content in
more detail.
3.2.2.1
Table 3.6 Error in approximating a
cylinder to a flat surface
r+ξ
——
r
Error / %
1.2
1.1
1.05
1.025
1.0125
10
5
3
1.3
0.8
Note: r is the radius of cylinder and ξ
is the thickness of the layer
The criterion which describes whether the radii of curved
structures are large is:
r+ξ
——– ≈ 1
r
Table 3.6 gives percentage errors introduced to the value
of the heat transfer rate by using the above formulae for
various ratios of actual structure radii.
3.2.2.2
Conduction through cylindrical
structures
For a single element:
2 π λ L (θso – θsi )
Φ = ————––——–
do
ln –––
di
For multi-layered structures:
2 π L (θso – θsi )
Φ = ————
––——
R +R +...
(3.50)
x
do1
R1 = — ln –––
, etc.
λ1
di1
(3.51)
1
λ (θso – θsi) A
Φ = ————––—
x
( )
3.2.2.3
For multi-layered structures or pipes having large radii:
A
Φ = — (θso – θsi)
R
(3.46)
x1
x2
R = —– + — + . . . .
λ1
λ2
(3.47)
where:
These equations are valid for steady state conditions, i.e.
when the rate of heat transfer is constant with respect to
time, and in the direction of the temperature gradient.
2
where:
(3.45)
where x is the thickness of the element (m).
(3.49)
( )
Conduction through flat structures
For single layer flat structures and for pipes and curved
structures of large radii, the heat transfer rate is given by:
(3.48)
Heat flow through structures by
conduction and convection
The effects of convection from the surfaces of structures
can be included in the above formulae by the addition of
surface convective heat transfer coefficients. For multilayered flat structures or structures with large radii of
curvature with convective heat transfer on both exposed
surfaces, the heat transfer rate is given by:
A (θi – θo)
Φ = ————––—
——————
1
1
R1 + R2 + . . . + —– + —–
hci hco
where:
(3.52)
3-10
Reference data
x
R1 = —
λ1
(3.53)
It can be shown that the relation between the view factors
for two surfaces is:
F12 A1 = F21 A2
For multi-layered cylindrical structures:
2 π L (θi – θo)
Φ = ————––—————————
2
2
R1 + R2 + . . . + —–— + —–—
hci d
hco d
i
o
(3.54)
and that the heat exchange between two black body finite
areas is given by:
where:
x
do1
R1 = — ln ––– , etc.
λ1
di1
( )
(3.55)
For structures having continuous air spaces, the resistance
of the air space, which takes account of radiative, convective, and conductive heat transfer can also be included in
the above equations, see chapter 3 of CIBSE Guide A(10).
3.2.3
Radiation
Φ = A1 σ F12 (T14 – T24 )
(3.58)
Φ = A2 σ F21 (T14 – T24 )
(3.59)
3.2.3.1
Radiation between parallel
flat surfaces
For surfaces so placed that negligible radiation escapes
from between them, the heat exchange for grey body
radiation is given by(1):
Φ = σ ε12 A1 (T14 – T24 )
(3.60)
ε1 ε2
ε12 = ——————
ε1 + ε2 – ε1 ε2
(3.61)
where:
Radiation, in the context of heating, is the emission, from
a source, of electromagnetic waves having wavelengths
between those of visible light and those of radio waves.
Radiation heat transfer is governed by the StefanBoltzmann law for black bodies which can be written:
φ = σ T4
(3.57)
(3.56)
A black body is defined as one which absorbs totally all
radiation falling onto its surface. A grey body has a surface
which absorbs all wavelengths equally but does not absorb
all the radiation. Emissivity is defined as the ratio of the
total emissive power of a body to the total emissive power
of a black body at the same temperature. Some values of
emissivity are given in Tables 3.7, 3.8 and 3.9.
for A1 = A2.
3.2.3.2
Radiation between concentric
curved surfaces
The following equation is valid for grey body radiation
with or without a specular reflection, assuming negligible
edge losses:
φ = σ ε12 (T14 – T24 )
Equations for black body radiation are simple, but in
practice black body radiation does not often occur. Most
of the following equations assume that the reflective,
emissive and absorptive properties of the surfaces remain
constant with wavelength, i.e. grey body radiation is
assumed, though these equations are also valid for black
body radiation. Unless otherwise stated, all equations
require that reflections are non-specular, i.e. have no
directional properties.
where:
For problems involving surfaces which are so placed that a
significant proportion of the radiation emitted by one
surface does not fall upon the other surface, or escapes
from between the surfaces, or for problems involving
enclosures with varying surface temperatures, then the
following equations can be modified. These terms will
include view factors (otherwise known as form factors or
angle factors), which are functions of the geometry of the
surfaces only, and are a measure of the proportion of the
field of view of one surface which is occupied by the other
surface. Table 3.10 and Figure 3.1 contain view factors for
some of the more common geometries. References 11, 12,
and 13 contain further work and examples of view factors.
A comprehensive catalogue of view factor relations may be
found in reference 14.
Note that:
( )
1
A 1
ε12 = — + —–1 — – 1
ε1 A2 ε2
(3.62)
(3.63)
for A1 < A2.
Φ = φ A1
3.2.3.3
(3.64)
Radiation between small surfaces
well separated
For surfaces which are small compared with their distance
apart, the amount of radiation reflected back to the radiating
surface from the other surface is negligible. The heat
exchange for grey bodies is given by:
Φ = σ ε1 ε2 F12 A1 (T14 – T24 )
(3.65)
Heat transfer
3-11
Table 3.7 Absorptivity and emissivity: impermeable materials
Material
Condition (where known)
Absorptivity
Emissivity
Aluminium
Polished
Dull/rough polish
Anodised
0.10–0.40
0.40–0.65
—
0.03–0.06
0.18–0.30
0.72
—
0.216
0.91–0.93
0.82–0.89
0.85–0.98
—
—
0.90–0.98
0.852–0.928
—
Aluminium surfaced roofing
Asphalt
Newly laid
Weathered
Block
Asphalt pavement
Bitumen/felt roofing
0.86–0.89
0.91
Bitumen pavement
0.86–0.89
0.90–0.98
0.30–0.50
0.40–0.065
—
0.03–0.05
0.20–0.30
0.59–0.61
0.34
—
Brass
Polished
Dull
Anodised
Bronze
Copper
Polished
Dull
Anodised
0.18–0.50
0.40–0.065
0.64
0.02–0.05
0.20–0.30
0.60
Glass
Normal
Hemispherical
*
*
0.88
0.84
Iron
Unoxidised
Bright/polished
Oxidised
Red rusted
Heavily rusted
—
0.40–0.65
—
—
0.737
0.05
0.20–0.377
0.736–0.74
0.61–0.65
0.85–0.94
Iron, cast
Unoxidised/polished
Oxidised
Strongly oxidised
—
—
—
0.21–0.24
0.64–0.78
0.95
Iron, galvanised
New
Old/very dirty
0.64–0.66
0.89–0.92
0.22–0.28
0.89
Lead
Unoxidised
Old/oxidised
—
0.77–0.79
0.05–0.075
0.28–0.281
Rubber
Hard/glossy
Grey/rough
—
—
0.945
0.859
Steel
Unoxidised/polished/stainless
Oxidised
0.20
0.20
0.074–0.097
0.79–0.82
Tin
Highly polished/unoxidised
0.10–0.40
0.043–0.084
Paint:
— aluminium
— zinc
0.30–0.55
0.30
0.27–0.67
0.95
Polyvinylchloride (pvc)
—
0.90–0.92
0.3–0.5
0.85–0.95
—
0.80–0.98
0.55
0.05
0.045–0.053
0.11–0.25
Tile
Light colour
Varnish
Zinc
Polished
Oxidised
* See manufacturers’ data
3.3.2.4
3.2.3.5
Radiation between an enclosure
and a contained surface
For a comparatively small area within an enclosure, it is
possible to assume that the enclosure behaves like a black
body. This is because negligible radiation from the
enclosed body will be reflected back to it from the enclosure. Hence F12 = 1 and ε2 = 1 so:`
Φ = σ ε1 A1 (T14 – T24 )
(3.66)
Surface 1 has the smaller area and this equation is valid for
grey body radiation.
Equivalent radiative heat transfer
coefficient
Very often it is useful to have a heat transfer coefficient for
radiation heat exchange such that:
Φ = f hr A1 (θs1 – θs2 )
(3.67)
The function f = f (ε12 , F12) is extremely complex unless
either the radiation is black body (in which case ε12 = 1)
or the radiation is independent of the geometry (in which
case F12 = F21 = 1).
3-12
Reference data
Table 3.8 Absorptivity and emissivity: inorganic, porous materials
Table 3.9 Absorptivity and emissivity: hygroscopic materials
Material
Material
Condition
(where known)
Absorptivity
Emissivity
New
Very dirty
—
—
—
0.61
0.83
0.96
0.93–0.94
0.90
0.95–0.96
0.95–0.96
Glazed/light
Light
Dark
0.25–0.36
0.36–0.62
0.63–0.89
0.85–0.95
0.85–0.95
0.85–0.95
0.73
0.93
0.60–0.69
0.81–0.82
0.85–0.95
0.85–0.95
Concrete
— tile
— block
0.65–0.80
0.65–0.80
0.56–0.69
0.85–0.95
0.85–0.95
0.94
Plaster
0.30–0.50
0.91
Stone:
— granite (red)
— limestone
— marble
— quartz
— sandstone
— slate
0.55
0.33–0.53
0.44–0.592
—
0.54–0.76
0.79–0.93
0.90–0.93
0.90–0.93
0.90–0.93
0.90
0.90–0.93
0.85–0.98
Asbestos:
— board
— paper
— cloth
— cement
Brick
Cement mortar,
screed
Clay tiles
Red, brown
Purple/dark
Condition
(where known)
Absorptivity
Emissivity
Paper
— white, bond
—
0.25–0.28
0.091–0.94
—
Cloth:
— cotton, black
— cotton, deep blue
— cotton, red
— wool, black
— felt, black
— fabric (unspecified)
0.67–0.98
0.82–0.83
0.562
0.75–0.88
0.775–0.861
—
—
—
—
—
—
0.89–0.92
Wood:
— beach
— oak
— spruce
— walnut
—
—
—
—
0.94
0.89–0.90
0.82
0.83
Aligned parallel rectangles
Perpendicular rectangles with common edge
0.7
1
x
0.6
A2
y
A2
Y
0.5
5
3
2
1.5
1.0
D
A1
A1
0.5
Ratio Y/ D = 10
x
z
Ratio y/ x=0.1
0.2
F12
0.4
0.2
1.0
1.5
0.2
2.0
4.0
0.1
0
0.1
6.0
10.0
1.0
Ratio Z / X
0.1
0.2
0.05
0.1
0.03
20.0
10
0.02
0.01
0.1
Concentric cylinders of finite length
1.0
L
0.4
0.3
F12
0.4
0.6
0.3
0.8
0.6
0.3
0.2
0.5
1
2
Ratio X/D
5
10
20
A2
Coaxial disks
r1
0.8
1.0
r2
0.9
R1 = r1 /r2 ; R2 = L / r2
0.8
0.6
R2 = 8
6 5
4
3
F12
1.0
0.5
0.6
0.5
0.4
0.2
0.1
0
0.6
R1
0.8
0.3
5
0.2
0.1
R2 =
0.4
1.25
0.4
0.2
0.2
0.6
0.5
1
0
1
1.5
=
2
R
2
0.4
L
r1
2
0.7
F21
r
2 2
R1=r1 / L
R2=r2 / L
0.8
1.0
0
0.1
0.2 0.3 0.4 0.6
1.0
1/ R1
R2 = 0.3
2
3 4 5 6 8 10
Figure 3.1 Radiation view factor for various geometries (from ASHRAE Handbook: Fundamentals 2005. © American Society of Heating, Refrigerating
and Air-Conditioning Engineers Inc. (www.ashrae.org))
Heat transfer
3-13
Table 3.10 View factors
Configuration
View factor
dA1
F12
w
l
{
{ [(
() ()
[(( ) ( ) ) ( ) ]
w
2l
w
l
A2
r
dA1
F12
w
y
1
2
2
1
A2
r
w 2
l
r
l
2
2
r
l
1
2
2
r
1 4
l
() ()
( ) () ) ()
w 2
y w
y
2
r 2
y 1
2
r 2
r
y 1 4 y
}
]}
1
0.5
2
0.5
dA1
θ λ
F12 sin2 k cos h
A2
dA1
w
F12 z
y
1
2p
{[
y
(w 2
y2) 0.5
arctan
z
(w2
y2) 0.5
] [
z
(w2
z2) 0.5
arctan
y
(w2
z2) 0.5
]}
Fp
A2
dA1
[
F12 Fp cos w FN sin
w
w
F12 z
y
1
{
z
arctan
2p
w
w
(w2
arctan
y2) 0.5
z
y2) 0.5
(w2
]}
FN
A2
ψ
dA1
w
A2
r
A2
w
F12 A1
l
z
A1
y
F12 w
A3
A2
F32 {
1
2
2
pyz
[
1
p
[
[
r2 w 2 l 2
l2
{[
{[
4y
y
4w
y
w
arctan
ln
ln
[(
y (w2 z2 ) 0.5 arctan
w y arctan
w
] [
y
w
z
w
y
(w2 z2) (w2 y 2)
y2 (w2 y 2 z2)
(y 2 z2) (w2 y 2)
(w2
z
w
z2 )0.5
] [
] [
] [
]}
arctan
w2 (w2 y2 z2)
l2
w z arctan
] [
) ]}
2
r2 w2 l2
y
z
z2
4wy
4 r2
0.5
l2
] [
w2
2
ln
z (w2 y2) 0.5 arctan
w2 (w 2 y2 z2)
( y2 w2) (w2 z2)
z
(w2
z2 (w2 y 2 z2)
( y2 z2) (w2 z2)
]
]}
(w2 z2 )0.5
y
arctan
2
w
(w z2)0.5
ln
y2 )0.5
]
]
dA1
F1(2345) F12 F13 F14 F15
A2
A4
A3
A5
Notes: (1) the arrowhead indicates the direction of the normal to the radiating element; (2) in some configurations a particular distance has been taken
as unity, since view factors are independent of the scale.
3-14
Reference data
Table 3.11 Values of radiative heat transfer coefficient hr
θ 1 / °C
Values of hr (/ W·m–2·K–1) for stated values of θ 2 (/ °C)
–40
–20
0
5
10
15
20
25
30
40
50
–10
–5
0
5
10
3.5
3.6
3.7
3.8
3.9
3.9
4.0
4.1
4.3
4.4
4.4
4.5
4.6
4.7
4.9
4.5
4.6
4.7
4.9
5.0
4.6
4.8
4.9
5.0
5.1
4.8
4.9
5.0
5.1
5.3
4.9
5.0
5.2
5.3
5.4
5.0
5.2
5.3
5.4
5.6
5.2
5.3
5.4
5.6
5.7
5.5
5.6
5.7
5.9
6.0
5.8
5.9
6.0
6.2
6.3
15
20
25
30
40
4.1
4.2
4.3
4.4
4.7
4.5
4.6
4.8
4.9
5.2
5.0
5.2
5.3
5.4
5.7
5.1
5.3
5.4
5.6
5.9
5.3
5.4
5.6
5.7
6.0
5.4
5.6
5.7
5.9
6.2
5.6
5.7
5.9
6.0
6.3
5.7
5.9
6.0
6.2
6.5
5.9
6.0
6.2
6.3
6.6
6.2
6.3
6.5
6.6
7.0
6.5
6.6
6.8
7.0
7.3
50
60
70
80
90
5.0
5.3
5.6
5.9
6.3
5.5
5.8
6.1
6.5
6.8
6.0
6.4
6.7
7.1
7.4
6.2
6.5
6.9
7.2
7.6
6.3
6.7
7.0
7.4
7.8
6.5
6.8
7.2
7.5
7.9
6.6
7.0
7.3
7.7
8.1
6.8
7.1
7.5
7.9
8.3
7.0
7.3
7.7
8.1
8.4
7.3
7.7
8.0
8.4
8.8
7.6
8.0
8.4
8.8
9.2
Hence, for black body radiation, equation 3.67 can be
simplified to:
Φ = F12 hr A1 (θs1 – θs2 )
(3.68)
or, for grey body radiation (with F12 = 1):
Φ = ε12 hr A1 (θs1 – θs2 )
(3.69)
It can be shown that:
hr = σ (T1 + T2) (T12 + T22 )
(3.70)
Table 3.11 gives values of hr for various values of surface
temperature.
When T1 = T2 then:
hr = 4 σ T 3
3.2.4
A detailed treatment of mass transfer is beyond the scope
of this section. For a general introduction to mass transfer
the reader is referred to references 2, 4, 15 and 16.
Reference 1 contains data and procedures involving
mixtures (as well as most other aspects of thermodynamics) and reference 17 has a section that covers the
simple aspects of water sprays.
(3.71)
Mass transfer
Mass transfer can be described as the diffusion of one
substance into another. Most commonly, a liquid vapourises
into, or condenses from, a gas with an accompanying
variation of vapour concentration, i.e. partial pressure,
within the gas. This variation occurs within a boundary
layer.
In buildings and building services systems, the most
common examples of mass transfer are condensation,
humidification and evaporation. These examples can all
take place within air conditioning equipment and cooling
towers but the first and last examples often occur within
structures, such as during the drying out period of
buildings and condensation on walls and windows. For
these examples, the previous heat transfer equations are
not applicable.
Calculations for most mass transfer problems are quite
complex although generally the equations follow the form
of the convection heat transfer equations.
3.3
Heat transfer practice
3.3.1
External environment
At the external surfaces of buildings, heat transfer takes
place via the processes of convection and radiation. While
radiation heat loss is a function of surface temperature and
emissivity, convection heat loss is more complex, being a
function of a number of variables such as wind speed and
direction, flow regime and surface roughness. This makes
difficult the accurate determination of heat transfer at a
building surface.
3.3.1.1
Radiative exchange at external surfaces
The longwave radiation exchange at the external surface
of a building is dependent upon the difference between
the incoming longwave radiation from the external environment (sky, other buildings and the ground) and the
outgoing longwave radiation emitted from the surface of
the building in question. Normally, calculation of the
radiative exchange is simplified by the use of linear
expressions, rather than retaining the fourth power
temperature term. This linearisation is produced by the
introduction of a longwave radiation heat transfer coefficient, hr. In order to determine a value for hr , certain
approximations are necessary. One approximation is the
assumption that the external environment radiates as a
black body at external air temperature; the other
approximation is that the surrounding external environment can be assigned a view factor of unity. This leads to
a value for the radiation component (E × hr) of
4.0 W·m2·K1, where the emissivity factor (E) is the
product of the view factor and the emissivity of the
building surface(18).
Heat transfer
3.3.1.2
3-15
Convective exchange at external
surfaces
1.823
hcn = ——— (Δθsa)0.293
dh0.121
For design purposes, the exposure of buildings has been
classified into three categories based on near-surface wind
speeds: ‘sheltered’, ‘normal’ and ‘severe’ exposure (see
CIBSE Guide A(10), section 3.3.9.4). These exposure levels
correspond to wind speeds at roof surfaces of 1.0, 3.0 and
9.0 m.s1, respectively; at wall surfaces, the corresponding
near-surface wind speeds are 0.7, 2.0 and 6.0 m.s1,
respectively.
Wind speed at the surface cs and the convection
coefficient hc at the external surface have to date been
correlated using the following expression derived from
wind tunnel studies(19):
hc = 5.8 + 4.1 cs
(3.72)
This equation has been assumed to be valid for all external
wind speeds.
Use of this correlation with the wind speeds given above
leads to the design values of external surface resistance,
Rse , based on the following relation:
Rse = 1 / (hc + E hr)
(3.73)
These values for Rse are given in Table 3.9 of CIBSE Guide
A(10), for the three levels of exposure. In recent years,
however, a number of experiments to measure hc at the
external surface of actual buildings have been made. These
results are discussed below.
3.3.1.3
Full-scale external measurements
Reference 20 presents a review of full-scale measurements
for hc at building external surfaces, and has suggested the
following combined correlation for use by designers for
the case of ‘normal’ exposure:
hc = 16.7 cs0.5
(3.74)
for hc in W·m–2·K–1 and cs in m.s1 up to a surface wind
speed of 3.5 m·s–1. Substituting a value for cs of 2.0 m·s–1
leads to a value for hc of 23.6 W·m–2·K–1 and a corresponding modified value of the external surface resistance Rse
for normal exposure of 0.04 m2·K·W–1.
(3.75)
For a heated floor:
2.175
hcn = ——— (Δθsa)0.308
dh0.076
(3.76)
For a heated ceiling:
0.704
hcn = ——— (Δθsa)0.133
dh0.601
(3.77)
Here, Δθsa was the difference between the surface and air
temperatures (measured at 0.1 m from the surface for wall
and floor and at the centre of the enclosure for the case of
the ceiling); Δθsa values ranged between 5 and 25 K. In
these expressions, the value for dh was evaluated as 4 As /P.
Note that values for the internal surface resistance Rsi can
be estimated from a knowledge of appropriate convective
and radiative heat transfer coefficients. Values are given in
Table 3.10 of CIBSE Guide A(10).
3.3.2.2
Radiation exchange between internal
surfaces
For a multi-surface enclosure of N surfaces, each with
area A1, A2 . . . AN and with emissivities of e1, e2 . . . eN ,
respectively, the following equations can be used, based
on radiosity formulation methods (see, for example, any
standard heat transfer text), to determine the net rate of
heat exchange by radiation to each surface:
ei Ai (Ebi – Ji )
Φi = ——————
(1 – e i )
(3.78)
N
ei Ai (Ebi – Ji)
——————–
= ( Ji – Jj ) (Ai Fij )
(1 – ei)
j1
(3.79)
and:
R
3.3.2
Internal environment
For N surfaces, equation 3.79 results in a set of N linear
equations with unknowns J1, J2 . . . JN. For the surface ‘i’
at a known surface temperature Ti , knowledge of the value
for Ji permits calculation of the net rate of heat transfer by
radiation, qi, to the surface ‘i’ by use of equation (3.79).
3.3.2.1
Internal surface convection
coefficients
If the surface ‘i’ is considered to be a black body of known
temperature Ti , then its radiosity Ji is equal to its emissive
power Ebi , that is:
There have been several studies of internal surface
convection coefficients(21–24), showing that a range of
variation exists in the measured values. Reference 21
presents correlations that give typical values for
convective heat transfer coefficients at heated wall, floor
and ceiling surfaces of a room-sized test enclosure; the
correlations were expressed in terms of a hydraulic
diameter dh, and a temperature difference Δθsa, as follows.
For a heated wall:
Ebi = Ji = σ Ti 4
(3.80)
and the net rate of heat transfer by radiation to the black
surface ‘i’ can be determined from the following
expression:
N
Φi = R ( Ji – Jj ) (Ai Fij )
j1
(3.81)
3-16
Reference data
To calculate the rate of radiation exchange between
surfaces within the multi-surface enclosure, the following
rules of view factor algebra must be applied:
(a) Reciprocity rule:
Ai Fij = Aj Fji
(3.82)
(b) Summation rule:
N
R Fij = 1
(3.83)
Therefore:
ε1 A1
———
(Ebl – J1) = ( J1 – J2) (A1 F12)
(1 – ε1)
( J1 – J3) (A1 F13)
(3.86)
Similarly, for surface 2 (i 2):
ε2 A2
———
(Eb2 – J2) = ( J2 – J1) (A2 F21)
(1 – ε2 )
( J2 – J3) (A2 F23)
(3.87)
j1
Values of view factors for some of the more commonly
encountered geometries are given in Table 3.10 or Figure
3.1. From a knowledge of view factors and known values
of radiosities, for all surfaces, the net rate of heat transfer
by radiation to each surface can be determined using
equation 3.78.
Example 3.1
A cuboidal room is 6 m long, 4 m wide and 3 m high. It
contains a chilled ceiling of surface temperature 18 C, and
a floor of surface temperature 22 C; each of its four walls
is at a surface temperature of 25 C. Determine the net rate
of heat transfer by radiation to the ceiling and to the floor,
assuming that the walls act as a black body surface, and
that the emissivities of the ceiling and the floor are 0.9 and
0.85, respectively.
The ceiling is treated as surface 1, the floor as surface 2,
and all the four walls can be treated as a single surface,
surface 3. Figure 3.2 illustrates the arrangement:
Using equation 3.79, calculate the radiosities J1 and J2 for
surfaces 1 and 2, respectively:
J3 = σ T34
(3.88)
The view factors are then evaluated as follows.
F12 (parallel plates) is 0.34, found from Table 3.10, or from
a suitable chart of view factors for various geometries, as
given in Figure 3.1(25).
From equation 3.83:
F11 + F12 + F13 = 1
(3.89)
But F11 = 0 for a flat surface, so:
F13 = 1 – F12
(3.90)
Therefore, F13 = 1 – 0.34 = 0.66.
Similarly, F23 = 0.66.
The value for F21 can be found from equation 3.82:
For surface 1 (i 1):
3
ε1 A1
———
(Ebl – J1) = R ( J1 – Jj ) (A1 F1j )
(1 – ε1)
j1
A1 F12 = A2 F21
(3.84)
3
R ( J1 – Jj) (A1 Fij) = ( J1 – J1) (A1 F11)
( J1 – J2) (A1 F12)
( J1 – J3) (A1F13)
(3.91)
In this case, A1 = A2 , and so F21 = F12 = 0.34.
Equations 3.86 and 3.87 can now be solved (using matrix
inversion, for example) for J1 and J2 , since values for all
other terms are now known. In situations where there are
a large number of ‘grey’ surfaces, necessitating the
calculation of J-values, a solution can be obtained from
matrix inversion or from the use of a suitable computer
program.
but:
j1
Surface 3 is assumed to be a black body surface, therefore,
from equation 3.80:
(3.85)
Solution gives:
J1 = 410.06 W·m–2
Surface 1:
T1 = 291 K
ε1 = 0.9
J2 = 430.17 W·m–2
J3 = 447.14 W·m–2
Surface 3:
T3 = 298 K
ε 3 = 1.0
Surface 2:
T2 = 295 K
ε2 = 0.85
Figure 3.2 Example 3.1: illustration of room as a 3-surface enclosure
Finally, the values for the rates of heat transfer by
radiation to each surface, Φ1, Φ2 and Φ3 can now be
evaluated from equations 3.78 and 3.79, giving:
ε1 A1
Φ1 = ———
(Eb i – J1)
(1 – e1)
(3.92)
Heat transfer
3-17
Example 3.2
Hence:
0.9 × 6 × 4
Φ1 = ————– (5.67 × 108 × 2914 – 410.06)
(1 – 0.9)
= –749.9 W
Estimate the rate of heat removal by radiation by the
chilled ceiling of Example 3.1 for the same room conditions, but using the simplified technique for rooms.
Calculate θf s for the four walls and floor using equation
3.95:
Similarly, Φ2 = –103.3 W, and Φ3 = 854.1 W.
Thus, the ceiling removes radiant heat at a rate of 749.9 W,
while the floor removes 103.3 W.
To check the results, the total rate of heat removal by the
ceiling plus the floor should equal the total rate of heat
supplied by the four walls, that is:
[((2 × 3 × 6) + (2 × 3 × 4)) × 25] + [(6 × 4) × 22]
θf s = ————————————————————
(2 × 3 × 6) + (2 × 3 × 4) + (6 × 4)
= 24.14 C
749.9 + 103.3 = 853.2 W
The rate of heat removal by radiation φr by the chilled
ceiling can now be estimated using equation 3.94:
The agreement is within rounding error.
Φr = 5 × 10–8 × (6 × 4) [(18 + 273)4 – (24.14 + 273)4]
3.3.2.3
= –749.6 W
Simplified technique for rooms
The multi-surface enclosure can be simplified by treating
it as a two-surface approximation(26). Here, the radiant
exchange in the room is modelled by assuming that one
surface (the heated or cooled surface) radiates to a single
fictitious surface (made up of the other surfaces in the
room, which are considered to be at a similar temperature
and emissivity to one another). View factors do not need
to be determined in the case of a two-surface enclosure.
This simplification leads to the following equation:
(3.94)
where θs is the temperature (C) of the heated or cooled
surface; the term θf s is the area-weighted average surface
temperature (C) for the fictitious surface, given by:
(R
j1
N
(Aj θ j) /
R Aj ; i ≠ j
j1
)
Combined convective and radiative
heat transfer in enclosures
The total rate of heat exchange at a surface in an enclosure
can be determined by adding the convective and radiative
components discussed in the previous sections:
Φt = Φc + Φr
(3.95)
(that is, when the emissivities of those surfaces comprising
the fictitious surface are nearly equal). Here, θj is the
temperature in C of a surface making up the fictitious
surface.
Equation 3.94 can be used by designers to estimate the
rate of heat removal by radiation by a heated or cooled
surface as a function of the temperature of the surface
and of θfs.
(3.97)
where Φc is given by:
Φc hc As (θs – θa)
Φr = 5 × 10–8 As [(θs + 273)4 – (θfs + 273)4]
(3.96)
For the ceiling of Example 3.2, the value for hr is
5.1 W·m–2·K–1; this is a typical value for indoor conditions
(see Table 3.7 of CIBSE Guide A(10)).
(3.93)
where Φr is the rate of radiant heat transfer exchanged by
the heated (or cooled) surface of area As at temperature Ts
(K), and Tf s is the area-weighted and emissivity-weighted
average temperature of the other surfaces in the room (K);
Fr is a radiation exchange factor for two surfaces and takes
a value of 0.87 for most rooms in which the emissivities of
the surfaces can be regarded as approximately 0.9 (see
reference 27). For this situation, reference 22 shows that
equation 3.93 can be expressed as:
N
Φr = hr As (θs – θfs)
3.3.2.4
Φr = σ Fr As (Ts4 – Tf s4 )
θfs =
In addition, a radiative heat transfer coefficient hr can be
determined using the following linear expression:
(3.98)
Values for hc are dependent upon conditions, but could be
evaluated, as hcn, for example, from equations 3.75, 3.76 or
3.77, as appropriate. The term Φr can be evaluated from
equation 3.94 when the simplified technique is adopted;
alternatively, Φi replaces Φr for that surface in equation
3.97, where Φi is evaluated from equation 3.78.
3.3.3
Human body heat transfer
3.3.1
Occupied enclosures
The presence of a human body in an enclosure can be
treated as the addition of a further surface which
exchanges heat by convection and by radiation with the
surroundings. Such a treatment can be of relevance to
the estimation of room thermal loads (see chapter 6 of
CIBSE Guide A(10)), and to the determination of human
thermal comfort (see chapter 1 of CIBSE Guide A(10)).
Here, correlations for natural (free) and for forced
3-18
Reference data
Heating
panel
convection for a human body are given, together with
view factors for use in estimation of radiant exchange.
3.3.3.2
Human heat exchange by convection
The rate of heat transfer per unit area by convection, φhb ,
between the human body surface and its surroundings is
given by:
North wall
φhb = fcl hc (θcl – θa)
C
Table 3.12 Human body convection coefficients
hc / W·m–2·K–1
Reference
D
C
D
C
C
A
B
1.5
D
D
East wall
A
0.6
A
1.5
1.5
2.0
B
4.5
A
0.6
2.0
2.0
B
B
Floor
2.0
1.6
A
0.6
E
0.4
1.6
Values for hc for natural or for forced convection can be
determined from a suitable correlation equation. Table
3.12 (after reference 29) summarises some of the existing
correlations available.
West wall
where Iclo is the thermal resistance of clothing (clo).
F
D
2.0
(3.100)
C
B
0.4
fcl ≈ 1 + 0.15 Iclo
1.1 0.4
where fcl is the clothing area factor, given by(28):
0.6
(3.99)
Remarks
South wall
3.0
D
Nishi and Gagge (1977)(30) Still body in still air
1.5
Natural convection:
2.38 Dθca0.25
4.0
Neilsen and Pedersen
(1952)(31)
Used in Fanger’s
equation(28)
Rapp (1973)(32)
Recommended (by
McIntyre)(29) for
sedentary people
A
2.0
1.5
E
F
1.5
3.0
B
C
Ceiling
Figure 3.7 Example 3.3: room dimensions and person placement
(adapted from reference 28)
Forced convection:
8.3 vr0.6
Mitchell (1974)(33)
Best average
—
12.1 √ vr
Winslow et al. (1937)(34)
Used in Fanger’s
equation(28)
—
8.3 √ vr
Kerslake (1972)(35)
Recommended (by
McIntyre)(29)
3.3.3.3
Human heat exchange by radiation
This can be treated using the radiosity technique as
described above (section 3.3.2.2). Here, the human body
is regarded as an additional surface for radiant exchange.
Human body view factors for use in the technique are
given in reference 36, and are reproduced here with
permission (Figures 3.3 to 3.6).
3.14. As a check on the calculations, the sum of all the
view factors between the person and the surrounding
surfaces should equal unity.
Note that once the view factors have been determined, the
rate of heat exchange by radiation between a person and the
room surroundings can be calculated using the radiosity
approach as illustrated in Example 3.1. Here, the person
can be regarded as an additional ‘surface’ within the
enclosure.
Table 3.13 Example 3.3: parameters for calculation of view factors
View factor = F′max (1 – e–(a′/c′)/ τ ) (1 – e–(b′/c′)/ β )
where: τ = A′ + B′ (a′/c′); β = C′ + D′ (b′/c′) + E′ (a′/c′)
Configuration
Parameter value
F′max
A′
B′
C′
D′
E′
Example 3.3 (adapted from reference 28)
Seated person (Fig. 3.3);
vertical surfaces (wall,
window)
0.118 1.216 0.169 0.717 0.087 0.052
Determine the view factors between a seated person (of
known position but unknown orientation) and the
surrounding surfaces of the room as shown in Figure 3.7
(upper figure).
Seated person (Fig. 3.4);
horizontal surfaces (floor,
ceiling)
0.116 1.396 0.130 0.951 0.080 0.055
Standing person (Fig. 3.5);
Vertical surfaces (wall,
window)
0.120 1.242 0.167 0.616 0.082 0.051
Standing person (Fig. 3.6);
horizontal surfaces (floor,
ceiling)
0.116 1.595 0.128 1.226 0.046 0.044
Each surface of the room is divided into rectangles as
shown in Figure 3.7 (lower figures). The view factors
pertaining to each rectangle can then be determined
graphically from Figures 3.3 and 3.4, or analytically from
the equations in Table 3.13. The results are given in Table
Heat transfer
3-19
b'
a'
a'
b'
c'
a'
c'
a'
c'
b' = 0.6 m
0.06
1
0.8
0.6
0.04
0.4
0.02
0.2
0.00
0.10
a'/c'=∞
3
2
1.5
0.08
0.06
1
0.8
0.6
0.4
0.04
0.2
0.02
2
4
6
b'/c'
8
10
0
0.4 0.8
1.2
b'/c'
5
3
2
1.5
0.08
0.04
0.00
0.10
1
0.8
0.6
0.4
0.06
0.2
0.02
1.6 2.0
a'/c'=∞
3
2
1.5
1
0.8
0.6
0.4
0.2
0.08
0.06
0.04
0.02
0.00
0 1 2 3 4 5 6 7 8 9 10
b'/c'
Example
Example
a' = 4 m; b' = 3 m; c' = 5 m;
b'/c' = 0.6; a'/c' = 0.8; Fp–N = 0.029
a' = 3 m; b' = 6 m; c' = 2 m;
b'/c' = 3.0; a'/c' = 1.5; Fp–N = 0.067
Figure 3.3 Mean value of view factor between a seated person and a
vertical rectangle (above or below his centre) when the person is rotated
around a vertical axis. (To be used when the location but not the
orientation of the person is known.) (Reproduced from BS EN ISO 7726
by permission of the British Standards Institution.)
Detail
0.12
a'/c'=∞
See
detail
0.10
0.00
0
Fp–N
0.12
View factor
5
3
2
1.5
0.08
Detail
0.12
View factor
See
detail
0.10
View factor
a'/c'=∞
b'
Fp–N
Fp–N
0.12
View factor
Fp–N
c' = 0.6 m
0
0.4 0.8 1.2
b'/c'
1.6 2.0
Figure 3.4 Mean value of view factor between a seated person and a
horizontal rectangle (on the ceiling or floor) when the person is rotated
around a vertical axis. (To be used when the location but not the
orientation of the person is known.) (Reproduced from BS EN ISO 7726
by permission of the British Standards Institution.)
a'
b'
a'
c'
c'
b'
a'
b'
a'
c'
5
3
2
1.5
See
detail
0.08
0.10
0.06
0.04
0.4
0.04
0.02
0.2
0.02
0
2
4
6
b'/c'
8
10
0.12
a'/c'=∞
3
2
1.5
0.08
1
0.8
0.6
0.00
Detail
0.12
1
0.8
0.6
0.4
0.06
0.00
0.2
0.10
0.4
0.8 1.2
b'/c'
1.6
2.0
Example
a' = 4.5 m; b' = 2.0 m; c' = 3.0 m;
b'/c' = 0.67; a'/c' = 1.5; Fp–N = 0.047
Figure 3.5 Mean value of view factor between a standing person and a
vertical rectangle (above or below his centre) when the person is rotated
around a vertical axis. (To be used when the location but not the
orientation of the person is known.) (Reproduced from BS EN ISO 7726
by permission of the British Standards Institution.)
a'/c'=∞
See
detail
0.08
0.06
0.02
Detail
0.12
5
3
0.10
2
1.5
0.08
1
0.8
0.6
0.4
0.2
0.04
0.00
0
Fp–N
View factor
View factor
0.10
Fp–N
Fp–N
a'/c'=∞
View factor
0.12
View factor
Fp–N
c' = 1.0 m
b' = 1.0 m
a'/c'=∞
0.06
3
2
1.5
1
0.8
0.6
0.4
0.2
0.04
0.02
0.00
0
2
4
6
8
10
b'/c'
0
0.4
0.8
1.2
b'/c'
1.6
2.0
Example
a' = 1.0 m; b' = 15 m; c' = 1.5 m;
b'/c' = 10; a'/c' = 0.67; Fp–N = 0.039
Figure 3.6 Mean value of view factor between a standing person and a
horizontal rectangle (on the ceiling or floor) when the person is rotated
around a vertical axis. (To be used when the location but not the
orientation of the person is known.) (Reproduced from BS EN ISO 7726
by permission of the British Standards Institution.)
3-20
Reference data
Table 3.14 Example 3.3: calculation of view factors (adapted from reference 28)
Surface
View factor equation
North wall (Figure 3.3)
FP–ABCD = FP–A + FP–B + FP–C + FP–D
Component
Dimension ratios
(b/c)
East wall (Figure 3.3)
South wall (Figure 3.3)
(a/c)
Component
value
View
factor
FP–A
FP–B
FP–C
FP–D
0.40
0.40
1.3
1.3
1.0
3.0
1.0
3.0
0.024
0.033
0.033
0.072
FP–ABCD
—
—
—
FP–A
FP–B
FP–C
FP–D
0.13
0.44
0.13
0.44
0.33
0.44
0.44
0.33
0.004
0.015
0.005
0.011
FP–ABCD
—
—
—
FP–A
FP–B
FP–C
FP–D
1.0
1.0
0.30
0.30
0.75
2.3
0.75
2.3
0.037
0.060
0.015
0.024
FP–ABCD
—
—
—
FP–B
FP–E
1.1
1.1
1.1
0.73
0.049
0.038
FP–BE
—
—
0.087
FP–A
FP–BC
FP–D
FP–EF
FP–BE
0.40
1.3
0.40
1.3
—
1.0
1.3
1.3
1.0
—
0.024
0.057
0.026
0.050
0.087
FP–ACDF
—
—
—
FP–A
FP–B
FP–C
FP–D
2.5
2.5
3.3
3.3
2.5
7.5
2.5
7.5
0.078
0.090
0.082
0.095
FP–ABCD
—
—
—
FP–A
FP–B
FP–D
FP–E
1.0
1.0
0.75
0.75
0.75
0.75
0.75
0.75
0.030
0.030
0.025
0.025
FP–ABDE
—
—
—
FP–BC
FP–B
FP–EF
FP–E
1.0
1.0
0.75
0.75
2.3
0.75
2.3
0.75
0.051
0.030
0.042
0.025
FP–CF
—
—
—
0.038
Fperson–all surfaces
—
—
—
1.000
0.179
FP–ABCD = FP–A + FP–B + FP–C + FP–D
0.035
FP–ABCD = FP–A + FP–B + FP–C + FP–D
0.136
West wall (Figure 3.3)
(a) Window
(b) Rest of the wall
FP–BE = FP–B + FP–E
FP–ACDF = FP–A + FP–C FP–D + FP–F
= FP–A + FP–BC – FP–B + FP–D + FP–EF – FP–E
= FP–A + FP–BC + FP–D + FP–EF – FP–BE
Floor (Figure 3.4)
0.070
FP–ABCD = FP–A + FP–B + FP–C + FP–D
0.345
Ceiling (Figure 3.4)
(a) Heating panel
(b) Rest of the ceiling
FP–ABDE FP–A + FP–B + FP–D + FP–E
0.110
FP–CF FP–C + FP–F
FP–BC – FP–B + FP–EF – FP–E
Heat transfer
3.3.3.4
3-21
Total human heat exchange with
surroundings
Sections 3.3.3.2 and 3.3.3.3 deal with heat transfer between
a human body and its surroundings by convection and by
radiation only. However, the total heat exchange includes
not only convective and radiative components, but also
heat exchange by evaporation, respiration and conduction.
For a treatment of these, refer to chapter 1 of CIBSE
Guide A(10) or to references 25 or 37.
λ
φc = —— Nu Δt
dop
(3.105)
For horizontal pipes in air, free convection, laminar flow,
and Gr < 108, the following equation can be used:
Nu = 0.53 (Gr Pr)0.25
(3.106)
Hence, equation 3.104 becomes:
3.3.4
3.3.4.1
Equipment and components
Ts – Ta 0.25
φc = 1.35 –––––– (Ts – Ta )
dop
[
Plane surfaces
Tables 3.15 and 3.16 (pages 3-22 and 3-23) give the heat
emission/absorption from freely exposed plane surfaces to
air. They have been prepared from the following
equations.
]
(3.107)
The emission per metre run may then be found from:
Φ / l = π dop (φr + φc )
(3.108)
Radiation (from equation 3.60):
φr = 5.67 × 10–8 ε (Ts4 – Tr4)
(3.101)
Convection (laminar flow from equation 3.6):
(θs – θf)1.25
φc = 0.64 ————
D0.25
(3.102)
In practice, for a given temperature difference, a change in
air temperature or mean radiant temperature of ±5 C
introduces an error of about 2% while a change of ±10 C
gives an error of about 5%.
(3.103)
Heat emission/absorption under site conditions may vary
from the tabulated data since:
Convection (turbulent flow from equation 3.5):
φc = 1.7 (θs – θf)1.33
Hence, for room applications and taking D = 1 m,
equations 3.102 and 3.103 can be put in the general form:
φc = C (Ts – Ta)n
(a)
draught-free surroundings may not occur in
practice; Table 3.22 gives some indication of the
effect on heat transfer
(b)
the actual surface emissivity may differ from those
used in preparing the tables; emissivities for other
materials and surface finishes are given in Tables
3.7, 3.8 and 3.9
(c)
British Standards(38,40,41) permit tolerances in pipe
diameters from the mean values used in preparing
the tables.
(3.104)
The values of C and n for particular arrangements are
given in Table 3.17.
The radiation and convection emissions are shown
separately in Tables 3.15 and 3.16 since there may be
significant differences between the mean radiant temperature of the enclosure and the air temperature within it.
Absorption by the surfaces is shown by negative values of
emission.
The radiation equation (equation 3.101) is strictly true
only for a panel of comparatively small area relative to the
rest of the room area.
In practice, the convection emission applies to draughtfree conditions and appreciable increases in heat transfer
occur if air movement is present(10). Table 3.18 gives some
indication of the effect of air velocity on heat transfer.
3.3.4.2
Tables 3.19, 3.20 and 3.21 assume that both the ambient
temperature and the mean radiant temperature are equal
to 20 oC. It is also assumed that the external surface of the
pipe is at the same temperature as the fluid contained
within it.
Bare pipes
The heat emissions per metre run of horizontal steel and
copper pipes are given in Tables 3.19, 3.20 and 3.21 (pages
3-24 to 3-26). Absorption by the surfaces is shown by
negative values of emission. These tables have been
prepared using equation 3.102 and for convection:
Considerations (b) and (c) may lead to the actual heat
emission of a given pipe varying by a further 10% from
the tabulated figure.
All these aspects should be taken into consideration in
system design and an appropriate allowance made according to circumstances.
Vertical pipes
Pipes set in a vertical position have a heat emission/absorption which differs from that arising from
horizontal fixing due to the variation in the thickness of
the boundary layer of air about the pipe surface.
Correction factors quoted in Table 3.23 are for use in
conjunction with the data listed in Tables 3.19, 3.20 and
3.21.
11
3.9
4.0
12
30
7.5
0
7.9
16
34
54
76
100
126
155
186
220
297
386
489
607
742
896
1070
1260
1480
1720
1990
2290
2620
2980
3380
5
10
15
20
30
40
50
60
70
80
90
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
2980
3370
1470
1720
1990
2280
2610
599
734
888
1060
1260
178
212
289
378
481
46
68
92
118
147
15
7.9
0
8.3
26
15
2970
3370
1470
1710
1980
2280
2610
595
730
884
1060
1250
174
208
285
374
477
42
64
88
114
143
20
12
4.1
4.2
22
17.5
2970
3360
1470
1710
1980
2280
2610
591
726
879
1050
1250
170
204
280
370
473
38
60
84
110
139
24
16
8.3
0
18
20
Surface emissivity = 0.3
2960
3360
1460
1700
1970
2270
2600
587
722
875
1050
1240
166
200
276
365
468
34
55
79
106
134
28
21
13
4.3
14
22.5
2960
3360
1460
1700
1970
2270
2600
582
717
871
1040
1240
161
195
272
361
464
29
51
75
101
130
33
25
17
8.8
9.2
25
5970
6760
2960
3450
3990
4590
5240
1210
1480
1790
2140
2530
372
440
593
772
978
108
152
200
253
310
15
0
16
33
69
10
5960
6750
2960
3440
3980
4580
5240
1210
1480
1780
2130
2520
365
432
586
764
970
100
144
192
245
302
23
7.8
8.0
25
61
12.5
5950
6740
2950
3430
3970
4570
5230
1200
1470
1780
2120
2510
357
424
577
756
962
92
136
184
237
294
31
16
0
17
53
15
5940
6740
2940
3430
3960
4560
5220
1190
1460
1770
2110
2500
348
416
569
747
954
84
128
176
229
286
39
24
8.2
8.4
44
17.5
5930
6730
2930
3420
3960
4550
5210
1180
1450
1760
2110
2490
340
408
561
739
945
76
120
168
220
278
48
33
17
0
36
20
Surface emissivity = 0.6
5930
6720
2920
3410
3950
4540
5200
1170
1440
1750
2100
2490
331
399
552
730
936
67
111
159
211
269
56
41
25
8.7
27
22.5
5920
6710
2910
3400
3940
4540
5190
1160
1430
1740
2090
2480
322
390
543
721
928
58
102
150
203
260
65
50
34
18
18
25
8950
10100
4440
5170
5980
6880
7870
1820
2230
2690
3210
3790
559
660
890
1160
1470
162
228
300
379
465
23
0
24
49
103
10
8940
10100
4430
5160
5970
6870
7850
1810
2220
2680
3200
3780
547
649
878
1150
1450
151
216
288
367
453
34
12
12
37
91
12.5
Heat emission (/ W·m–2) for stated surface emissivity and enclosure mean radiant temperature (/ °C)
Note: values above 1000 rounded to nearest 10, values above 10 000 rounded to nearest 100
2980
3380
1480
1720
1990
2290
2620
603
738
892
1070
1260
182
216
293
382
485
50
72
96
122
151
12.5
10
Surface
temp.
/ °C
Table 3.15 Heat emission from plane surfaces by radiation (based on equation 3.101)
8930
10100
4420
5150
5960
6850
7840
1800
2200
2660
3180
3770
535
637
866
1130
1440
139
204
276
355
441
46
24
0
25
79
15
8920
10100
4410
5140
5950
6840
7830
1790
2190
2650
3170
3760
523
624
854
1120
1430
126
192
264
343
429
59
36
12
13
67
17.5
8900
10100
4400
5120
5930
6830
7820
1770
2180
2640
3160
3740
510
612
841
1110
1420
114
179
251
330
416
71
49
25
0
54
20
8890
10100
4380
5110
5920
6820
7800
1760
2170
2630
3150
3730
497
599
828
1100
1400
101
166
238
317
403
84
62
38
13
41
22.5
Surface emissivity = 0.9
8880
10100
4370
5100
5910
6800
7790
1750
2150
2610
3130
3720
484
585
815
1080
1390
87
153
225
304
390
98
75
51
26
28
25
3-22
Reference data
2.5
5.8
2.0
7.9
23
14
0
4.8
11
27
45
64
85
107
130
153
177
228
281
336
393
451
512
573
636
700
766
832
900
969
1040
1110
5
10
15
20
30
40
50
60
70
80
90
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
1020
1090
684
749
816
883
952
378
437
496
558
620
141
165
215
267
322
36
54
75
96
118
36
14
0
4.8
19
15
1010
1080
676
741
807
875
943
371
429
489
550
612
135
159
209
261
315
31
50
69
90
112
49
25
5.8
2.0
15
17.5
1000
1070
668
733
799
866
934
364
422
481
542
605
130
153
202
254
308
27
45
64
85
107
62
36
14
0
11
20
Surface emissivity = 0.3
995
1060
660
725
791
858
926
357
415
474
535
597
124
147
196
248
301
23
40
59
80
101
77
49
25
5.8
7.9
22.5
986
1060
652
717
782
849
917
350
407
466
527
589
118
141
190
241
295
19
36
54
75
96
91
62
36
14
4.8
25
3650
3910
2400
2640
2880
3130
3390
1300
1500
1720
1940
2160
476
556
726
907
1100
129
189
255
324
398
12
0
12
30
75
10
3610
3880
2370
2610
2850
3100
3350
1270
1480
1690
1910
2140
456
536
705
884
1070
115
174
238
307
379
20
4.7
4.7
20
63
12.5
3580
3840
2340
2580
2820
3070
3320
1250
1450
1660
1880
2110
436
516
683
861
1050
101
158
221
289
361
30
12
0
12
51
15
3550
3810
2310
2550
2790
3040
3290
1220
1420
1640
1850
2080
417
495
661
838
1020
88
144
205
272
342
40
20
4.7
4.7
40
17.5
3520
3780
2280
2520
2760
3010
3260
1200
1400
1610
1830
2050
398
476
640
816
1000
75
129
189
255
324
51
30
12
0
30
20
Surface emissivity = 0.6
3480
3740
2250
2490
2730
2970
3230
1170
1370
1580
1800
2020
379
456
619
793
977
63
115
174
238
307
63
40
20
4.7
20
22.5
3450
3710
2220
2460
2700
2940
3190
1150
1350
1560
1770
1990
361
436
598
771
954
51
101
158
221
289
75
51
30
12
12
25
4430
4750
2910
3200
3500
3800
4110
1570
1820
2080
2350
2630
578
675
882
1100
1330
157
230
309
394
484
4.8
0
14
36
91
10
4390
4710
2880
3170
3460
3760
4070
1540
1790
2050
2320
2590
554
651
856
1070
1300
140
211
289
372
461
7.9
2.0
5.8
25
77
12.5
Heat emission (/ W·m–2) for stated surface emissivity and enclosure mean radiant temperature (/ °C)
Note: values above 1000 rounded to nearest 10, values above 10 000 rounded to nearest 100
1030
1100
692
758
824
892
960
386
444
504
565
628
147
171
222
274
329
40
59
80
101
124
12.5
10
Surface
temp.
/ °C
Table 3.16 Heat emission from plane surfaces by free convection (based on equation 3.104 and Table 3.17
4350
4670
2840
3130
3420
3730
4030
1510
1760
2020
2280
2560
530
626
829
1050
1270
123
192
269
351
438
11
4.8
0
14
62
15
4310
4630
2800
3090
3390
3690
4000
1480
1730
1990
2250
2520
507
602
803
1020
1240
107
174
249
330
416
15
17.9
2.0
5.8
49
17.5
4270
4590
2770
3060
3350
3650
3960
1450
1700
1950
2220
2490
484
578
777
990
1220
91
157
230
309
394
19
11
4.8
0
36
20
4230
4550
2730
3020
3310
3610
3920
1420
1670
1920
2180
2460
461
554
751
963
1190
77
140
211
289
372
23
15
7.9
2.0
25
22.5
Surface emissivity = 0.9
4190
4510
2700
2980
3280
3570
3880
1390
1640
1890
2150
2420
438
530
726
936
1160
62
123
192
269
351
27
19
11
4.8
14
25
Heat transfer
3-23
3-24
Reference data
Table 3.18 Effect of air velocity on convective heat
transfer from plane surfaces
Table 3.17 Values of coefficients in equation 3.104
Situation
C
n
Warm or cold vertical planes
1.4
1.33
Warm horizontal planes facing up
1.7
1.33
Cold horizontal planes facing down
1.7
1.33
Warm horizontal planes facing down
0.64
1.25
Cold horizontal planes facing up
0.64
1.25
Velocity / m·s–1
Multiplying factor
0
0.5
1.0
2.0
3.0
1
1.3
1.7
2.4
3.1
Table 3.19 Heat emission from single horizontal steel pipes (ε = 0.95) freely exposed in surroundings at 20 °C
Temp. diff. between
surface and
*15
surroundings / †21.3
Heat emission (/ W·m–1) for stated pipe nominal size* and outside diameter†, dop (/ mm)
20
25
32
40
50
65
80
100
125
150
200
250
300
350
400
26.9
33.7
42.4
48.3
60.3
76.1
88.9
114.3
139.7
168.3
219.1
273.0
323.9
355.6
406.4
–15
–10
–5
0
–12
–7.7
–3.5
0
–15
–9.4
–4.3
0
–18
–11
–5.3
0
–22
–14
–6.5
0
–24
–16
–7.3
0
–29
–19
–8.9
0
–36
–23
–11
0
–41
–27
–13
0
–52
–33
–16
0
–62
–40
–19
0
–71
–46
–22
0
–92
–60
–28
0
–112
–73
–35
0
–130
–85
–40
0
–142
–92
–44
0
–160
–104
–50
0
5
10
15
20
3.6
8.1
13
18
4.5
9.8
16
22
5.5
12
19
27
6.7
15
23
33
7.5
16
26
37
9.1
20
32
45
11
25
39
55
13
28
45
63
16
35
56
78
19
42
67
94
23
49
78
109
29
63
100
140
36
77
123
171
42
90
143
199
46
98
156
217
52
111
176
245
25
30
35
40
24
29
35
42
29
36
43
51
35
44
53
62
43
53
64
75
48
60
72
84
58
72
87
102
71
88
106
125
81
101
122
143
102
126
152
179
122
151
182
214
141
175
211
248
182
226
272
319
221
275
331
389
258
320
385
453
281
349
419
493
317
393
473
556
45
50
55
60
48
55
62
69
59
67
75
84
71
81
92
102
87
99
112
125
98
111
125
140
118
135
152
169
145
165
186
207
166
189
213
238
207
236
266
297
247
281
317
354
287
327
368
411
369
421
474
529
449
512
577
644
524
597
673
751
570
649
732
817
642
732
825
921
65
70
75
80
77
84
92
100
93
103
112
122
114
125
137
149
138
152
167
181
155
170
186
203
188
206
226
246
230
253
277
301
263
290
317
345
329
362
396
431
392
432
473
515
456
502
549
598
586
646
706
769
714
786
860
937
832
916
1000
1090
905
997
1090
1190
1020
1120
1230
1340
100
120
140
160
135
173
215
261
164
211
262
318
200
257
320
389
244
314
391
476
273
352
438
534
331
427
532
648
406
523
653
796
466
600
750
915
582
750
937
1140
695
897
1120
1370
808
1040
1310
1600
1040
1340
1680
2060
1270
1640
2050
2520
1480
1910
2400
2940
1610
2080
2610
3200
1820
2350
2950
3620
180
200
220
240
311
366
425
490
380
447
520
600
465
547
637
735
569
670
781
902
638
753
878
1010
776
916
1070
1240
954
1130
1320
1520
1100
1300
1510
1750
1370
1620
1900
2200
1650
1950
2280
2650
1920
2270
2660
3090
2480
2940
3450
4000
3030
3600
4220
4900
3540
4200
4930
5740
3860
4580
5380
6260
4360
5180
6090
7080
260
280
300
320
560
635
717
806
686
780
881
990
842
957
1080
1220
1030
1180
1330
1500
1160
1320
1500
1690
1420
1620
1830
2060
1750
2000
2260
2550
2010
2300
2610
2940
2530
2890
3280
3710
3040
3480
3950
4470
3550
4060
4620
5230
4610
5280
6010
6800
5650
6470
7370
8350
6620
7220
8180
7590
8280
9380
8650
9440 10 700
9800 10 700 12 100
* Nominal pipe sizes are to BS EN 10255: 2004(38) and BS EN 545: 2006(39)
† Outside diameters are to BS EN 10220: 2002(40)
Multiple banks of pipes
Where horizontal pipes are arranged one above another at
close pitch, the heat emission is reduced overall owing to a
cumulative interference with the convection output. Table
3.24 lists correction factors which illustrate the reduction
in single pipe emission.
Effect of proximity of walls
Where pipes are installed near to cold external walls, the
emission by radiation is likely to increase and that by
convection to remain unchanged. With internal walls,
there may be a reduction in radiation and a slight increase
in convection. These variations are, however, probably
appreciably smaller than variations in emission due to
draughts, etc.
Finned surfaces
Owing to the wide variation in geometrical arrangement
and fin efficiency, it is impractical to give any formulae for
heat emission by forced or free convection from such
surfaces. References should be made to manufacturers’
catalogues and to other test data, etc.(2,42–46).
Heat transfer
3-25
Table 3.20 Heat emission from single horizontal copper pipes (ε = 0.5) freely exposed in surroundings at 20 °C
Temp. diff. between
surface and
surroundings / K *8
Heat emission (/ W·m–1) for stated pipe nominal size*
10
12
15
18
22
28
35
42
54
66.7
76.1
108
133
159
–15
–10
–5
0
–4.3
–2.7
–1.2
0
–5.2
–3.2
–1.4
0
–6.0
–3.8
–1.7
0
–7.2
–4.5
–2.0
0
–8.4
–5.2
–2.3
0
–9.9
–6.2
–2.8
0
–12
–7.5
–3.4
0
–14
–9.1
–4.1
0
–17
–11
–4.8
0
–21
–13
–5.9
0
–25
–16
–7.1
0
–28
–17
–7.9
0
–37
–23
–11
0
–44
–28
–13
0
–51
–33
–15
0
5
10
15
20
1.2
2.8
4.5
6.4
1.5
3.3
5.4
7.7
1.7
3.9
6.3
8.9
2.0
4.6
7.5
11
2.4
5.4
8.8
12
2.8
6.4
10
15
3.5
7.8
13
18
4.2
9.4
15
21
4.9
11
18
25
6.0
14
22
31
7.2
16
26
37
8.1
18
29
41
11
24
39
55
13
29
47
66
15
34
55
77
25
30
35
40
8.4
10
13
15
10
13
15
18
12
15
18
21
14
17
21
25
16
20
24
29
19
24
29
34
23
29
35
42
28
35
42
50
33
41
49
58
40
50
61
72
48
60
72
85
54
67
81
95
72
90
109
128
86
107
130
153
100
125
151
178
45
50
55
60
17
20
22
25
21
24
27
30
24
27
31
34
29
33
37
41
33
38
43
48
39
45
51
56
48
55
62
69
58
66
74
83
67
77
86
96
83
94
106
119
99
112
127
141
110
126
142
158
148
169
190
212
177
201
227
253
205
234
264
294
65
70
75
80
27
30
33
36
33
36
39
43
38
42
46
50
46
50
55
60
53
58
64
69
62
69
75
81
76
84
91
99
92
101
110
120
107
117
128
139
131
144
158
171
156
172
188
204
175
192
210
229
235
258
282
307
280
308
337
366
326
358
392
426
100
120
140
160
48
61
74
89
57
73
89
107
66
84
104
125
80
101
125
150
92
118
145
174
109
139
171
206
133
170
209
252
160
204
252
304
186
238
294
354
230
293
363
438
274
350
433
523
306
392
485
586
412
527
653
790
492
630
781
945
572
733
910
1100
180
200
220
240
105
122
140
160
126
147
169
192
147
171
196
224
177
206
237
270
206
240
276
315
244
284
327
373
298
347
400
457
360
420
484
553
419
490
565
646
519
606
701
802
620
726
839
961
695
814
941
1080
938
1100
1270
1460
1120
1320
1530
1760
1310
1540
1780
2050
260
280
300
320
180
202
225
249
217
243
271
301
253
284
316
351
305
342
382
425
356
400
447
497
422
475
531
590
518
583
653
727
627
707
792
882
734
827
927
1030
911
1030
1150
1290
1090
1230
1390
1550
1230
1390
1560
1740
1660
1880
2120
2370
2000
2270
2550
2860
2340
2650
2990
3350
* Nominal pipe sizes are to BS EN 1057: 2006(41)
3.3.4.3
Insulated pipes
and where the thermal resistance of the insulation is given
by:
If the external surface temperature of insulation concentric to a pipe is known, then the theoretical heat emission
may be calculated in the same way as for an exposed pipe.
In practice, however, it is the surface temperature of the
pipe itself which can be more readily ascertained so that
an equation relating the temperature difference between
this and ambient air is more useful. The main variables
are the thermal conductivity of the insulation material, its
thickness and the nature of the final surface finish. The
data are, therefore, given per unit area of pipe.
The heat exchange from insulated pipes is given by:
φ = U (θs – θa)
(3.109)
or, more conveniently, per metre run of pipe by:
Φ / l = π dop (θs – θa)
(3.110)
where the overall thermal transmittance is given by:
1
U = —————–
dop
Rn + ———
hso don
(3.111)
( )
d
dop
R = ——
ln —on–
dop
2 kn
(3.112)
The surface temperature of the exterior of the insulation is
a function of the value assumed for the surface heat
transfer coefficient (see Table 3.25) and may be calculated
from:
φ dop
θn = ———
+ θa
hso don
(Φ / l)
= ———–– + θa
π hso don
(3.113)
(3.114)
Outside surface heat transfer coefficient, hso
Values for the outside heat transfer coefficient (hso)
appropriate to normal finishes are recommended in BS
5422(47) where they are defined as giving ‘reasonable
approximations to the surface temperature of insulation
fully exposed in still air and not influenced by other
external sources of heat, including sunshine’. Table 3.25
gives these values and also those for moving air.
3-26
Reference data
Table 3.21 Heat emission from single horizontal copper pipes (ε = 0.95) freely exposed in surroundings at 20 °C
Heat emission (/ W·m–1) for stated pipe nominal size*
Temp. diff. between
surface and
surroundings / K *8
10
12
15
18
22
28
35
42
54
15
10
5
0
5.2
3.3
1.5
0
6.3
4.0
1.8
0
7.4
4.7
2.1
0
8.9
5.7
2.6
0
10
6.6
3.1
0
12
7.9
3.6
0
15
9.7
4.5
0
18
12
5.5
0
22
14
6.4
0
27
17
8.0
0
5
10
15
20
1.5
3.5
5.6
7.8
1.9
4.2
6.7
9.4
2.2
4.9
7.9
11
2.7
5.9
9.5
13
3.1
6.9
11
16
3.7
8.3
13
19
4.6
10
16
23
5.6
12
20
28
6.6
15
23
32
8.3
18
29
40
66.7
108
133
159
36
23
11
0
49
32
15
0
59
38
18
0
69
45
21
0
10
22
35
49
11
25
39
55
15
34
53
75
19
41
64
90
22
48
76
105
32
21
9.7
0
76.1
25
30
35
40
10
13
15
18
12
15
19
22
14
18
22
25
17
22
26
31
20
25
31
36
24
30
36
43
30
37
45
53
36
45
54
64
42
53
63
75
53
66
79
93
63
79
95
112
71
89
107
125
97
120
145
171
117
145
175
205
137
170
204
240
45
50
55
60
21
24
27
30
25
29
32
36
29
34
38
42
36
41
46
51
42
47
53
60
49
56
63
71
61
69
78
87
74
84
95
106
86
98
111
124
107
122
138
154
129
147
166
185
145
165
186
208
197
225
253
283
237
270
305
340
278
317
357
399
65
70
75
80
33
37
40
43
40
44
48
52
47
51
56
61
57
62
68
74
66
73
79
86
78
86
94
103
97
106
116
126
117
129
141
153
137
151
165
179
171
188
205
223
205
225
247
268
230
253
277
302
313
345
377
411
377
415
454
494
442
486
532
579
100
120
140
160
58
75
92
112
70
90
112
135
82
105
131
158
99
127
158
192
116
149
185
224
138
177
220
267
170
218
272
330
206
265
330
401
242
311
387
471
301
387
483
588
362
466
581
709
407
525
655
798
554
715
893
1090
668
862
1080
1320
783
1010
1260
1550
180
200
220
240
133
155
180
207
161
188
218
251
188
221
256
294
228
268
311
358
267
314
365
420
319
375
436
502
394
464
539
622
479
565
658
759
563
664
774
893
704
830
969
1120
848
1000
1170
1350
956
1130
1320
1530
1310
1550
1810
2100
1580
1870
2190
2540
1860
2200
2580
2990
260
280
300
320
235
266
299
335
286
324
364
408
336
380
428
480
409
463
522
586
480
545
615
690
574
652
736
827
712
809
914
1030
869
989
1120
1260
1020
1170
1320
1480
1280
1460
1660
1870
1550
1770
2010
2260
1750
2000
2270
2560
2410
2750
3130
3530
2920
3340
3790
4290
3440
3930
4470
5060
* Nominal pipe sizes are to BS EN 1057: 2006(41)
Table 3.22 Effect of air velocity on heat transfer
Emissivity of
surfaces
Correction factor to be applied to Tables 3.19,
3.20 and 3.21 for stated air velocity (/ m·s–1)
0
0.5
1.0
2.0
0.5 (dull metal)
1.0
1.05
1.15
1.25
0.95
1.0
1.04
1.12
1.20
Table 3.24 Correction factors for multiple banks of pipes
(horizontal, one above another at close pitch)
Number of pipes in bank
Emission from each pipe as a fraction
of the theoretical single pipe value
2
4
6
8
0.95
0.85
0.75
0.65
Table 3.23 Correction factors for heat
emission/absorption from vertical pipes
Nominal pipe
size / mm
Correction factor
for Tables 3.19, 3.20
and 3.18
8
10
15
20
0.72
0.74
0.76
0.79
25
32
40
50
0.82
0.84
0.86
0.88
65
80
100
125
0.90
0.92
0.95
0.97
150
200
250
300
0.99
1.03
1.05
1.07
Heat transfer
3-27
Table 3.25 Outside surface heat transfer coefficients (hso) for insulated
surfaces at various wind speeds
0.07
Calcium
silicate
High
(ε ≥ 0.9)
Medium
(0.2 < ε < 0.9)
Low
(ε < 0.2)
Still air
1
2
10.0
13.5
16.5
8.0
11.5
14.5
5.7
9.0
12.5
3
5
10
20.0
26.0
40.0
18.0
24.0
38.0
15.5
22.0
36.0
Thermal conductivity / W.m1.K1
Surface coefficient, hso (/ W·m–2·K–1)
for stated surface emissivity
Wind speed
/ m·s–1
If the average wind speed is unknown, it is recommended(47) that the following values be assumed:
—
0.06
85% Magnesia
Glass
fibre
Mineral
wool
0.05
0.04
0.03
20
40
60
80 100 120 140 160 180 200 220
Temperature / C
sheltered situations: wind speed = 1 m·s–1
Figure 3.8 Thermal conductivities of insulating materials
—
normal situations: wind speed = 3 m·s–1
—
exposed situations: wind speed = 10 m·s–1
point of view, heat transfer under site conditions may vary
from the tabulated data for the following reasons:
Thermal conductivity of insulation
Thermal conductivities (λ) for commonly used insulating
materials are shown in Figure 3.8. These values are
derived from chapter 3 of CIBSE Guide A(10) and reference
48. The insulating effect of a hard setting finish is
insignificant and may be neglected in the calculations.
(a)
Draught-free surroundings may not occur in
practice; Table 3.22 may be used to assess the effect
of air velocity on heat transfer.
(b)
For brighter surface finishes than those tabulated,
the heat emission will be reduced, the amount of
the reduction varying according to the surface
area, i.e. the pipe size and the insulation thickness.
With a bright metallic finish, e.g. aluminium, the
reduction in emission will be about 8 per cent. For
dull metallic finishes the reduction will be about
4 per cent. Such reductions in heat emissions lead
to an increase in outside surface temperature of
insulation and sheathing.
(c)
Damp insulation will also have an important effect
on emission and can increase losses up to fivefold
on installations which have the appearance of
being satisfactory.
Tabulated data
Table 3.26 gives heat emission or absorption per degree
temperature difference between the pipe surface and the
ambient air using equation 3.110; here, thermal conductivities of 0.025, 0.040, 0.055 and 0.070 W·m–1·K–1 are
selected as examples covering the range of values encountered in thermal heating practice, together with a value of
10 W·m–2·K–1 for the surface coefficient. From a practical
Table 3.26 Heat emission or absorption from insulated pipes per unit length and per unit temperature difference
Heat emission or absorption from insulated pipework per unit temperature difference (/ W·m–1 K–1)
for stated thermal conductivity of insulation (/ W·m–1 K–1) and thickness of insulation (/ mm)
Nominal
pipe size
0.025
0.040
0.055
0.070
12.5 19
25
38
50
12.5 19
25
38
50
12.5 19
25
38
50
12.5 19
25
38
50
15
20
25
32
0.18
0.21
0.25
0.29
0.14
0.16
0.19
0.22
0.12
0.14
0.16
0.19
0.10
0.11
0.13
0.15
0.09
0.10
0.11
0.13
0.27
0.31
0.36
0.43
0.22
0.25
0.29
0.34
0.19
0.22
0.25
0.29
0.16
0.18
0.20
0.23
0.14
0.16
0.18
0.20
0.34
0.40
0.47
0.55
0.29
0.33
0.38
0.45
0.25
0.29
0.33
0.39
0.21
0.24
0.27
0.31
0.19
0.21
0.24
0.27
0.41
0.47
0.56
0.66
0.35
0.40
0.46
0.54
0.31
0.36
0.41
0.47
0.27
0.30
0.34
0.38
0.24
0.26
0.30
0.34
40
50
65
80
0.32
0.39
0.47
0.54
0.25
0.29
0.35
0.40
0.21
0.24
0.29
0.33
0.16
0.18
0.22
0.24
0.14
0.16
0.18
0.20
0.48
0.57
0.69
0.79
0.37
0.44
0.55
0.60
0.32
0.37
0.44
0.50
0.25
0.29
0.34
0.38
0.21
0.24
0.28
0.32
0.61
0.73
0.88
1.0
0.49
0.58
0.69
0.78
0.42
0.49
0.58
0.66
0.33
0.39
0.45
0.50
0.29
0.33
0.38
0.43
0.72
0.86
1.04
1.19
0.59
0.70
0.83
0.94
0.52
0.60
0.71
0.80
0.42
0.48
0.56
0.63
0.36
0.41
0.48
0.53
100
125
150
200
0.67
0.81
0.96
1.22
0.49
0.58
0.69
0.88
0.40
0.47
0.55
0.70
0.29
0.34
0.40
0.50
0.24
0.28
0.32
0.40
0.98
1.18
1.37
1.78
0.74
0.88
1.02
1.32
0.61
0.72
0.83
1.07
0.45
0.53
0.61
0.77
0.38
0.44
0.50
0.63
1.25
1.49
1.74
2.26
0.96
1.14
1.32
1.70
0.80
0.95
1.09
1.40
0.61
0.71
0.81
1.03
0.51
0.59
0.67
0.84
1.47
1.76
2.05
2.66
1.16
1.38
1.59
2.05
0.98
1.16
1.33
1.71
0.75
0.88
1.01
1.27
0.63
0.73
0.84
1.05
250
300
1.50 1.07 0.86
1.77 1.26 1.00
0.60
0.70
0.48
0.56
2.19 1.61
2.58 1.89
1.30
1.52
0.94
1.09
0.75
0.87
2.77 2.09
3.26 2.44
1.71
2.00
1.25
1.45
1.01
1.17
3.27 2.51
3.84 2.94
2.08
2.48
1.54
1.79
1.26
1.46
Note: the pipes sizes are to BS EN 10255: 2004(38) and BS EN 545: 2006(39). It is assumed that the outside surface of the insulation has been painted, is in
still air at 20 °C and hso = 10 W·m–2·K–1
3-28
Reference data
The corrections given for vertical pipes, multiple banks of
pipes and the effect of the proximity of walls in the section
on bare pipes are applicable to insulated pipes.
untreated space. The temperature change in the fluid
passing through a pipe is given by:
Thicknesses of insulation
Minimum thicknesses of insulation for the prevention of
freezing or condensation are given in BS 5422(47) for a
range of applications and conditions. These include
refrigeration, chilled and cold water supplies in industrial
and commercial applications, central heating, air conditioning and direct hot water supply installations in both
non-domestic and domestic applications.
In some circumstances it is important to relate the
thickness of insulation to the financial cost involved. This
can be addressed by introducing the concept of the
‘economic thickness of insulation’. According to BS
5422(47), the ‘economic thickness’ is defined as the thickness of insulation that gives a minimum total cost over a
chosen evaluation period.
The costs to be considered are:
(a)
the cost of heat lost from the insulated surfaces
during the evaluation period
(b)
the cost of the insulation system during the
evaluation period.
Methods of calculating these costs and hence the economic thicknesses of insulation for the applications stated
above are given in BS 5422(47), to which the reader is
referred.
Temperature changes in insulated pipes
In a piping system, the heat gains or losses of the fluid can
be significant, especially when passing through an
θu – θa
Dθ = θu – θd = ———–
0.5 + f
(3.115)
M cp × 103
f = ———–—–
π l dop U
(3.116)
where:
For water, cp = 4.19 kJ·kg–1·K–1 and the loss per metre run
is approximately:
U (θu – θa) dop
Δθm = ———–——–
1330 M
(3.117)
Equation 3.117 is illustrated in Figure 3.9 for various
values of overall transmittance. The U-values for various
thermal conductivities, thicknesses of insulation and pipe
sizes may be found by dividing the values in Table 3.26 by
π dop or by using equation 3.111.
3.3.4.4
Buried pipes
The heat emission from underground piping, whether
buried in ducts, pressure-tight casings, insulating
materials in situ or laid directly in the earth, varies from
that of the insulated pipe exposed freely to ambient air;
this is the result of the additional insulating effect of the
air gap within the duct or outer pipe, where present, and
that of the earth cover. Equation 3.110 may be adapted to
each of these cases with sufficient accuracy for practical
purposes, bearing in mind the thermal resistance of the air
gap is not greatly significant and that of the earth cover
Temperature change along 10 m of pipe of diameter 1 m per unit
temperature difference between pipe and surroundings / K
0.001
0.0005
U = 0.9 W.m–2.K–1
.
0.7
0.5
0.3
0.0001
0.1
0.00005
0.00001
2
5
10
Figure 3.9 Temperature change along insulated pipes in air
20
50
Flow rate / kg·s–1
100
200
500
1000
Heat transfer
3-29
Ground
Level
will vary dependent upon its wetness. BS 4508(49)
describes methods for the determination of heat losses.
The heat loss per metre run of buried pipe is given by the
following expression:
Φ / l = π dop U (θs + θe)
m
dop
don
(3.118)
dic
where the overall thermal transmittance is given by:
1
U = ——————
Rn + Ra + Re
(3.119)
The thermal resistance of the insulation is given by:
( )
dop
don
Rn = —— ln —–
2 λn
dop
(3.120)
Figure 3.10 Twin pipe underground mains
loss calculation gives answers agreeing closely with field
test results:
(a)
Use equation 3.118 to calculate the heat losses
from the flow pipe assuming it to be alone in the
centre of a large casing.
(b)
Repeat this procedure for the return pipe.
(c)
Add (a) and (b) to give the total loss.
The thermal resistance of the air gap is given by:
dop
dop
Ra = ——– + ——–
hso don
hsi dic
(3.121)
The thermal resistance of the earth cover is given by:
(( ) {
dop
2m
Re = —— ln ––––
2 λe
di c
[ ( ) ] })
dic
1 + 1 – ––––
2m
2
0.5
(3.122)
If the burial depth m is greater than 2 don , then equation
3.122 reduces to approximately:
2 a1 a2
dh = ———
a1 + a2
(3.126)
Thermal conductivity of insulation
( )
4m
dop
Re = —— ln —–
2 λe
dic
(3.123)
If there is no air gap, dic equals don.
The outside surface temperature of the insulation or
pressure tight casing is often an important factor and may
be calculated from:
θc = θs – Rn ( θs – θe) U
Thermal resistance of air space
)
θs1 – θe
M cp ln ———
θs2 – θe
U = ———————
π dop l
The values shown in Figure 3.8 are for dry insulants. If
the insulation becomes wet, a considerable increase in the
thermal conductivity may be expected. Thoroughly
saturated insulation may approach the thermal conductivity of water (approximately 0.6 W·m–1·K–1). If evaporation
occurs, the heat loss will be even greater.
(3.124)
The overall thermal transmittance required to prevent the
fluid temperature falling below a specified value over a
given distance may be calculated from:
(
If the duct is of rectangular cross-section (dimension a1 by
a2) then the equivalent diameter should be used, given by:
(3.125)
Although an air space around an encased insulated pipe is
essential for the detection of leaks and for the drainage
and drying of wet insulation, it has only a small insulation
value compared with normal dry insulants. A typical value
for resistance of the air space (Ra) would be in the order of
0.06 m2·K–1·W–1.
Thermal conductivity of earth cover
In equations 3.118 to 3.125, it is assumed that the surface
temperature of the pipe is equal to the fluid temperature
and that the thermal resistances of the pressure tight
casing and the surface of the ground are negligible.
The depth of the earth cover, the physical properties of the
soil including the porosity and permeability and the external temperature of the casing are all factors affecting the
thermal conductivity of the earth. Table 3.27 lists typical
values of thermal conductivity for various soils (λe)(50).
Twin pipe arrangements
Ground ambient temperature
Underground flow and return mains are often run
together in a pressure tight casing or concrete duct as
illustrated in Figure 3.10. The following method of heat
Table 3.28 lists mean values of ground ambient temperature (θe) for various parts of the UK, measured at a depth
of one metre.
3-30
Reference data
Table 3.27 Thermal conductivity of soils, λe
Soil
description
(d)
Summer
Winter
Moisture
content
/%
Thermal
conductivity
/ W·m–1·K–1
Moisture
content
/%
Thermal
conductivity
/ W·m–1·K–1
Pea ballast
2.3
0.7
11.8
1.8
Poorly graded sand:
(one predominant
particle size)
2.4
0.5
7.7
1.6
Well graded sand
9.3
0.9
21.8
2.1
15.0
0.9
33.0
1.9
—
—
—
1.3*
Predominantly clay 26.3
0.8
33.7
1.5
Chalk
18.2
0.9
30.4
1.2
Mean values
<12%
0.7
>25%
1.7
Sand/clay
mixture (∼20%)
Ditto (if under
impervious cover,
e.g. paving)
*Areas in the order of 103 to 104 m2
There are now many proprietary underground
piping systems available and reference should be
made to manufacturers’ literature.
Cross conduction between pipes
Where flow and return pipes at different temperatures are
close together, heat will flow between them. Whilst this is
not a heat loss, it amounts to an extra pump load on the
system involving extra running costs. For example, an
increase of only 3% in the mass flow rate to maintain flow
temperature would result in 10% extra pumping costs.
Insulation systems which can positively ensure an
adequate degree of insulation between flow and return will
therefore show an additional economic benefit.
3.3.4.5
Air ducts
In an air duct system heat gains or losses of the ducted air
can be significant, especially when passing through an
untreated space in a supply system. This also has the effect
of reducing the heating or cooling capacity of the air. The
heat emission or absorption from air ducts is given by:
Table 3.28 Ground ambient temperature θe at the depth of 1 m
Region
Summer
18
8
Northern Ireland, North Wales and
East Midlands
17
7
Central Midlands, North West
England and Scotland
16
6
North East England and Scotland
15
5
1 °C should be added to the above values for built-up areas
Tabulated data
Owing to the number of variables involved, tables of heat
emissions are not presented. However, for convenience,
values of ln (don / dop) and ln (4 m / dic) are listed in Tables
3.29 and 3.30 for different thicknesses of insulation and
burial depths.
The following practical considerations should be taken
into account.
(b)
(c)
(3.127)
Winter
South of England and South Wales
(a)
Φ = U A Δθ
Mean ground temp. / °C
To use theoretical figures based on dry insulation
could sometimes lead to technical or economic
failures except in those systems that are pressuretight to at least 200 kPa and the insulation is
capable of being dried out to its original thermal
and physical condition.
Damp insulation conditions are frequently
observed and measurement of heat losses, even on
installations which appear satisfactory, have shown
that they can be several times greater than theoretical figures and of the same order as bare pipes in
dry soils. Flooded ducts and wet soil will result in
excessive heat losses.
The thermal conductivity of the soil makes a
relatively small contribution to the overall heat
loss from a well-insulated pipe. Therefore, where
the type and state of the earth cover are not
known, the mean value may be used without
undue error.
or more conveniently per metre run of duct:
Table 3.29 Solutions of 1n (don/dop) for steel pipe
Nominal pipe
size / mm
Value of 1n (don/dop) for stated thickness
of insulation / mm
12.5
19
25
38
50
75
100
15
20
25
32
0.77
0.66
0.55
0.46
1.0
0.88
0.75
0.64
1.2
1.1
0.91
0.78
1.5
1.3
1.2
1.0
1.7
1.6
1.4
1.2
2.1
1.9
1.7
1.5
2.3
2.1
1.9
1.7
40
50
65
80
0.42
0.35
0.28
0.25
0.58
0.49
0.41
0.36
0.71
0.60
0.51
0.45
0.94
0.82
0.69
0.62
1.1
0.98
0.84
0.75
1.4
1.2
1.1
0.99
1.6
1.5
1.3
1.2
100
125
150
200
0.20
0.16
0.14
0.11
0.29
0.24
0.21
0.16
0.36
0.31
0.26
0.21
0.51
0.43
0.38
0.30
0.63
0.54
0.47
0.38
0.84
0.73
0.65
0.52
1.0
0.89
0.79
0.65
250
300
350
400
0.088
0.074
0.068
0.060
0.13
0.11
0.10
0.089
0.17
0.14
0.13
0.12
0.25
0.21
0.19
0.17
0.31
0.27
0.25
0.22
0.44
0.38
0.35
0.31
0.55
0.48
0.45
0.40
Table 3.30 Solutions of 1n (4 m / dic)
Nominal pipe
size / mm
Value of 1n (4 m / dic ) for stated burial depth / mm
0.5
1.0
1.5
2.0
2.5
3.0
50
75
100
125
3.7
3.3
3.0
2.8
4.4
4.0
3.7
3.5
4.8
4.4
4.1
3.9
5.1
4.7
4.4
4.2
5.3
4.9
4.6
4.4
5.5
5.1
4.8
4.6
150
175
200
225
2.6
2.4
2.3
2.2
3.3
3.1
3.0
2.9
3.7
3.5
3.4
3.3
4.0
3.8
3.7
3.6
4.2
4.1
3.9
3.8
4.4
4.2
4.1
4.0
250
275
300
2.1
2.0
1.9
2.8
2.7
2.6
3.2
3.1
3.0
3.5
3.4
3.3
3.7
3.6
3.5
3.9
3.8
3.7
3-31
]
(3.128)
The temperature change in a ducted air stream is given
by:
θu – θa
θu – θd = ———
0.5 + f
(3.129)
where:
cp dh ρ c × 103
f = ——————
4Ul
(3.130)
The hydraulic mean (equivalent) diameter is found from
equation 3.126 or from the following equation:
dh = 4 Ac / P
(3.131)
and cp = 1.02
For air at 20 C, ρ = 1.2
the temperature change per metre is:
kg·m–3
U (θu – θa)
Δθm = ————–
306 dh c
kJ·kg–1·K–1,
(3.132)
This relationship is illustrated in Figure 3.11 for various
thicknesses of insulation, where a thermal conductivity of
0.045 W·m–1·K–1 has been used. Figure 3.12 relates the
change in temperature to air volume flow for various air
velocities and for 25 mm of insulation.
Overall thermal transmittance
In this context, the overall thermal transmittance is
given by:
1
U = ——————––
1
ln
1
— + —–
+ —–
hsi kn
hso
(3.133)
Table 3.31 lists values of U for various thicknesses and
thermal conductivities of insulation.
Inside surface heat transfer coefficient
U-value (/ W·m–2·K–1) for given
thickness of insulation (/ mm)
50
25 mm of insulation
50
75
100
0.001
0.0005
0.0001
0.2
0.4
0.6 0.8 1
2
4
6
8 10
Figure 3.11 Temperature change along insulated ducts for various
thicknesses of insulation
0.01
Correction factors for
rectangular ducts
0.005
2.5 m·s–1
Aspect ratio
1.1
1.2
1.3
1.4
1.5
Factor
1.15
1.24
1.37
1.51
1.65
5
10
15
0.001
20
0.0005
0.0001
0.2
0.4
0.6 0.8 1
2
4
6
8 10
–1
Air flow / (m ·s )
Table 3.31 U-values for insulated air ducts
25
0.005
3
The internal surface heat transfer coefficient (hsi) is a
function of the Reynolds number as shown by equation
3.41. The value for hsi can be determined from equation
3.41, applied for the appropriate conditions.
Thermal conductivity
of insulation / W·m–1·K–1
0.01
(dh v)
Temperature change along 1 m of duct per unit temperature
difference between duct and surrounding air / K
[
(θu + θd)
Φ / l = U P ————
– θa
2
Temperature change along 1 m of duct per unit temperature
difference between duct and surrounding air / K
Heat transfer
75
100
0.025
0.03
0.035
0.04
0.045
0.89
1.04
1.19
1.33
1.47
0.47
0.56
0.64
0.73
0.81
0.32
0.38
0.44
0.50
0.56
0.24
0.29
0.34
0.38
0.43
0.05
0.055
0.06
0.07
0.08
1.60
1.72
1.84
2.07
2.28
0.89
0.97
1.04
1.19
1.33
0.61
0.67
0.73
0.83
0.94
0.47
0.51
0.56
0.64
0.73
Figure 3.12 Temperature change along insulated ducts for various air
flow velocities (for 25 mm of insulation)
Outside surface heat transfer coefficient
A typical value for the outside surface heat transfer
coefficient (hso) is 10 W·m–2·K–1 but this value may well be
lower if the duct is in close proximity to its surroundings.
Values for other conditions may be obtained from Table
3.25.
Practical considerations
As the temperature difference in equation 3.132 is
expressed in terms of the initial temperature difference
rather than the mean temperature difference, some error
will be introduced if the value of the length of ductwork
chosen for calculation is too large. The smaller the value
of dh × v, the larger the error. A maximum length of 10 m
is recommended. It may be noted from Figure 3.11 that as
3-32
Reference data
10 000
·K–1
1000
30
Asi
so
W
100
50
0
20
15
0
0
·m –2
·K –1
20
10
10
50
100
500 1000
Values for hso / (W·m–2·K–1)
5000 10000
Figure 3.13 Values of Uc
or more conveniently:
The overall heat transfer coefficient between two
separated fluids can be calculated from:
1
U = —————————————
1
lzo
lw
lzi
1
—– + —–
+ —–
+ —–
+ —–
λw
λzi
hsi
hso λzo
(3.138)
Values for Uc can be obtained from Figure 3.13.
l
U = —————————————————–––––
1
lzo
lw
l
Aso
1
A
—– + —–
+ —–
+ —zi– × —–
—– × —–so
hso
λzo
λw
λzi Asi
hsi Asi
(
Asi
hso hsi —–
Aso
Uc = —————–
A
hso + hsi —–si
Aso
(3.135)
The overall heat transfer coefficient for thin-walled
tubes is:
)(
)
(3.136)
In the case of clean tube surfaces and neglecting the tube
wall resistance, equation 3.136 simplifies to:
l
Uc = ———————––
1
1
A
—– + —– × —–so
hso
hsi Asi
(
0
30
Overall heat transfer coefficient
40
7
6 0
50 0
90
80
50 0
0
40
10
(3.134)
0
10
U c
500
The basic equation for heat transfer between the two
fluids separated by a solid surface is:
Φ = U A Δθλ
00
10
15
A heat exchanger transfers heat from one fluid to another
by conduction, radiation or convection or by a combination of these. The two fluids can stay as liquids or gases
or they can change from one state to the other as, for
example, in evaporators and condensers. The commonest
arrangement is for the two fluids to flow in separate
channels with heat exchange between them and without
change of state. This arrangement is discussed below.
00
9 0
8 00 0
7 0
60 00 0
( A ) / W·m
Heat exchangers
(3.137)
)
Values of hsi for water flow through tubes and hso for
forced water flow over tubes are shown in Tables 3.32 and
3.33. Values for lzo / λzo and lzi / λzi (fouling resistances) are
usually determined by experience although the values
given in Table 3.34 provide a guide(51). The fouling resistance can be a significant proportion of the total resistance
and hence should be taken into account in heat exchanger
design.
For heat transfer calculations in shell and tube heat
exchangers, it is necessary to determine values for the
surface heat transfer coefficients for particular flow
configurations:
(a)
For forced convection flow inside tubes, use can be
made of equation 3.41 or 3.43.
Table 3.32 Convective film coefficient (hsi) for turbulent water flow through straight plain tubes
Tube inside
diameter / mm
00
20
15
Values for hsi
3.3.4.6
30
5000
–2
the value of dh × v falls below 1.5, the rate of temperature
drop in ducts with 50 mm or less of insulation increases
considerably. It is usually not practical to keep the value
above this by changing dh or v, so extra insulation should
be considered.
Inside film coefficient (/ W·m–2·K–1) for a water temperature of 75 °C and stated water velocities (/ m·s–1)
0.2
0.4
0.6
0.8
1.0
1.5
2
3
20
25
32
40
1760
1680
1600
1530
3060
2930
2790
2670
4240
4060
3860
3690
5340
5110
4860
4650
6380
6100
5810
5560
8820
8440
8040
7680
11 100
10 600
10 100
9620
15 400
14 700
14 000
13 400
19 300
18 500
17 600
16 800
50
80
100
1470
1330
1280
2550
2320
2220
3540
3210
3080
4450
4050
3870
5320
4830
4630
7350
6690
6400
9260
8420
8050
12 800
11 600
11 100
16 100
14 700
14 000
Correction factors for other water temperatures
Temperature / °C
10
25
50
100
150
200
Multiplying factor
0.65
0.65
0.84
1.11
1.34
1.37
4
Heat transfer
3-33
200
Tube outside
diameter / mm
0.1
0.2
0.3
0.4
0.5
0.6
2120
1920
1720
1550
1400
3100
2810
2520
2270
2050
3880
3510
3150
2840
2570
4540
4110
3680
3320
—
5130
4650
4170
—
—
5680
5140
—
—
—
Correction factors for other water temperatures
Temperature / °C
Multiplying factor
(b)
(c)
10
25
50
100
150
200
0.70
0.79
0.85
1.10
1.21
1.25
For free or forced correction flow outside single
tubes, refer to Tables 3.2 and 3.4, respectively.
For forced convection flow outside tube bundles,
details can be found in reference 4.
15
0
100
80
60
50
40
30
25
70
30
20
20
Δ
10
8
6
8
15
=
6
9
10
°C
7
5
4
4
3
3
2
2
1
60
10
9 0
80 0
40
θ
20
25
32
40
50
Outside film coefficient (/ W·m–2·K–1) for a
water temperature of 75 °C and stated
water velocities (/ m·s–1)
Greatest terminal temperature difference / K
Table 3.33 Convective film coefficient, hso , for turbulent water flow over
straight plain tubes
2.
5
1.
5
1
2
3 4
6 8 10
20 30 40 60
100 150
Smallest terminal temperature difference / K
Figure 3.14 Values of logarithmic mean temperature difference
Logarithmic mean temperature difference
The logarithmic mean temperature difference can be
calculated from:
Δθtg – Δθts
Δθl = ————–
Δθtg
ln ——
Δθts
(3.139)
( )
ature difference. Typical values of this factor are given in
Figures 3.15 and 3.16 and more detailed information can be
obtained from references 51 to 54.
Effectiveness — NTU method
Equation 3.139 is not solvable if Δθtg and Δθts are equal. In
this case, and when the ratio Δθtg / Δθts is close to unity,
Δθtl can be taken as the arithmetic mean value of Δθtg and
Δθts. Values of Δθl can be obtained directly from Figure
3.14. Here, the term ‘terminal’ temperature difference
refers to the temperature difference between hot and cold
fluid streams at a given end of the heat exchanger. The use
of the logarithmic mean temperature difference in
equation 3.134 is strictly correct only for constant U,
constant specific heat capacity and parallel or counterflow
arrangements under steady state conditions.
The logarithmic mean temperature difference method(54)
is convenient for calculating the heat transfer rates in heat
exchangers when terminal temperatures are known. More
commonly, however, the terminal temperatures are
unknown, rendering impractical the adoption of the
logarithmic mean temperature difference method. In this
situation, the alternative ‘effectiveness-NTU’ method can
be used(54). This method is based upon three dimensionless parameters:
actual rate of heat transfer, Φ
η = —————–—————————————
maximum possible rate of heat transfer, Φmax
For multipass shell and tube heat exchangers, a correction
factor should be applied to the logarithmic mean temper-
(3.140)
Table 3.34 Fouling resistances, lz / λz
Type of water
Fouling resistances ( / m–2·K–1·W–1) for stated temperatures and water velocities
Heating medium ≤ 120 °C;
water ≤ 50 °C
≤ 1 m·s–1
> 1 m·s–1
Heating medium 120–200 °C;
water > 50 °C
≤ 1 m·s–1
> 1 m·s–1
Sea water
0.0001
0.0001
0.0002
0.0002
Brackish water
0.0004
0.0002
0.0005
0.0004
Cooling tower make-up water:
— treated
— untreated
0.0002
0.0005
0.0002
0.0005
0.0004
0.0009
0.0004
0.0007
Well water
0.0002
0.0002
0.0004
0.0004
River water:
— clean
— polluted
0.0004
0.0014
0.0002
0.0011
0.0005
0.0018
0.0004
0.0014
Boiler blowdown
0.0004
0.0004
0.0004
0.0004
Boiler feedwater (treated)
0.0002
0.0001
0.0002
0.0002
3-34
Reference data
0.2
0.4
0.6
0.8
1.0
0.9
2.0
1.8
1.6
1.4
1.2
4.0
3.0
2.5
hi
0.8
to
– θ ho
– θ ti
)
0.9
change in phase occurs, as in condensers and evaporators
in refrigeration), Z becomes zero. For any heat exchanger
configuration where Z is zero, the heat exchanger effectiveness is:
( θθ
Correction factor
1.0
η = 1 – e–NTU
0.7
0.6
References 11 and 55 give relationships for η,
for other configurations.
0
0.1
0.2
0.3
0.5 0.6 0.7 0.8 0.9 1.0
θ to – θ ti
θ hi – θti
Figure 3.15 Correction factors for assessing mean temperature difference
of multipass heat exchangers (one shell pass, two or more tube passes)
)
0.9
0.2
0.4
0.6
0.8
1.0
1.2
1.4
2.0
1.8
1.6
2.5
4.0
3.0
)
hi
to
– θ ho
– θ ti
0.6
( θθ
Correction factor
1.0
0.7
0
0.1
0.2
0.3
0.5 0.6 0.7 0.8 0.9 1.0
θ to – θ ti
θ hi – θti
Figure 3.16 Correction factors for assessing mean temperature difference
of multipass heat exchangers (two shell pass, four or more tube passes)
and Z
Example 3.4
Hot oil enters a counterflow heat exchanger at a mass flow
rate of 2.0 kg·s–1 with an inlet temperature of 150 C and
an outlet temperature of 45 C. The hot oil is being cooled
by water that enters at a temperature of 20 C and at a
mass flow rate of 1.8 kg·s–1. The diameter of the heat
exchanger inner tube is 0.025 m and its length is 10.0 m.
Determine the overall heat transfer coefficient, U, of this
heat exchanger using (a) the logarithmic mean temperature method (LMTD), and (b) the effectiveness-NTU
method.
0.4
(
)
Data: specific heat capacity of oil = 2.1 kJ·kg–1·K–1,
specific heat capacity of water = 4.2 kJ·kg–1·K–1.
(a)
NTU
NTU
0.4
(
0.8
(3.147)
AU
= ——
Cmin
(3.141)
(3.142)
(3.143)
The maximum possible heat transfer rate Φmax is given by:
Φmax = Cmin ( θhfi – θcfi)
(3.144)
where θhfi and θcfi are the inlet temperatures of the hot and
cold fluids, respectively. From a knowledge of these
temperatures, together with values for Cmin and g, the
actual heat transfer rate of the heat exchanger can be
determined from equation 3.140. Note that fluid inlet
temperatures and mass flow rates are commonly known in
a given application. The heat exchanger effectiveness g is a
function of NTU, Z and heat exchanger configuration.
For the parallel flow configuration:
1 – exp[–NTU (1 + Z)]
η = —————–————
1+Z
(3.145)
(3.148)
The outlet temperature of the cold fluid (water) is:
θcfo = θcfi + (Φ / M cp)
(3.149)
= 20 + (441/(1.8 × 4.2)) = 78.3 °C
Now that the outlet temperatures of both fluids are
known, the LMTD method can be used to determine the
overall heat transfer coefficient.
The greatest terminal temperature difference, Δθtg , is:
Δθtg = θhfi – θcfo
(3.150)
= 150 – 78.3 = 71.7 C
The smallest terminal temperature difference, Δθts , is:
Δθts = θhfo – θcfi
(3.151)
= 45 – 20 = 25 C
The logarithmic mean temperature difference, Δθl, can
then be determined either graphically from Figure 3.14 or
analytically from equation 3.139 giving:
(71.7 – 25)
Δθl = ————— = 44.3 °C
ln (71.7/25)
For the counterflow configuration:
1 – exp[–NTU (1 + Z)]
η = —————–————–
1 – Z exp[–NTU (1 – Z)]
The actual rate of heat transfer from the hot fluid (oil) is:
= 2.0 × 2.1 (150 – 45) = 441 kW
where η is the heat exchanger effectiveness, NTU is the
number of heat exchanger heat transfer units, Z is the heat
capacity rate ratio, Cmin and Cmax are the smaller and
greater, respectively, of the fluid heat capacity rates, i.e:
C(min, max) = M cp
method
Φ = M cp (θhfi – θhfo)
and:
Cmin
Z = ——
Cmax
LMTD
(3.146)
Note that for the case where one fluid remains at a
constant temperature throughout the heat exchanger (i.e. a
The overall heat transfer coefficient, U, is then given by:
U = Φ / A Δθl
(3.152)
= 441/(π × 0.025 × 10 × 44.3) = 12.7 kW·m–2·K–1
Heat transfer
(b)
3-35
Effectiveness — NTU method
The actual part which each component contributes to the
total heat transfer depends on prevailing conditions. In
the case of indoor pools and tanks, this will normally
depend on the environment provided by the heating and
ventilating installation.
The heat capacity rate of the hot fluid (oil) is:
M cp = 2.0 × 2.1 = 4.2 kW·K–1
Similarly, the heat capacity rate of the cold fluid (water) is:
M cp = 1.8 × 4.2 = 7.56 kW·K–1
The heat capacity rate ratio, Z, from equation 3.142 is:
Z = 4.2/ 7.56 = 0.56
The maximum possible heat transfer rate, Φmax , is given
by equation 3.144:
Φmax = 4.2 (150 – 20) = 546 kW
The actual rate of heat transfer from the hot fluid (oil)
from equation 3.149 is:
Φ = 2.0 × 2.1 (150 45) 441 kW
The heat exchanger effectiveness, g , is given by equation
3.141:
η = 441/546 = 0.81
For the counterflow configuration, equation 3.146 can be
rearranged to give:
NTU
η–1
1
= ——— ln ———–
ηZ–1
(Z – 1)
(
)
(
(3.153)
)
1
0.81 – 1
= ———– ln ——————— = 2.4
0.56 – 1
(0.81 × 0.56) × 1
From equation 3.141, the overall heat transfer coefficient,
U, can be calculated to give:
U = (2.4 × 4.2) / (π × 0.025 × 10)
= 12.8 kW·m–2·K–1
3.3.4.6
Evaporators and condensers
For heat exchangers where one or both of the fluids
undergoes a change of state, the fundamental equations
are complex. They depend on the mode of boiling and
condensing and this, in turn, depends on the fluid
conditions and mechanical design of the heat exchanger.
Information on the design of heat exchangers for boiling
and condensing is given in references 5 and 56.
3.3.4.7
Open water surfaces
Heat transfer from open water surfaces takes place by:
(a)
evaporation, i.e. conversion of part of the water to
vapour and the transfer of the vapour through
diffusion and convection (Φe)
(b)
convection to, and from, the air in contact with the
surface (Φc).
(c)
Radiation to, and from, the surface (Φr).
(d)
Conduction to, and from, the surrounds (Φcd).
In the case of outdoor pools, reservoirs, cooling ponds,
etc., it will depend on the prevailing weather conditions
and hence the time of the year. During the hottest part of
summer up to 90% or more of the total heat transfer from
the water is by evaporation. In winter, at low air temperature, the surface evaporation is reduced to approximately
50% of the total, and convection increases proportionately.
Heat transfer by radiation can be an important factor in
the performance of outdoor cooling ponds where solar
radiation can seriously reduce the cooling effect.
Conversely, solar radiation can contribute to the heating of
outdoor swimming pools.
Conduction between the water and the surrounds when
the containing walls are sunk in the ground is generally
small, even when heating up or cooling down, because of
the large masses involved. The mass of earth surrounding
the pool eventually warms up to a temperature close to
that of the water and acts as a stabiliser because of its large
thermal capacity.
Where the containing walls are surrounded by air,
conduction can be significant but is still small in relation
to the total heat transfer.
The total heat loss rate from unit area of an open water
surface, in W·m–2, can be expressed as:
ΣΦ = Φe + Φc + Φr + Φcd
(3.154)
Φe = (91.5 + 77.6 ca ) (psw – pv)
(3.155)
Φc = 3.18 ca0.8 (θsw – θa )
(3.156)
Φr = 5.67 × 10–8 εw (Tsw4 – Trs4) – I
(3.157)
Φcd = Ut (θsw – θa )
(3.158)
where:
Values of Φe are given in Figure 3.17 and values of
convective heat transfer coefficient for estimation of Φc
are given in Figure 3.18. Where the tank walls and floor
are surrounded by a large mass, Φcd is generally negligible.
The emissivity of water can be taken as 0.96 and radiation
gains, for the UK, are given in Table 3.35(57).
The mass rate of evaporation from an open water surface
is:
Φe
W = ———–
hfg × 103
(3.159)
The mean radiant absolute temperature of the sky can be
approximated as:
Trs = 253 + θa
(i.e. 20 K below the air temperature).
(3.160)
3-36
Reference data
Table 3.35 Radiation gains to outside pools and reservoirs in the UK
Period
Daily gain
/ MJ·m–2
May–September
January–December
Average duration
of radiation gain
/h
Average night
loss rate
/ W·m–2
Night loss
/ MJ·m–2
Net radiation
gain per 24-hours
/ MJ·m–2
13.8
16
240
50
1.4
12.4
8.4
14
167
41
1.5
6.9
18
8m
·s –1
7m
·s –1
8000
16
=
Convective heat transfer coefficient / W·m–2·K–1
6m
·s –1
Ve
loc
ity
7000
5
m
·s –1
6000
m
·s –1
5000
4
Heat transfer by evaporation / W·m–2
Average
intensity
/ W·m–2
4000
–1
3
m
·s
3000
–1
s
·
2m
2000
–1
·s
1m
–1
·s
5 m –1
0.7 5 m·s
0.
Still air
1000
14
12
10
8
6
4
2
–1
0 m·s
0
0
2.5
5.0
7.5
10.0
0
12.5
Vapour pressure difference / kPa
Figure 3.17 Values of evaporative heat transfer
If there is no artificial heat source, an equilibrium state is
reached when the rate of heat loss by evaporation equals
the rates of heat gain by convection plus radiation and
conduction, i.e.:
(3.161)
If Φr and Φcd are approximately zero, then the water temperature will approach the wet bulb temperature of the air.
The heat transfer by evaporation is based on empirical
data. Various references give results covering a fairly wide
range. Many of the experiments that have been carried out
have been based on relatively small surface areas and
errors are probably introduced when extrapolating to larger areas. The equation given appears to give reasonable
results in practice.
3.3.4.8
8
Figure 3.18 Values of convective heat transfer
Assumptions for water temperature values must be made
in order to solve these equations. If there is an artificial
heat source and this is thermostatically controlled to
maintain the water at a constant temperature, no problem
exists. In the case of a cooling pond the outlet temperature
should be used.
Φe = Φc + Φr + Φcd
2
4
6
Air velocity at water surface / m·s–1
necessary because of the variability of conditions that can
be encountered in practice. For example, for the purpose
of Building Regulations, U-values (thermal transmittances) are calculated for conditions of steady state heat
transfer and on the basis of standardised heat transfer
coefficients. The reader is therefore referred to references
58–64 which cover in more detail the measurement, simulation or calculation of parameters, such as U-values, in
accordance with accepted standards.
For example, windows (glazing and framework) can have a
significant influence upon the internal environment of a
building. In this respect, the thermal, acoustic, solar and
daylight performances of windows are important and need
to be evaluated in an integrated manner. With respect to
glazing only, such factors have been investigated for a
number of configurations(65), and the reader is referred to
the latter reference. For double glazed windows, factors
such as temperature distribution of the inner glazing,
condensation occurrence and the influence of framework
are discussed in reference 66. For further information on
overall window performance, refer to the standards cited
above.
Building components
The thermal performance of building components (e.g.
walls, windows, doors, shutters, etc.) is evaluated for
design purposes using standardised procedures. This is
References
1
Rogers G F C and Mayhew Y R Engineering Thermodynamics,
Work and Heat Transfer 4th edn. (London: Longman) (1992)
Heat transfer
3-37
2
Eckert E R G and Drake R M Heat and Mass Transfer (London:
McGraw-Hill) (1959)
26
Walton G N ‘A new algorithm for radiant interchange in room
load calculations’ ASHRAE Trans. 2 190–208 (1980)
3
Cengel, Y A, Introduction to Thermodynamics and Heat Transfer,
(New York, NY: McGraw-Hill) (1997)
27
HVAC Systems and Equipment ASHRAE Handbook (Atlanta,
GA: American Society of Heating, Refrigerating and Airconditioning Engineers) (2004)
4
Incropera F P and De Witt D P Fundamentals of Heat and Mass
Transfer 3rd edn. (New York: Wiley) (1990)
28
Fanger P O Thermal Comfort Analysis and Applications in Environmental Engineering (Copenhagen: Danish Technical Press)
(1970)
29
McIntyre D A Indoor Climate (London: Applied Science
Publishers) (1980)
30
Nishi Y and Gagge A P ‘Effective temperature scale useful
for hyperbaric environments’, Aviation, Space and
Environmental Medicine 48 97–107 (1977)
31
Neilson M and Pedersen L ‘Studies on the heat loss by
radiation and convection from the clothed human body’, Gita
Psychologica Scandinavia 27 272–294 (1952)
32
Rapp G M ‘Convective heat transfer and convective coefficients
of nude man, cylinders and spheres at low air velocities’,
ASHRAE Trans. 79(1) 75–87 (1973)
33
Mitchell D ‘Convective Heat Loss from Man and Other
Animals’ in Monteith I L and Mount L E (eds.) Heat Loss from
Animals and Man (London: Butterworth) (1974)
34
Winslow C E A, Herrington L P and Gagge A P ‘Physiological
Reactions of the Human Body to Varying Environmental
Temperatures’ American J. of Physiology 120(1) 1–22 (1937)
35
Kerslake D McK The Stress of Hot Environments (Cambridge:
Cambridge University Press) (1972)
36
Siegel R and Howell J R Thermal Radiation Heat Transfer 3rd
edn. (New York, NY: Hemisphere Publishing Corporation)
(1992)
BS EN ISO 7726: 2001: Ergonomics of the thermal environment.
Instruments for measuring physical quantities (London: British
Standards Institution) (2001)
37
Kays W M and Crawford M E Convective Heat and Mass
Transfer 3rd edn. (New York, NY: McGraw-Hill) (1993)
Parsons K C Human Thermal Environments (London: Taylor
and Francis) (1993)
38
BS EN 10255: 2004: Non-alloy steel tubes suitable for welding or
threading. Technical delivery conditions (London: British
Standards Institution) (2004)
39
BS EN 545: 2006: Ductile iron pipes, fittings, accessories and their
joints for water pipelines. Requirements and test methods (London:
British Standards Institution) (2006)
5
Jakob M Heat Transfer Vol. 1 (New York, NY: Wiley) (1949)
6
Zhukauskas A ‘Heat transfer from tubes in cross flow’, in
Hartnett J P and Irvine T F Jr. (eds.) Advances in Heat Transfer,
Vol. 8 (New York NY: Academic Press) (1972)
7
Gnielinski V ‘New equations for heat and mass transfer in
turbulent pipe and channel flow’ Int. Chemical Engineering
16(2) 359 (1976)
8
Kreith F and Bohm M S Principles of Heat Transfer 5th
edn. (West) (1993).
9
Holman J P Heat Transfer 7th edn. (New York, NY: McGrawHill) (1992)
10
Environmental design CIBSE Guide A (London: Chartered
Institution of Building Services Engineers) (2006)
11
McAdams W H Heat Transmission (New York, NY: McGrawHill) (1954)
12
Moon P H Scientific Basis of Illuminating Engineering (New
York, NY: McGraw-Hill) (1936)
13
Hamilton D C and Morgan W R Radiant interchange
configuration factors NACA Technical Note 2536 (Washington
DC: National Advisory Council on Aeronautics) (1952)
14
15
16
Mills A F Basic Heat and Mass Transfer 2nd edn. (Englewood
Cliffs, NJ: Prentice Hall) (1999)
17
Threlkeld J L Thermal Environmental Engineering 2nd edn.
(Englewood Cliffs, NJ: Prentice Hall) (1970)
18
Rowley F B, Algren A B and Blackshaw J L ‘Effects of Air
Velocities on Surface Coefficients’ ASHVE Trans. 36 426–446
(1930)
40
BS EN 10220: 2002: Seamless and welded steel tubes. Dimensions
and masses per unit length (London: British Standards
Institution) (2002)
19
Jürges W ‘Der Wärmeubergang an einem ebenen Wand (Heat
transfer at a plane wall)’ Beizh. Z Giesundh. Ing. Ser. 1(19)
(1924)
41
BS EN 1057: 2006: Copper and copper alloys. Seamless, round
copper tubes for water and gas in sanitary and heating applications
(London: British Standards Institution) (2006)
20
Loveday D L and Taki A H ‘Outside surface resistance:
proposed new value for building design’, Proc. CIBSE A:
Building Serv. Eng. Res. Technol. 19(1) 23–29 (1998)
42
Gardner K A ‘Efficiency of extended surface’, Trans. ASME,
67(8) 621 (November 1945)
43
21
Awbi H B and Hatton A ‘Natural Convection from Heated
Room Surfaces’, Energy and Buildings 30(3) (1999)
Schneider R J Conduction Heat Transfer (Addison-Wesley)
(1955)
44
22
Min T C, Schutrum L F, Parmelee G V and Vouris J D,
‘Natural convection and radiation in a panel heated room’,
ASHVE Trans. 62 337 (1956)
Norris R H and Spofford W A ‘High performance fins for heat
transfer’ Trans. ASME 64 489 (1942)
45
Joyce T F ‘Optimisation and design of fin-tube heat exchangers
JIHVE (35) 8 (April 1967)
46
Peach J ‘Radiators and other convectors’ JIHVE 39 239
(February 1972) and JIHVE 40 85 (July 1972)
47
BS 5422: 2001: Method for specifying thermal insulating materials
on pipes, ductwork and equipment (in the temperature range –40 °C
to +700 °C) (London: British Standards Institution) (2001)
48
BS 3958: Thermal insulation materials (London: British
Standards Institution) (1972–1986)
49
BS 4508: Thermally insulated underground pipelines (2 parts)
(London: British Standards Institution) (1977, 1986)
23
Alamdari F and Hammond G P ‘Improved correlations for
buoyancy-driven convection in rooms’, Building Serv. Eng. Res.
Technol. 4 106–112 (1983)
24
Khalifa A J N and Marshall R H ‘Validation of heat transfer
coefficients on interior building surfaces using a real-sized
indoor test cell’ Int. J. Heat and Mass Transfer 33 2219–2236
(1990)
25
Fundamentals ASHRAE Handbook (Atlanta, GA: American
Society of Heating, Refrigerating and Air-conditioning
Engineers) (2005)
3-38
Reference data
50
Mochlinski K and Gosland L Field evidence on soil properties
affecting cable ratings ERA 70–88 (Electrical Research
Association) (1970)
60
BS EN 673: 1998: Glass in building. Determination of thermal
transmittance (U- value). Calculation method (London: British
Standards Institution) (1998)
51
Standards of the Tubular Exchanger Manufacturers Association 8th
edn. (New York, NY: Tubular Exchanger Manufacturers
Association) (1998)
61
BS EN 12412: 2003: Thermal performance of windows, doors and
shutters. Determination of thermal transmittance by hot box method
(2 parts) (London: British Standards Institution) (2003)
52
Smith D M ‘Mean temperature difference in cross flow’
Engineering 138 479 and 606 (1934)
62
53
Bowman R A, Mueller A C and Nagle W M ‘Mean temperature
difference in design’ Trans. ASME 283 (May 1940)
BS EN ISO 10077: Thermal performance of windows, doors and
shutters. Calculation of thermal transmittance: Part 1: 2006:
General; Part 2: 2003: Numerical method for frames (London:
British Standards Institution) (2006, 2003)
54
Cengel Y A Heat Transfer: A Practical Approach (New York, NY:
McGraw-Hill) (1998)
63
BS EN ISO 6946: 1997: Building components and building
elements. Thermal resistance and thermal transmittance. Calculation
method (London: British Standards Institution) (1997)
55
Kays W M and London A L Compact Heat Exchangers 3rd edn.
(New York, NY: McGraw-Hill) (1984)
64
56
Kern D Q Process Heat Transfer (New York, NY: McGraw-Hill)
(1950)
BS EN ISO 10211: Thermal bridges in building construction; heat
flows and surface temperatures: Part 1: 1996: General calculation
methods (London: British Standards Institution) (1996)
65
57
Holt J S C Some Aspects of Swimming Pool Design HVRA
Technical Note No. 10 (Bracknell: Heating and Ventilating
Research Association) (1962)
Muneer T and Han B ‘Multiple glazed windows: design charts’
Proc. CIBSE A: Building Serv. Eng. Res. Technol. 17(4) 223–229
(1996)
66
58
BS 874: Methods for determining thermal insulating properties with
definitions of thermal insulating terms. Tests for thermal
transmittance and conductance: Part 3.1: 1987: Guarded hot-box
method; Part 3.2: 1990: Calibrated hot-box method (London:
British Standards Institution) (1987, 1990)
Muneer T, Abodahab N and Gilchrist A ‘Combined
conduction, convection and radiation heat transfer model for
double-glazed windows’ Proc. CIBSE A: Building Serv. Eng.
Res. Technol. 18(4) 183–191 (1997)
59
BS 6993: Thermal and radiometric properties of glazing: Part 1:
1989: Method for calculation of the steady state U-value (thermal
transmittance); Part 2: 1990: Method for direct measurement of Uvalue (thermal transmittance) (London: British Standards
Institution) (1989, 1990)
4-1
4
Flow of fluids in pipes and ducts
4.1
Introduction
4.10
Pressure loss factors for pipework components
4.2
Notation
4.11
Pressure loss factors for ductwork components
4.3
Fluid flow in straight pipes and ducts
4.4
Components and fittings
4.5
Water flow in pipes
4.6
Flow of steam in pipes
4.7
Natural gas in pipes
4.8
Air flow in ducts
Appendix 4.A4: Steam flow in pipes
4.9
Pressure loss factors for components and fittings
Appendix 4.A5: Compressible flow
4.1
Introduction
4.1.1
New to the 2007 edition
References
Appendix 4.A1: Properties of various fluids
Appendix 4.A2: Pipe and duct sizing
Appendix 4.A3: Capacity (K) and complex networks
At the time of publication of the previous (2001) edition of
this Guide, the report of a major European Research
Programme(1) on more than 500 different ductwork
components was not available. Data from this report for
the most important items are simplified for inclusion in
the present edition. Some data in the 2001 edition have
been amended in the light of this recent and comprehensive research. Furthermore the European Research
Programme was the first to test each component
comprehensively at a variety of air speeds (i.e. Reynolds
numbers). Where possible therefore, data on Reynolds
number effects have now been added, as the effect is not
negligible. Being now more certain that values of the
pressure loss factor (ζ ) depend upon Reynolds number
and size, this renders much earlier research work
inadequate. Thus data from Idelchik(2), on which the 2001
edition leaned heavily, must now be viewed with
circumspection.
The method for calculating the pressure drop along
pipes and ducts is now much simplified. Hitherto, only
cumbersome iterative methods were possible, therefore
many pages of pre-calculated values were provided.
Since a much simpler, but still accurate equation is now
available (equation 4.5), pipe sizing can be carried out
directly on a simple spreadsheet for any temperature and
indeed for any fluid. The CD-ROM that accompanies this
Guide contains Microsoft® Excel spreadsheets for pipe
and duct sizing. Pre-calculated pressure-drop tables are
therefore no longer needed, and such tables have been
omitted from this edition of Guide C. However, for those
wishing to use the familiar pipe sizing tables, these may
be generated using the spreadsheet provided. Similar
tables may also be generated for duct sizing.
Every effort has been made to present data in a consistent
manner, to spare the user the perplexity which has
troubled the author. Even new research data have been
found to contain many irregularities. Such contradictory
data have been ‘massaged’, and such values are printed in
italics.
For the correct selection of pumps and fans, and the sizing
of pipes/ducts on a life-cycle cost-effective basis, it is
essential that calculated predictions of pressure loss
should be reasonably accurate. The range of data provided
has been extended to enable this. This Guide is intended
for everyday use. Complex as some of these data might
appear to be, it is nevertheless often the result of
simplifications in an effort to produce guidance which is
at the same time both easy to use and of acceptable
accuracy.
Two versions of the Moody chart have been in circulation,
one using a factor 4 f and another f or λ . In 2001, the
CIBSE adopted λ to be in harmony with British
hydraulics engineers and international practice. The new
chart has the appropriate version of the D’Arcy equation
printed on it to avoid any chance of misuse. Nevertheless,
with personal computers now so widespread, numerical
calculations are preferred to the more difficult and
inaccurate graphical method.
4.2
Notation
A
Cross-section area of duct (m2)
Ac
Clear area of mesh screen (m2)
Cα
Correction factor for bends of angle α , relative to
α = 90°
Ccp
Interaction factor for components in close
proximity
4-2
Reference data
CRe
Correction factor for Reynolds number effect,
relative to Re = 2 × 105
γ
Included angle of contraction or expansion
(degrees)
C1
Correction factor
δ
Thickness of orifice plate (mm)
K
Capacity (sometimes called ‘flow capacity’)
(litre·h–1·bar –0.5 or m3·s–1·Pa–0.5)
ε
Pipe wall thickness (mm)
ζ
Pressure loss factor
P
Perimeter (mm)
η
Dynamic viscosity (kg·m–1·s–1)
Pf
Fan power (W)
θ
Temperature (°C)
R
Gas constant (kJ·kg–1·K–1)
λ
Friction coefficient
Re
Reynolds number
λc
Friction coefficient for a circular duct
T
Temperature (absolute) (K)
λr
Friction coefficient for a rectangular duct
ν
Kinematic viscosity (m2·s–1)
Density (kg·m–3)
(m3)
V
Volume
Z
Pressure factor for compressible flow (steam and
air) (kPa1.929)
ρ
c
Velocity (m·s–1)
Suffices for tees
cp
Specific thermal capacity
pressure) (kJ·kg–1·K–1)
d
(at
constant
b
Branch
Diameter (m or mm)
c
Combined flow
de
Equivalent diameter (mm)
s
Single flow along straight path (not combined)
dec
Equivalent diameter at position of combined flow
(tees) (mm)
dh
Hydraulic diameter (= 4 × hydraulic mean radius)
(mm)
g
Gravitational acceleration (= 9.807) (m·s–2)
h
4.3
Fluid flow in straight pipes
and ducts
Breadth of rectangular duct (perpendicular to the
turning plane for bends) (mm)
4.3.1
General
k
Equivalent roughness (mm)
This section gives the basic principles for predicting the
pressure drop in pipes and ducts.
l
Length (m or mm)
n
Number of damper blades
p
Pressure (Pa)
pv
Velocity pressure (= 1/2 ρ c2) (Pa)
qv
Volume flow (m3·s–1 or litre·s–1)
qm
Mass flow (kg·s–1)
qc
Combined flow at tees
qb
Branch flow at tees
qs
Minor flow in the straight of a tee
r
Mean radius of a bend (mm)
ri
Inner radius of a bend (mm)
ro
Outer radius of a bend (mm)
v
Specific volume (m3·kg–1)
w
Width of rectangular duct (in the turning plane for
bends) (mm)
x
Distance between blades of louvres (mm)
z
Height or head of liquid (m or mm)
Δp
Pressure difference (Pa)
Δpb
Pressure difference, buoyancy (Pa)
Δpf
Drop in total pressure, caused by friction (Pa)
α
Angle turned by a bend (degrees)
β
Angle of a branch tee (degrees)
The D’Arcy equation for pressure loss due to friction may
be given as:
l
Δp = λ — 1/2 ρ c2
d
(4.1)
The friction factor, λ , may be obtained mathematically or
from the Moody chart, Figure 4.1, and depends upon the
values of Reynolds number, Re, and relative roughness,
where:
ρcd cd
Re = —— = —–
η
ν
(4.2)
and:
relative roughness = k / d.
Values of roughness k are given in Table 4.1.
Values of internal diameters of pipes, d, are given in Tables
4.2, 4.3 and 4.4. For copper pipes (Table 4.3), the sizes
listed are the preferred sizes given in BS EN 1057: 2006(9).
Although manufacturers may not as yet supply the entire
range, they may be manufacturing other sizes as a transitional arrangement. CEN has defined the recommended
dimensions as a first step towards rationalisation. It is
aiming for not more than three wall thicknesses for any
diameter, and to have a restricted number of diameters.
Three categories of pipe are given: R220 (annealed), R250
Flow of fluids in pipes and ducts
0.08
λ = 64 / Re
laminar
flow
l
Δ pf = λ — 1/2 ρ c2
d
0.072
0.05
0.064
0.04
0.056
0.03
0.048
0.02
0.015
0.04
0.032
0.01
0.008
0.006
0.028
0.004
0.036
0.024
0.002
0.020
0.001
0.0008
0.0006
0.0004
0.016
Roughness coefficient (k / d)
0.1
4-3
0.0002
0.012
0.0001
Smooth
pipes
0.010
0.00005
0.000001
0.000005
0.008
0.00001
3
4
10
10
5
6
10
10
10
7
10
8
Reynolds number, Re
Figure 4.1 Moody chart: variation of friction coefficient (λ) with Reynolds number (Re) and relative roughness (k / d)
(half hard) and R290 (hard). Specification involves two
numbers: e.g. 28 × 1.2 means that the outside diameter is
28 mm and the wall thickness is 1.2 mm.
Surface roughness of the duct or pipe is found to have no
effect.
For pipes of PVC -U, grey Imperial (inch) pipes are still
available. The internal diameters given in Table 4.4 were
obtained from Annex B of BS EN 1452-2: 1999(10).
4.3.3
Values of ρ, η, and ν for some fluids are given in Appendix
4.A1.
4.3.2
Laminar flow
Laminar flow occurs for values of Reynolds number less
than 2000. This is most unlikely to occur for water flow or
air flow, but is very likely for more viscous fluids such as
oil. Rather than use Figure 4.1, the value of λ is more
easily obtained from the Poisseuille equation:
This occurs for values of Re greater than 3000. Since air
flow in ducts is more likely to have a Reynolds number in
the region of 100 000 (i.e. 105), it is clear that air flow is
almost invariably turbulent. Water flow is also likely to be
turbulent.
It will be seen from Figure 4.1 that the friction coefficient
depends upon values of both Reynolds number and
relative roughness, k / d. The family of curves on the chart
was generated from the following equation, developed by
Colebrook–White, which may be used directly instead of
using the chart:
(
1
2.51
k/d
—– = –2 log —––—
– + ——
Re √λ
3.7
√λ
For Re < 2000:
64
λ = ——
Re
Turbulent flow
(4.3)
With increasing velocity, Re increases and λ is seen to
decrease. Nevertheless when substituted into equation 4.1,
it will be found that the pressure drop increases with
increasing velocity. With laminar flow, the pressure drop
is directly proportional to velocity. This type of flow
sometimes occurs for air passing through HEPA filters
where the air passageways are particularly small, and with
liquids of high viscosity.
)
(4.4)
Note that the square of the above equation might appear
more elegant, but the essential negative sign would
–
thereby be lost. It is √λ that is needed for the iteration.
The Colebrook–White equation, (equation 4.4), gives
values of λ which are some 2 to 4 per cent greater than
others and so can be considered to include a small margin
of safety(2). The Moody chart was constructed using this
equation.
Several texts give abbreviated forms of equation 4.4 for
particularly smooth pipes and for high values of Re. It is
4-4
Reference data
Table 4.1 Values of equivalent roughness, k , for various pipe and duct materials
Type of material
Condition
Roughness, k / mm
Source
Seamless copper, brass, lead
Commercially smooth
0.0015–0.0100
Idelchik(2)
Cast iron
New
Corroded
With appreciable deposits
Heavily corroded
0.25–1.00
1.00–1.25
2.0–4.0
up to 3.0
Idelchik(2)
Idelchik(2)
Idelchik(2)
Idelchik(2)
Steel pipe, seamless
New
Old but cleaned
Moderately corroded
Water pipelines, used
Encrusted
Poor condition
0.02–0.10
0.04
0.4
1.2–1.5
0.8–0.9
> 5.0
Idelchik(2)
Idelchik(2)
Idelchik(2)
Idelchik(2)
Lamont(3)
Idelchik(2)
Steel pipe, welded
New
With small deposits
With appreciable deposits
Poor condition
0.04–1.0
1.5
2.0–4.0
> 5.0
Idelchik(2)
Idelchik(2)
Idelchik(2)
Idelchik(2)
Steel pipe, galvanised
Bright galvanisation, new
Ordinary galvanisation
0.07–0.10
0.10–0.15
Idelchik(2)
Idelchik(2)
Steel duct, galvanised
Longitudinal seams
Spiral seams
0.05–0.10
0.06–0.12
ASHRAE(4)
ASHRAE(4)
Coated steel
Glass enamel
Asphalt
0.001–0.01
0.12–0.30
Idelchik(2)
Idelchik(2)
0.0015–0.010
Idelchik(2)
Glass
Brick
Fair-faced brickwork
Rough
1.5–7.5
3.5–40
Schneider(5)
Schneider(5)
Plaster
New
0.05–0.15
Idelchik(2)
Concrete pipes
New
Carefully smoothed
Brushed, air-placed
Non-smoothed, air-placed
0.25–0.34
0.5
2.3
3.0–6.0
Idelchik(2)
Idelchik(2)
Idelchik(2)
Idelchik(2)
New
0.0015–0.010*
0.0015–0.010
0.0015–0.010
0.007*
Schneider(5)
Schneider(5)
Schneider(5)
0.05
ASHRAE(4)
Polymers:
— PVC-U
— poly-butylene (PB)
— poly-ethylene (PE-X)
— ABS
Aluminium
Flexible duct
Fully extended
1.0–4.6
ASHRAE(4)
Fibrous glass duct
Spray coated
4.5
ASHRAE(4)
Rock tunnels
Blast-hewed, little jointing
100–140
Roughly cut, highly uneven surface 500–1500
Idelchik(2)
Idelchik(2)
* No original source has been found for the surface roughness of PVC-U or ABS, their values being generally assumed to be
identical to that of PB and PE-X. The values of k = 0.007 mm quoted above are merely those used by manufacturers in
their calculations of pressure drop. In this range, the surface is so ‘smooth’ that the value chosen has little effect on the
pressure drop calculation.
considered safer not to risk making false assumptions with
the consequential risk of using an inappropriate equation.
Since λ appears on both sides of equation 4.4, values can
only be obtained iteratively. Altshul was the first to derive
an equation to give λ directly. Since then, Haaland(14) has
provided an even more useful equation:
[
1
6.9
k/d
—– = –1.8 log —– + ——–
Re
3.71
√λ
( )
]
Example
Calculation of λ, for copper pipe R290 76.1 × 1.5, having
di = 73.1 mm; k = 0.0015 mm, Re = 2.16 × 105
[ ( )]
(
[
1
6.9
k /d
— = –1.8 log —– + ——–
–
√λ
Re
3.71
1.11
(4.5)
The Haaland equation (equation 4.5) is found to have a
narrower band of accuracy over the entire turbulent zone
of the Moody diagram. Relative to the Colebrook-White
equation, the Haaland equation gives values which differ
by no more than ± 1.5%. In the light of this, the use of
equation 4.5 is recommended.
1.11
1
6.9
0.0015 ⫼ 73.1
—– = –1.8 log —–——––– + ——–––––—––
5
√λ
2.16 × 10
3.71
[
= –1.8 log 31.94 × 10–6 + 1.4605 × 10–6
= 8.057
λ = 0.01540
]
) ]
1.11
Flow of fluids in pipes and ducts
4-5
Table 4.2 Internal diameters of steel and iron pipes
Nominal
pipe size
Non-alloy steel (BS EN 10255)
Specified
outside
diameter / mm
Ductile iron (BS EN 545)
Inside diameter / mm
‘Medium’
‘Heavy’
Nominal
outside
diameter / mm
Seamless and welded steel
‘Series 1’ (BS EN 10220)*
Inside diameter / mm
‘Class 40’
‘Type K9’
Outside
diameter
/ mm
Wall
thickness
/ mm
Inside
diameter
/ mm
6
8
10
15
20
10.2
13.5
17.2
21.3
26.9
6.2
9.0
12.5
16.2
21.7
5.0
7.8
11.3
15.0
20.5
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
10.2
13.5
17.2
21.3
26.9
1.4
1.6
1.8
2.0
2.3
7.4
10.3
13.6
17.3
29.1
25
32
40
50
60
33.7
42.4
48.3
60.3
—
27.4
36.1
42.0
53.1
—
25.8
34.5
40.4
51.3
—
—
—
56
66
77
—
—
46.4
56.4
67.4
—
—
44.0
54.0
65.0
33.7
42.4
48.3
60.3
76.1
2.3
2.3
2.6
2.6
2.6
22.3
37.8
43.1
55.1
70.9
65
80
100
125
150
76.1
88.9
114.3
139.7
165.1
68.8
80.8
105.1
129.7
155.2
67.0
78.8
103.3
128.9
154.4
82
98
118
144
170
72.4
88.4
108.4
134.4
160.0
70.0
86.0
106.0
132.0
158.0
—
88.9
114.3
139.7
168.3
—
2.6
2.9
3.2
3.2
—
83.7
108.5
133.3
161.9
200
250
300
350
400
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
222
274
326
378
429
211.2
262.4
313.6
364.0
413.4
209.4
260.4
311.6
362.6
412.8
219.1
273.0
323.9
355.6
406.4
3.6
3.6
4.0
4.0
4.0
211.9
265.8
315.9
347.6
398.4
450
500
600
700
800
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
480
532
635
738
842
—
—
—
—
—
462.8
514.0
615.2
716.4
818.6
457.0
508.0
610.0
711.0
813.0
4.5
4.5
4.5
5.0
5.0
448.0
499.0
601.0
701.0
803.0
900
1000
1100
1200
—
—
—
—
—
—
—
—
—
—
—
—
945
1048
1152
1255
—
—
—
—
919.8
1021.0
1123.2
1224.4
914.0
1016.0
1067.0
1118.0
5.0
5.0
5.4
5.4
904.0
1006.0
1056.2
1107.2
1400
1500
1600
1800
2000
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
1462
1565
1668
1875
2082
—
—
—
—
—
1427.8
1529.0
1630.2
1833.6
2037.0
1219.0
1422.0
1626.0
—
—
5.4
5.6
6.3
—
—
1208.2
1410.8
1613.4
—
—
* BS EN 10220 quotes such a wide range of possible sizes for large steel pipes that the values given should only be regarded as typical.
Table 4.3 Wall thickness and internal diameters of copper pipes (BS EN 1057(9)) (The pipes tabulated are those marked ‘R’
in BS EN 1057 but all might not be readily available in the UK.)
Nominal pipe
size / mm
Combinations of nominal wall thickness, ε (/ mm), and mean internal diameter, di (/ mm)
ε
di
ε
di
ε
di
ε
di
ε
di
6
8
10
12
15
0.6
0.6
0.6
0.6
0.7
4.8
6.8
8.8
10.8
13.6
0.8
0.8
0.7
0.7
0.8
4.4
6.4
8.6
10.6
13.4
1.0
1.0
0.8
0.8
1.0
4.0
6.0
8.4
10.4
13.0
—
—
1.0
1.0
—
—
—
8.0
10.0
—
—
—
—
—
—
—
—
—
—
—
16
18
22
28
35
1.0
0.8
0.9
0.9
1.0
14.0
16.4
20.2
26.2
33.0
—
1.0
1.0
1.0
1.2
—
16.0
20.0
26.0
32.6
—
—
1.1
1.2
1.5
—
—
19.8
25.6
32.0
—
—
1.2
1.5
—
—
—
19.6
25.0
—
—
—
1.5
—
—
—
—
19.0
—
—
42
54
66.7
76.1
88.9
1.0
1.0
1.2
1.5
2.0
40.0
52.0
64.3
73.1
84.9
1.2
1.2
2.0
2.0
—
39.6
51.6
62.7
72.1
—
1.5
1.5
—
—
—
39.0
51.0
—
—
—
—
2.0
—
—
—
—
50.0
—
—
—
—
—
—
—
—
—
—
—
—
—
2.5
3.0
3.0
—
—
103
127
153
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
108
133
159
219
267
1.5
1.5
2.0
3.0
3.0
105
130
155
210
261
4-6
Reference data
Table 4.4 Internal diameters of polymer pipes
PVC-U (BS EN 1452-2(10))
Nom. outside
diam. / mm
Nom. outside
diam. / inch
Nom. internal diameter / mm
PN 6
PN 8
PN 10
PN 12.5
PN 16
PN 20
12
16
20
25
32
—
—
—
—
—
—
—
—
—
29.0
—
—
—
—
28.8
—
—
—
22.0
28.2
—
—
17.0
21.2
27.2
9.0
13.0
16.2
20.4
26.2
40
50
63
75
90
37.0
46.8
59.0
70.4
84.4
36.8
46.0
58.0
69.2
83.0
36.2
45.2
57.0
67.8
81.4
35.2
44.0
55.4
66.0
79.2
34.0
42.6
53.6
63.8
76.6
32.6
40.8
51.4
61.4
73.6
PN 6
PN 7.5
PN 8
PN 10
PN 12.5
PN 16
PN 20
PN 25
110
125
140
160
180
104.6
118.8
133.0
152.0
171.2
103.6
117.6
131.8
150.6
169.4
103.2
117.2
131.4
150.2
169.0
101.6
115.4
129.2
147.6
166.2
99.4
113.0
126.6
144.6
162.8
96.8
110.2
123.4
141.0
158.6
93.8
106.6
119.4
136.4
153.4
90.0
102.2
114.6
130.8
147.2
200
225
250
280
315
190.2
214.0
237.6
266.2
299.6
188.2
211.8
235.4
263.6
296.6
187.6
211.2
234.6
262.8
295.6
184.6
207.8
230.8
258.6
290.8
180.8
203.4
226.2
253.2
285.0
176.2
198.2
220.4
246.8
277.6
170.6
187.8
213.2
238.8
268.6
163.6
—
—
—
—
355
400
450
500
560
337.6
380.4
428.0
475.4
532.6
334.2
376.6
423.6
470.8
527.2
333.2
375.4
422.4
469.4
525.6
327.8
369.4
415.6
461.8
517.2
321.2
361.8
407.0
452.2
506.6
312.8
352.6
396.6
440.6
—
302.8
341.2
383.8
426.4
—
—
—
—
—
—
630
710
800
900
1000
599.2
675.2
760.8
856.0
951.0
593.2
668.6
753.4
847.4
941.6
591.4
666.4
751.0
844.8
938.8
581.8
655.6
738.8
—
—
570.0
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
Nom. outside
PB and PE-X
diam. / mm
(BS 7291(11)/BS EN 1057(9))
—
—
Nom. internal diameter / mm
PN 8
PN 12
PN 15
3/4
1
1 1/4
—
—
—
—
—
—
—
—
—
37.9
14.2
18.0
23.0
29.2
36.9
1 1/2
2
3
4
6
—
55.4
81.9
105.3
155.1
43.3
54.2
79.7
102.3
150.7
42.1
52.6
77.5
99.7
146.7
8
10
12
16
18
203.5
253.6
300.9
377.4
424.6
198.5
247.4
293.5
368.4
414.4
187.7
235.6
277.1
—
—
20
24
471.8
566.2
—
—
—
—
3/8
1/2
Nom. outside
PB and PE-X
diam. / mm (BS 7291(11)/BS ISO 4065(12))
Nom. int. diam. / mm
PVC-U (Annex B) (Imperial)
Nom. outside
diam. / mm
PN
Nom. int. diam. / mm
ABS (BS 2782-11(13)
/BS ISO 4065(12))
Nom. int. diam. / mm
0
12
15
18
22
6.7
8.7
11.7
14.2
17.7
10
12
16
20
25
6.8
8.8
12.3
16.0
20.2
16
20
25
32
40
10
10
10
10
10
13.0
16.8
21.2
27.8
34.6
28
35
22.5
28.3
32
26.0
50
63
75
90
110
10
10
10
10
10
43.2
54.6
65.0
78.0
95.4
PB
40
50
63
75
90
32.0
40.2
50.8
60.6
72.6
125
140
160
200
225
10
10
10
10
10
108.6
121.4
139.0
173.6
195.4
110
88.8
250
315
10
8
217.8
273.4
Note: PVC-U = unplasticized polyvinyl chloride; PB = polybutene; PE-X = cross-linked polyethylene; ABS = acrylonitrile butadiene styrene
Flow of fluids in pipes and ducts
4.3.4
4-7
Unpredictable flow
The equivalent head and head loss are then given by:
In the region 2000 < Re < 3000 the flow may be laminar
or turbulent depending upon upstream conditions. The
nature of the flow may even be unstable and oscillate
between laminar and turbulent. Applying caution in
pressure drop estimates, it would appear prudent to base
calculations on turbulent flow in this region.
4.3.5
Flexible steel-reinforced smooth
rubber hoses
Δp
Δ z = —–
ρg
(4.8)
It should be noted that several pump manufacturers quote
‘pump head’ or ‘delivery pressure’ when meaning the
increased head or pressure of the outlet compared with the
inlet.
4.3.8
Buoyancy
As these hoses are usually used under pressure, the
internal diameter will extend slightly with pressure. For
instance, a nominal internal diameter of 50 mm may
extend to 55 mm at a pressure of 150 kPa. If these
dimensional changes are known they should be included
in the calculation using equation 4.1.
Natural circulation may occur whenever there are density
differences in a circuit and a vertical height. Fan or pump
pressures will usually render the buoyancy effect
negligible. However, in the absence of a pump or fan,
natural circulation will take place. This is sometimes
called a ‘thermosyphon’.
Since lengths are not likely to be great, only a few guidance figures are given in Table 4.5, taken from Idelchik(2)
at a pressure of 150 kPa.
The pumping pressure difference due to buoyancy is given
by the following formula where the densities ρc and ρh of
the cold and hot parts of the fluid are the average of the
downward and upward flowing parts of the circuit respectively. Note that it is only the vertical height, z, which is
significant, not the length of pipe:
Table 4.5 Values of λ for flexible rubber hose (from
Idelchik(2))
Nominal
diameter
/ mm
d / mm
25
32
38
50
65
25
32.2
40.5
55
67.4
4.3.6
λ
Δp = g z ( ρc – ρh )
0.051–0.057
0.053–0.066
0.072–0.090
0.083–0.094
0.085–0.100
4.3.9
Non-circular ducts
The basic equation given in section 4.3.1 (equation 4.1)
needs to be rewritten in terms of hydraulic mean diameter
instead of diameter, where hydraulic mean diameter dh is
given by:
4A
dh = ——
P
(4.6)
where A is the cross-sectional area (m2) and P is the
perimeter of the duct (m). (For a circular duct the
hydraulic diameter dh is equal to the actual diameter d.)
Then:
l
Δp = λ —– 1/2 ρ c2
dh
(4.7)
For airflow through ducts, improved equations for
‘equivalent diameter’ are given in section 4.8.
Pressure measurements
With air flow, where pressure measurements are small, it
has been common practice to use manometers and to
quote the pressure in a height of the manometer fluid.
Care should be taken in the case of liquid flow where the
density of the manometer fluid, ρm, may be of the same
order of magnitude as that of the flowing fluid, ρ . The
equation to be used is:
Δp = g z ( ρm – ρ )
Head and head loss
An alternative method of presenting pressure and pressure
loss of liquids (but not of gases) is in terms of an
imaginary column of the liquid with standard atmospheric
pressure acting on the free surface. Technically this height
or ‘head’ would also depend on the temperature of the
liquid.
(4.10)
4.4
Components and fittings
4.4.1
Pressure loss factor, ζ
To obtain the extra pressure loss due to the installation of
any fitting, data are generally presented in terms of a
pressure loss factor, ζ . The data obtained experimentally
are complex but a simplified collection of the data is
available in sections 4.9 and 4.10. Whether for liquids in
pipes, or gases in ducts, the same fundamental equation
applies:
Δp = ζ 1/2 ρ c2
4.3.7
(4.9)
(4.11)
In particular it should be noted that where velocity
changes occur due either to changes in section or flow
splitting in tees, there may be instances where the static
pressure increases despite a loss in total pressure due to
friction. Δp is always the ‘drop in total pressure’:
Δp = ( p1 + 1/2 ρ c12) – ( p2 + 1/2 ρ c22)
(4.12)
4-8
Reference data
4.4.2
Capacity, K
Most valve manufacturers and damper manufacturers
quote the performance of their components in terms of
capacity, K, defined in the following relationship:
—
qv = K √Δp
(4.13)
This implies that K has units, usually of m3·h–1·bar –0.5 for
liquids, or m3·s–1·Pa–0.5 for gases. Some manufacturers may
quote values of K with different units so care is needed.
There is a relation between K and ζ , but it is not really
necessary to convert one to the other. Pressure drops are
more simply calculated separately for those components
for which K is given.
K is also useful when dealing with the authority of a valve,
and in the prediction of flows in complex circuits. Further
information can be obtained from Appendix 4.A3.
4.5
Water flow in pipes
4.5.1
Pipe sizing: desirable velocities
There are no rules concerning pipe sizing. The most cost
effective will be the design based on life-cycle costing
including the pumping costs. The smaller the pipework,
the greater the pumping power and energy consumption.
Increasing the pipe diameter by one size can have a large
effect in decreasing pumping power: smaller friction
pressure drops of the basic circuit will require smaller
pressure drops through control valves, for the same value
of valve authority. The optimum sizing from the point of
view of life-cycle costing must consider the length of the
system, the capital cost, the mean pressure drop, the
running time at full and partial flow, the efficiency of the
pump–motor combination, and anticipated electrical
tariffs (i.e. ‘on-peak’ or ‘off-peak’ operation).
To give a starting point in selecting pipe sizes, rule of
thumb water velocities are reproduced from BSRIA(15)
(1995) in Table 4.6. An alternative starting point might be
to consider a typical pressure drop per unit length of
360 Pa·m–1(15) or 250 Pa·m–1(4), but this is arbitrary.
Ultimately, sizing ought to be based on life-cycle costing.
and Rogers(17). In this respect larger pipes should be able
to tolerate higher velocities without a noise problem.
Similarly higher velocities are possible with polymer
piping due to the noise absorption effect of such piping.
Noise problems are more likely to occur if entrained air is
not separated and vented. Arrangements should be made
so that this is achieved easily. An upstand and air vent at
the top of each vertical run of pipe is recommended;
during pump-off periods, entrained air will separate out
into the higher position. This will simultaneously reduce
corrosion by eliminating oxygen as soon as possible.
4.5.3
Corrosion and scaling of the internal diameter of pipework
will occur with age depending on the chemical composition of the water. This will increase the surface roughness
of the pipe and decrease the internal diameter, both of
which will increase the friction pressure drop. No firm
recommendation can be made on the allowance to be
made. A large allowance is more justifiable with small
diameter pipes. Open systems will suffer more than closed
systems. ASHRAE(4) reports others finding an increase of
15 to 20% in the friction factor λ, compared with new
pipework. This was for closed systems. For open systems,
there could be a 75% increase. ASHRAE also reports that
work of the Plastic Plastic Pipe Institute (1971) shows that
there is little corrosion with plastic pipe.
4.5.4
Velocity
/ m·s–1
Total pressure
drop / kPa
Small bore
<1.0
—
Diam. 15 to 50 mm
0.75–1.15
—
Diam. > 50 mm
1.25–3.0
—
Heating/cooling coils
0.5–1.5
28
4.5.5
Noise
With small pipes, excessive velocities can lead to noise
generation where, with hot water, cavitation may occur at
elbows, valves, pumps and especially orifice plates. Some
information has been provided by Ball and Webster(16),
Water expansion
Between a heating system being cold (usually under the
‘fill’ situation), and warm under the design running
condition, the water contained in the system will expand.
The expansion, as a percentage, has been calculated with
reference to a cold situation of 4 °C using:
(
ρ4 – 1
ΔV
–––
V4 = —–
ρ
)
(4.14)
The volumetric expansion of the pipework may be
deduced from the volumetric expansion of the water, if
desired. Values of the density of water are given in Table
4.7. Pre-calculated values for the expansion of water are
given in Table 4.8.
4.5.6
4.5.2
Water hammer
Large pressures can arise when the fluid flow is stopped
abruptly by the sudden closure of a valve. This pressure
wave then reverberates within the pipework. The
magnitude of the pressure wave is in proportion to the
momentum of the flowing fluid and thus to its velocity.
Table 4.6 Typical water velocities for pipework (BSRIA(15))
Situation/diameter
Allowances for ageing
Buoyancy; thermosyphon
In any closed system, when one vertical section of the
pipework is at a different temperature from another, a
pressure difference will exist and create a driving pressure
difference so as to cause a natural thermosyphon. Using
equation 4.9, some pre-calculated values for hot water are
given in Table 4.9.
Flow of fluids in pipes and ducts
4-9
Table 4.7 Properties of water: density, dynamic and kinematic viscosity
Temperature
θ / °C
Density
ρ / kg·m–3
0.001
4
10
20
30
Dynamic viscosity
η / 10–6 kg·m–1·s–1
tures. Since the much simpler, but still accurate, equation
of Haaland (equation 4.5) is now available, pipe sizing can
be carried out directly on a simple spreadsheet for any
temperature and, indeed, for any fluid. A Microsoft®
Excel spreadsheet is provided on the CD -ROM that
accompanies this Guide. This enables fluid velocities,
pressure losses and velocity pressures to be calculated for
water and water–glycol mixtures at various temperatures
in pipes of various materials and sizes. The mathematical
steps required for the spreadsheet calculations are given in
Appendix 4.A2, (based on section 4.3), where a worked
example is also given. Pre-calculated pressure-drop tables
are therefore no longer needed. However, the spreadsheet
also enables such tables to be produced, if desired.
Kinematic viscosity
ν / 10–6 m2·s–1
999.8
1000.0
999.7
999.8
995.6
1752
1551
1300
1002
797
1.7524
1.5510
1.3004
1.0022
0.8005
40
50
60
70
80
992.2
988.0
983.2
977.8
971.8
651
544
463
400
351
0.6561
0.5506
0.4709
0.4091
0.3612
90
100
110
120
130
965.3
958.4
950.6
943.4
934.6
311
279
252
230
211
0.3222
0.2911
0.2651
0.2438
0.2258
140
150
160
170
180
925.9
916.6
907.4
897.7
886.5
195
181
169
158
149
0.2106
0.1975
0.1862
0.1760
0.1681
190
200
875.6
864.3
141
134
0.1610
0.1550
Traditionally the tables were given for just two water
temperatures, 10 °C and 75 °C. In the interests of boiler
efficiency which, especially with condensing boilers,
improves with lower water temperatures, designers should
not choose 75 °C merely because such data had previously
been given in CIBSE Guide C.
It should be noted that, particularly for small pipes, the
flow is sometimes in the laminar regime, Re < 2000. For
Re > 3000 the flow is almost invariably turbulent. In the
intermediate zone, the flow may be either laminar or
turbulent depending upon upstream conditions. This is
sometimes referred to as the ‘transition zone’ though in
reality the flow does not change gradually from one form
to the other, but may ‘flip-flop’ and oscillate between the
two conditions. Thus in the zone 2000 < Re < 3000 the
pressure drop conditions are impossible to predict.
Table 4.8 Percentage expansion of water at different temperatures,
relative to the volume at 4 °C
Temp. / °C
Expansion / %
Temp. / °C
Expansion/ %
40
50
60
70
80
90
100
110
120
0.786
1.21
1.71
2.27
2.90
3.63
4.34
5.20
6.00
130
140
150
160
170
180
190
200
7.00
8.00
9.10
10.2
11.4
12.8
14.2
15.7
4.5.7
4.5.8
Pipework fittings; water flow
Since in the course of the simple calculation of the
previous section, the value of 1/2 ρ c2 is available, the
calculation of the extra pressure drop due to components
is easily obtained using equation 4.11 with appropriate
values of ζ .
Nevertheless some values of the velocity pressure (1/2 ρ c2)
of water are given in Table 4.10, but these are valid only
for water at 10 °C.
Pipe-sizing
Until recently, the best curve-fit for pressure drop data was
the equation of Colebrook-White (equation 4.4), an
equation which could only be solved iteratively.
Therefore, earlier editions of CIBSE Guide C provided
many tables of pressure-loss data for water at two tempera-
The values of velocity pressure in Table 4.10 may be
corrected for different temperatures by dividing by the
density of water at 10 °C (= 999.7 kg·m–3) and multiplying
by the density at the required temperature.
Table 4.9 The thermosyphon driving pressure for a gravity hot water system, Δpb , using equation 4.9
Flow temp.
/ °C
Circulating pressure (/ Pa per metre height) for stated flow–return temperature difference / K
2
4
6
8
10
12
14
16
18
20
22
40
45
50
55
7.37
8.07
8.73
9.36
14.4
15.9
17.2
18.5
21.2
23.4
25.4
27.3
27.6
30.6
33.3
35.9
33.7
37.5
41.0
44.3
39.5
44.1
48.4
52.3
44.9
50.4
55.4
60.2
49.9
56.3
62.2
67.7
54.6
61.9
68.6
74.9
58.8
67.1
74.7
81.8
62.7
72.0
80.5
88.4
60
65
70
75
9.95
10.5
11.1
11.6
19.7
20.8
21.9
23.0
29.1
30.9
32.6
34.2
38.4
40.7
43.0
45.1
47.4
50.3
53.1
55.9
56.1
59.7
63.1
66.4
64.6
68.8
72.8
76.7
72.8
77.6
82.3
86.8
80.7
86.2
91.5
96.6
88.4
94.6
101
106
95.7
103
109
116
80
85
90
95
12.1
12.6
13.1
13.5
24.0
25.1
26.0
26.9
35.8
37.3
38.7
40.1
47.3
49.3
51.3
53.1
58.5
61.1
63.6
65.9
69.6
72.7
75.7
78.5
80.5
84.1
87.6
91.0
91.1
95.3
99.3
103
112
117
122
127
122
128
133
139
102
106
111
115
4-10
Reference data
Table 4.10 Velocity pressures, pv (= 1/2 ρ c2), for water at 10 °C
c / m·s–1
pv / Pa
c / m·s–1
0.01
0.02
0.03
0.04
0.05
0.049 99
0.199 95
0.449 88
0.799 78
1.249 66
0.85
0.9
0.95
1
1.1
361.152
404.891
451.128
499.865
604.837
0.06
0.07
0.08
0.09
0.10
1.799 51
2.449 34
3.199 14
4.048 91
4.999
1.2
1.3
1.4
1.5
1.6
719.806
844.772
979.735
1124.69
1279.65
1444.61
1619.56
1804.51
1999.46
3124.2
pv / Pa
0.15
0.25
0.30
0.35
0.40
11.247
31.242
44.988
61.233
79.978
1.7
1.8
1.9
2
2.5
0.45
0.50
0.55
0.6
0.65
101.223
124.966
151.209
179.951
211.193
3
3.5
4
4.5
5
4498.8
6123.3
7997.8
10 122.3
12 496.6
0.7
0.75
0.8
244.934
281.174
319.914
5.5
6
6.5
15 120.9
17 995.1
21 119.3
Values of ζ for pipework are to be found in sections 4.9
and 4.10. Since the additional pressure drop caused by a
fitting is largely due to the internal friction of the fluid
suffering an abrupt change of direction, rusting and
scaling have traditionally been considered not to have a
significant effect on pressure drop. However, for elbows,
the values of ζ are found to vary considerably with
diameter, which implies that surface effects are significant.
An allowance for ageing is therefore needed.
as the drop in pressure along the pipe does not exceed 10%
of the initial (absolute) inlet pressure.
Some data are given in Appendix 4.A1. It should be
remembered that the density varies considerably with
pressure.
4.8
Air flow in ducts
4.8.1
Duct sizing: desirable velocities
The are no rules concerning duct sizing. The most cost
effective will be the design based on life-cycle costing
including the fan running costs. The smaller the ductwork, the greater the fan power and energy consumption.
Increasing the duct size can have a large effect in
decreasing fan power: smaller friction pressure drops of
the basic circuit will require smaller pressure drops
through control dampers, for the same value of control
authority thus leading to a further saving. The optimum
sizing from the point of view of life-cycle costing must
consider the length of the system, the capital cost, the
mean pressure drop, the running time at full and partial
flow, the efficiency of the fan–motor combination and
anticipated electrical tariffs (i.e. ‘on-peak’, ‘off-peak’
operation).
To provide a starting point in selecting duct sizes, rule of
thumb air velocities are reproduced from BSRIA(15) in
Table 4.11. An alternative starting point might be to
consider a typical pressure drop per unit length of 1 Pa·m–1
for low velocity systems and 8 Pa·m–1 for high velocity
systems(15). Typical air velocities for air handling and other
components are given in Table 4.12(4,18).
Table 4.11 Typical air velocities for ductwork(4,15)
4.6
Flow of steam in pipes
Due to the considerable variation in steam conditions
which may be encountered, and the fact that the steam
conditions themselves (notably temperature and pressure)
do not remain constant as the steam flows along the pipe,
this is a very complex subject. Advice of specialists ought
to be sought.
Some property data are is given in Appendix 4.A4. It
should be remembered that density varies with temperature.
System type
Velocity
/ m·s–1
Maximum
pressure
drop per unit
length / Pa·m–1
Total pressure
drop / kPa
Low velocity
3–6
1
0.900 (supply)
0.400 (extract)
High velocity
7.5–15
8
1.5–2.0 (supply)
Table 4.12 Typical air velocities (face velocities) for air handling units
and other components(4,18)
Situation
4.7
Natural gas in pipes
Natural gas is a mixture of many gases; a mixture which
depends on the geographical source of the gas. In the UK,
natural gas consists predominantly of methane. It should
be noted that gases are highly compressible and that the
density therefore varies considerably with pressure and
temperature. Although the viscosity varies little with
pressure, that too varies with temperature. Thus pressure
drops are therefore best obtained by direct calculation
using the method explained in section 4.3. Although
section 4.3 assumes incompressible flow (ρ = constant),
the method may be used with reasonable accuracy so long
Velocity / m·s–1
Pressure drop / Pa
Heating system
2.5–4 (through face area)
50–125
Cooling system
1.5–2.5 (through face area)
60–180
Inlet louvres
2.5 (through free area)
35 max(4)
Extract louvres
2.5 (through free area)
60 max(4)
As duct
< 3.8
1.3
2.5
—
—
—
1.0
—
0.8–1.8
—
Filters(4):
— flat panel
— pleated
— HEPA
— moving curtain
viscous
— moving curtain
dry
— electronic,
ionising
Flow of fluids in pipes and ducts
4.8.2
4-11
Noise
Values of viscosity and specific thermal capacity do not
vary significantly with pressure.
The major source of duct-generated noise is caused by the
vortices created in diffusers, grilles, fittings and the fan
itself. Higher air velocities will create more noise. The
ductwork and sharp elbows can have an attenuating effect
especially of the higher frequencies. Frequently a noise
problem may be due to noise from one zone being able to
be propagated to another either via grilles and the
ductwork, or by ‘break-in’ to the ductwork itself or ‘breakout’. For detailed consideration, see CIBSE Guide B(19),
chapter 5.
4.8.3
Pressure drop for circular ducts
The pressure drop per unit length can be calculated for
any duct material, and for any air condition using the
pressure loss factor λ , as explained in section 4.3.
Repeating the D’Arcy equation for pressure loss due to
friction (equation 4.1):
l
Δp = λ — 1/2 ρ c2
d
Useful property values for air are given in Table 4.13, and
in Appendix 4.A1.
Table 4.13 Some properties of air at a relative humidity of 50% and at a
pressure of 1.013 25 bar
Temperature,
θ / °C
Density,
ρ / kg·m–3
Dynamic viscosity,
η / 10–6 kg·m–1·s–1
Specific heat
capacity,
cp / kJ·kg–1·K–1
0
5
10
1.29
1.27
1.24
17.15
17.39
17.63
1.006
1.009
1.011
15
20
25
1.22
1.20
1.18
17.88
18.12
18.36
1.014
1.018
1.022
30
35
40
1.16
1.14
1.11
18.55
18.78
19.01
1.030
1.039
1.050
Note that values of density, being the reciprocal of the
specific volume, are best obtained from the psychrometric
chart which covers any value of humidity.
The variation of density with pressure can be obtained
using a value ρ0 from Table 4.13 or from the psychrometric
chart, and the ideal gas equation:
ρ = ρ0
(
p
——–––
1.01325
)
(4.15)
where p is pressure (bar).
4.8.4
Pre-calculated values of pressure
drop for circular ducts
Until recently, the best curve-fit for pressure drop data was
the equation of Colebrook-White (equation 4.4), which
could only be solved by iteration. To help with ductsizing, a chart is provided (Figure 4.2), but this is valid
only for one condition of air, see (a) below. However, since
the much simpler, but still accurate, equation of Haaland
(equation 4.5) is now available, duct-sizing can be carried
out directly on a simple spreadsheet for any temperature
and air density. The mathematical steps required for the
spreadsheet calculations are given in Appendix 4.A2,
(based on section 4.3), where a worked example is
included. A Microsoft® Excel spreadsheet is provided on
the CD-ROM that accompanies this Guide. This enables air
velocities, pressure losses and velocity pressures to be
calculated at various temperatures in various types and
sizes of duct. The spreadsheet also enables duct sizing
tables to be produced, if desired.
The chart (Figure 4.2) was produced using values for the
appropriate variables as follows:
(a)
air at 20 °C, 101.325 kPa, 43% saturation
(b)
density, ρ = 1.200 kg·m–3
(c)
viscosity, η = 18.2 × 10–6 kg·m–1·s–1
(d)
roughness, k = 0.15 mm (longitudinal seams).
Compared with values from equation 4.5 (for k = 0.075 mm,
from Table 4.1), the chart gives slightly greater pressure
drops, reading +1.5% high, over much of the chart. There is
some evidence that small ducts give greater pressure drops
than expected, the suspicion being that the connections
play a relatively larger role. Such work as has been done to
investigate this was inconclusive.
For air at a temperature other than 20 °C, the pressure loss
read from the chart may be corrected by use of the
following expression, where T must be in kelvins:
( )
293
Δp = Δp20 —
—
T
4.8.5
0.86
(4.16)
Spirally wound ductwork
Table 4.14 illustrates the small extra pressure drop
incurred by using spirally wound galvanised ductwork
instead of ductwork with longitudinal seams. This comparison was made using k = 0.09 mm for spirally wound
and k = 0.075 mm for longitudinal seamed ductwork.
Table 4.14 Additional pressure drop (%) incurred by using spirally wound galvanised ductwork rather than longitudinal seamed
ductwork
Diameter,
d / mm
200
500
1000
2000
Additional pressure drop for spirally wound ductwork (/ %) for stated value of
pressure drop (longitudinal seam) / Pa·m–1
0.1
0.2
0.5
1
2
5
10
20
50
100
0.4
0.6
0.7
0.8
0.5
0.7
0.9
1.1
0.8
1.0
1.2
1.4
1.1
1.3
1.5
1.7
1.3
1.6
1.8
2.1
1.8
2.1
2.2
2.3
2.1
2.4
2.5
2.6
2.5
2.6
2.7
—
2.9
3.0
—
—
3.21
—
—
—
4-12
Reference data
Pressure drop per unit length, (Δ p / l) / Pa·m–1
0.1
0.2
0.4
0.6 0.8 1
2
4
6
8 10
20
40
60
80 100
200
200
100
100
80
80
3.0
2.8
2.6
60
60
2.4
2.2
40
40
2.0
1.8
20
1.6
1.5
1.4
1.3
1.2
1.1
1.0
10
m
Dia
10
40
lo
Ve
c
y,
cit
12
10
0.4
/m
8
5
1
–1
s
0.3
0.8
6
0.8
0.6
0.3
5
Volume flow, qv / m3·s–1
18
16
5
0.4
1
2
14
0.5
20
0.6
2
0.6
4
5
0.2
0.4
3
0.4
6
25
0.7
8
4
30
4
35
0.8
45
0.9
50
6
/m
60
55
8
r, d
ete
2
0.2
0.2
0.2
.15
0
0.1
0.1
0.08
0.08
0.1
0.06
0.06
75
0.0
0.04
0.04
1
0.02
0.02
5
0.0
0.01
0.1
0.2
0.4
0.6 0.8 1
2
4
6
8 10
Pressure drop per unit length, (Δ p / l ) / Pa·m–1
Figure 4.2 Pressure drop for air in galvanised circular ducts (ρ = 1.2 kg·m–3; T = 293 K)
20
40
0.01
60 80 100
Volume flow, qv / m3·s–1
20
Flow of fluids in pipes and ducts
4-13
When the spiral is additionally swaged for stiffness, a
further pressure drop can be expected but no data are
available.
4.8.6
l
Δp = λ —– 1/2 ρ c2
dh
Ducts of other materials
Using the values for surface roughness given in Table 4.1,
and Haaland’s equation (equation 4.5) a duct friction
factor λ is easily obtained for any material.
4.8.7
Flexible ductwork
The use of flexible ductwork for making final connections
to supply diffusers is very convenient. However such
ductwork produces pressure drops much greater than
those for the equivalent smooth galvanised steel ductwork.
Flexible ductwork naturally has an equivalent roughness
which is appreciably more than for galvanised steel
ductwork (1.0–4.6 mm, compared to 0.15 mm, see Table
4.1). This alone causes a much greater pressure drop. If the
flexible duct is not fully extended then, according to
ASHRAE(4), if the length is only 70% of the extended
length, the pressure loss can be greater by a factor of 4.
Thus, when using flexible ductwork, it is recommended
that:
—
lengths should be kept as short as possible
—
it should be almost fully extended.
Based on a worst case of roughness k = 4.6 mm, and
extended to only 70% of full length, Table 4.15 has been
derived as guidance to give the multiplying factor to be
applied to the equivalent rigid circular galvanised duct.
Table 4.15 Correction factors to be applied to the pressure drop
of a rigid duct (obtained from Figure 4.2) for flexible duct
having a roughness of 4.6 mm and extended to only 70% of full
length (from ASHRAE(4))
Velocity, c / m·s–1
2.5
4.5
6.0
The pressure loss is then given by:
200
500
6.70
7.35
7.66
7.47
8.05
8.21
8.3
8.7
8.9
To obtain a value of λ , the Haaland equation (4.5) should
be used. For this the hydraulic diameter dh should be used
for obtaining relative roughness k / d and Re. The use of
equation 4.18 then gives the pressure drop for any
condition of air and duct material. A worked example is
illustrated in Appendix 4.A2.2.
The concept of using hydraulic diameter is nevertheless
fundamentally flawed. The flow in a circular duct is
totally symmetrical about the axis, giving identical fluid
velocities close to all parts of the duct surface; this does
not exist within non-circular ducts. For ductwork having
particularly sharp apex angles, it has been shown that the
use of equation 4.17 does not give a good correlation.
4.8.8.2
Manual method using charts
and tables
Prior to the use of the Haaland equation, values of λ could
only be obtained by iteration; a process so tedious that
engineers preferred to use pre-calculated tables or charts
to obtain the pressure drop along a duct, even though
these were for only one condition of air, one ductwork
material, and only for circular ducts. To enable the use of
these charts for non-circular ducts, the concept of an
‘equivalent diameter’ (de) was conceived, relating to an
equivalent circular duct. Since most design problems have
as their starting point a desired volume flow qv , the most
convenient form of equivalent diameter is that which will
give the same pressure drop per unit length and for the
same volume flow.
When hydraulic diameter is used in conjunction with
equation 4.18 to determine a circular equivalent for a noncircular duct, to give the same pressure drop for the same
volume flow, the following equation is easily derived:
Correction factor for flexible duct
of stated diameter, d / mm
100
(4.18)
A0.6
de = 1.453 ——
P 0.2
(4.19)
There is nothing empirical about this equation. Its
validity rests solely on an assumed validity for hydraulic
mean diameter.
4.8.8
Non-circular ducts
4.8.8.1
Direct calculation
For ducts of non-circular cross section, the use of equation
4.1 necessitates the use of a value for a ‘diameter’ characteristic of the non-circular duct. For this, hydraulic mean
diameter has traditionally been used, defined by:
4A
dh = ——
P
(4.17)
where A is the cross-sectional area (m2) and P is the
perimeter (m2) of the duct. (For a circular duct the
hydraulic diameter dh is equal to the actual diameter d.)
Once the equivalent diameter has been obtained, using
equation 4.19, it may be used in conjunction with precalculated tables for a circular duct, or with Figure 4.2.
Care must be taken to use such circular duct data only
with the same volume flow qv .
Rectangular ducts
Huebscher(20) carried out tests on a square duct and a
rectangular duct (of aspect ratio w/h = 8), for a wide range
of velocities. His results, recently re-analysed by CIBSE,
are not sufficiently reliable to prove the validity of using
hydraulic diameter in the above equation 4.18, nor did
they provide an alternative. The direct calculation
approach should therefore be used as explained above.
4-14
Reference data
Table 4.16 Equivalent diameters for rectangular ductwork, to give the same pressure drop for the same volume flow, surface roughness and friction
coefficient k; calculated from equation 4.19
Dimen.
of side, h 100
100
110
Dimension of side of duct, w
125
123
138
150
134
151
165
175
145
162
178
193
200
154
173
190
206
220
225
250
300
350
400
450
500
550
600
900
Dimen.
of side, h
211
238
264
287
308
222
251
278
302
325
232
263
291
317
341
242
275
304
331
356
251
285
316
344
371
260
295
327
357
384
268
305
338
369
397
276
314
348
380
409
284
323
358
391
421
291
331
368
401
433
298
339
377
411
444
100
125
150
175
200
248
261
275
286
301
330
308
325
357
385
328
346
381
412
440
346
366
403
436
467
364
385
424
459
492
380
402
443
481
515
395
419
462
501
537
410
434
479
520
558
424
449
496
539
578
437
463
512
556
597
450
477
527
573
616
462
490
542
589
633
474
503
556
605
650
225
250
300
350
400
496
522
551
547
577
606
571
603
632
661
594
627
658
688
716
615
650
682
713
743
636
672
706
738
768
655
693
728
761
793
674
713
749
784
817
693
732
770
806
840
450
500
550
600
650
771
798
826
824
853
881
849
879
908
936
873
904
934
963
991
700
750
800
850
900
484
225
250
300
350
400
485
515
570
620
667
496
527
583
635
682
507
538
596
649
698
517
549
608
662
713
527
560
620
676
727
570
632
689
741
643
701
755
450
500
550
600
650
710
751
790
827
862
727
770
809
847
884
744
787
828
867
905
760
804
846
887
925
776
821
864
905
944
791
837
881
923
964
805 820 848 874
853 868 898 927 954
898 915 946 976 1005 1033
941 958 992 1024 1054 1084 1112
982 1000 1035 1069 1101 1132 1162 1191
713
768
794
896 918 940 961 982 1002
928 952 974 997 1018 1039
959 984 1007 1030 1053 1075
989 1015 1039 1063 1086 1109
1018 1044 1070 1095 1119 1142
1022
1059
1096
1131
1165
1041
1079
1116
1152
1187
1077
1118
1156
1194
1230
1112
1154
1195
1234
1271
1146
1189
1231
1272
1311
1179
1223
1266
1308
1349
1210
1256
1300
1343
1385
1240
1287
1333
1378
1420
1269
1318
1365
1410
1455
1347
1396 1425
1442 1473
1488 1520
1503
1551 1581
1046 1073 1100 1125
1101 1128 1155
1156 1183
1211
1198
1230
1261
1291
1320
1221
1253
1285
1316
1346
1265
1299
1332
1365
1396
1308
1343
1378
1411
1444
1349
1385
1421
1456
1490
1388
1426
1463
1499
1534
1426
1465
1503
1540
1576
1462
1503
1542
1580
1618
1497
1539
1580
1619
1657
1532
1574
1616
1657
1696
1565
1609
1651
1693
1733
1597
1642
1686
1728
1770
1629
1675
1719
1763
1805
1659
1706
1752
1796
1840
950
1000
1050
1100
1150
1321 1349 1375 1426
1376 1404 1456
1432 1485
1542
1476
1507
1537
1596
1652
1523
1555
1586
1647
1706
1568
1601
1634
1697
1758
1612
1646
1680
1745
1808
1654
1690
1724
1792
1856
1695
1732
1767
1837
1903
1735
1772
1809
1880
1949
1773
1812
1850
1923
1993
1810
1850
1889
1964
2036
1847
1887
1927
2004
2078
1882
1924
1964
2043
2119
1200
1250
1300
1400
1500
1762 1816 1868 1919
1872 1926 1978
1982 2036
2092
1967
2029
2089
2146
2202
2015
2078
2140
2199
2257
2061
2126
2189
2250
2309
2106
2172
2237
2300
2361
2149
2218
2284
2348
2411
2191
2262
2330
2395
2459
1600
1700
1800
1900
2000
2312 2367
2423
2420 2471 2521
2477 2530 2581
2533 2587 2640
2643 2697
2753
2100
2200
2300
2400
2500
950 1000 1050 1100 1150 1200 1250 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200
2300 2400 2500
1150
1180
1210
1238
1266
1174
1205
1236
1265
1294
1.453 A0.6
de = ————
P 0.2
2100
2200
2300
2400
2500
Dimen.
of side, h
850
199
225
248
269
289
440
474
1600
1700
1800
1900
2000
800
185
209
231
251
269
394
430
464
1200
1250
1300
1400
1500
750
171
192
212
230
246
347
386
421
454
950
1000
1050
1100
1150
700
163
183
201
218
234
125
150
175
200
700
750
800
850
900
650
Dimension of side of duct, w
Dimen.
of side, h
Flow of fluids in pipes and ducts
4-15
For those wishing to use a manual graphical approach, the
concept of circular duct equivalent is useful. Hubscher has
sometimes been credited with an equation which is
erroneous and should not be used. Table 4.16 was obtained
using equation 4.19, and gives pre-calculated values of
equivalent diameter for rectangular ductwork of preferred
sizes.
Flat-oval spirally wound ducts
Heyt and Diaz(21) carried out tests on several flat-oval
ducts having a range of aspect ratios w / h from 2.0 to 4.2
for a wide range of velocities. Their results, recently re-
analysed by CIBSE, are not sufficiently reliable to prove
the validity of using hydraulic diameter in the above
equation 4.18, nor did they provide an alternative. The
direct calculation approach should therefore be used as
explained above.
For those wishing to use a manual graphical approach, the
concept of circular duct equivalent is useful. Heyt and
Diaz(21) have sometimes been credited with an equation
which is erroneous and should not be used. Table 4.17
gives values of perimeter P and area A. The pre-calculated
values of de given in Table 4.18 have been obtained using
equation 4.19.
Table 4.17 Areas and perimeters for flat-oval ductwork; the dimensions are those of the preferred sizes of ductwork(22)
Area, A (/ mm2), for stated width, w (/ mm), and height, h / mm
Dimension
75
100
125
150
200
250
300
350
400
450
500
Perimeter,
P / mm
w
A
320
22793
w
A
360
25793
350
32854
330
37897
320
43171
w
A
400
28793
390
36854
370
42897
360
49171
w
A
440
31793
430
40854
410
47897
400
55171
w
A
480
34793
470
44854
450
52897
440
61171
1048
w
A
520
37793
505
48354
490
57897
480
67171
1126
545
52354
530
62897
520
73171
1206
w
A
720
808
h
888
968
w
w
A
555
78421
525
96416
w
A
635
90421
605
112416
580
131587
w
A
715
102241
690
129416
660
151587
630
169686
w
A
800
115171
770
145416
740
171587
710
193686
685
213461
655
227664
w
A
880
127171
845
160416
825
192837
790
217686
765
241461
735
259664
705
273793
680
286350
1927
w
A
960
139171
930
177416
900
211587
875
243186
845
269461
815
291664
785
309793
755
323850
2067
w
A
1040
151171
1010
193416
985
232837
955
267186
925
297461
895
323664
865
345793
835
363850
2249
w
A
1120
163171
1090
209416
1065
252837
1035
291186
1005
325461
975
355664
945
381793
915
403850
2409
w
A
1200
175171
1170
225416
1145
272837
1115
315186
1085
353461
1055
387664
1025
417793
1000
446350
2570
1335
258416
1305
312837
1275
363186
1245
409461
1215
451664
1190
492043
1160
526350
2892
w
A
1465
352837
1435
411186
1405
465461
1375
515664
1350
564043
1320
606350
3211
w
A
1625
392837
1595
459186
1570
523211
1540
581664
1510
636043
1480
686350
3535
w
A
1785
432837
1760
508686
1730
579211
1700
645664
1670
708043
1640
766350
3856
w
A
1280
1442
1604
1767
4-16
Reference data
Table 4.18 Equivalent diameters for flat-oval ductwork to give the same pressure drop for the same volume flow, surface roughness and friction
coefficient λ; values of de have been obtained using equation 4.19; the dimensions are those of the preferred sizes of ductwork(22)
Dimension
Equivalent diameter, de (/ mm) for stated width, w (/ mm), and height, h / mm
75
100
125
150
w
de
320
160
w
de
360
169
350
195
330
213
320
230
w
de
400
177
390
205
370
225
360
244
w
de
440
185
430
215
410
236
400
257
w
de
480
192
470
223
450
247
440
269
w
de
520
199
505
230
490
257
480
281
545
238
530
266
520
291
w
de
200
250
300
350
400
450
500
Perimeter,
P / mm
720
808
h
888
w
968
1048
A0.6
1.453
de = ————
P 0.2
1126
1206
w
de
555
300
525
340
w
de
635
319
605
364
580
400
w
de
715
337
690
388
660
426
630
456
w
de
800
354
770
408
740
450
710
484
685
513
655
534
w
de
880
370
845
425
825
475
790
510
765
543
735
567
705
586
680
602
1927
w
de
960
384
930
444
900
494
875
537
845
571
815
599
785
621
755
638
2067
w
de
1040
398
1010
461
985
515
955
560
925
597
895
628
865
653
835
674
2249
w
de
1120
411
1090
477
1065
534
1035
581
1005
621
975
655
945
684
915
707
2409
w
de
1200
423
1170
492
1145
552
1115
602
1085
645
1055
681
1025
713
1000
741
2570
1335
522
1305
585
1275
640
1245
688
1215
729
1190
768
1160
799
2892
w
de
1465
616
1435
675
1405
727
1375
773
1350
816
1320
852
3211
w
de
1625
644
1595
708
1570
765
1540
815
1510
860
1480
901
3535
w
de
1785
671
1760
739
1730
799
1700
853
1670
902
1640
946
3856
w
de
1280
1442
1604
1767
Flow of fluids in pipes and ducts
4.8.9
4-17
Data for ζ for ductwork components are given in sections
4.9 and 4.11.
Components and fittings
Whether for liquids in pipes or gasses in ducts, the same
fundamental equation applies:
Δ pf = ζ 1/2 ρ c2
(4.23)
Values of 1/2 ρ c2 for air at 20 °C, normal atmospheric
pressure, and 50% saturation are given in Table 4.19.
Values of 1/2 ρ c2 are easily calculated for other conditions.
Table 4.19 Velocity pressure, pv (= 1/2 ρ c2), for air having a density ρ = 1.20 kg·m–3; this is the case at 20 °C, 50% saturation and pressure of 101.325 bar
Velocity
c / m·s–1
Velocity pressure, pv (/ Pa), for stated velocity, c / m.s–1
0.0
0.1
0.2
0.3
0.4
0.5
0.7
0.8
0.9
0
1
2
3
4
5
0.00
0.60
2.40
5.40
9.60
15.00
0.01
0.73
2.65
5.77
10.09
15.61
0.02
0.86
2.90
6.14
10.58
16.22
0.05
1.01
3.17
6.53
11.09
16.85
0.10
1.18
3.46
6.94
11.62
17.50
0.15
1.35
3.75
7.35
12.15
18.15
0.6
0.22
1.54
4.06
7.78
12.70
18.82
0.29
1.73
4.37
8.21
13.25
19.49
0.38
1.94
4.70
8.66
13.82
20.18
0.49
2.17
5.05
9.13
14.41
20.89
6
7
8
9
10
21.60
29.40
38.40
48.60
60.00
22.33
30.25
39.37
49.69
61.21
23.06
31.10
40.34
50.78
62.42
23.81
31.97
41.33
51.89
63.65
24.58
32.86
42.34
53.02
64.90
25.35
33.75
43.35
54.15
66.15
26.14
34.66
44.38
55.30
67.42
26.93
35.57
45.41
56.45
68.69
27.74
36.50
46.46
57.62
69.98
28.57
37.45
47.53
58.81
71.29
11
12
13
14
15
72.60
86.40
101.40
117.60
135.00
73.93
87.85
102.97
119.29
136.81
75.26
89.30
104.54
120.98
138.62
76.61
90.77
106.13
122.69
140.45
77.98
92.26
107.74
124.42
142.30
79.35
93.75
109.35
126.15
144.15
80.74
95.26
110.98
127.90
146.02
82.13
96.77
112.61
129.65
147.89
83.54
98.30
114.26
131.42
149.78
84.97
99.85
115.93
133.21
151.69
16
17
18
19
20
153.60
173.40
194.40
216.60
240.00
155.53
175.45
196.57
218.89
242.41
157.46
177.50
198.74
221.18
244.82
159.41
179.57
200.93
223.49
247.25
161.38
181.66
203.14
225.82
249.70
163.35
183.75
205.35
228.15
252.15
165.34
185.86
207.58
230.50
254.62
167.33
187.97
209.81
232.85
257.09
169.34
109.10
212.06
235.22
259.58
171.37
192.25
214.33
237.61
262.09
21
22
23
24
25
264.60
290.40
317.40
345.60
375.00
367.13
293.05
320.17
348.49
378.01
269.66
295.70
322.94
351.38
381.02
272.21
298.37
325.73
354.29
384.05
274.78
301.06
328.54
357.22
387.10
277.35
303.75
331.35
360.15
390.15
279.94
306.46
334.18
363.10
393.22
282.53
309.17
337.01
366.05
396.29
285.14
311.90
339.86
369.02
399.38
287.77
413.65
342.73
372.01
402.49
26
27
28
29
30
405.60
437.40
470.40
504.60
540.00
408.73
440.65
473.77
508.09
543.61
411.86
443.90
477.14
511.58
547.22
415.01
447.17
480.53
515.09
550.85
418.18
450.46
483.94
518.62
554.50
421.35
453.75
487.35
522.15
558.15
424.54
457.06
490.78
525.70
561.82
427.37
460.37
494.21
529.25
565.49
430.94
463.70
497.66
532.82
569.18
434.17
467.05
501.13
536.41
572.89
31
32
33
34
35
576.60
614.40
653.40
693.60
735.00
580.33
618.25
657.37
697.69
739.21
584.06
622.10
661.34
701.78
743.42
587.81
625.97
665.33
705.89
747.65
591.58
629.86
669.34
710.02
751.90
595.35
633.75
673.35
714.15
756.15
599.14
637.66
677.38
718.30
760.42
602.93
641.57
681.41
722.45
764.69
606.74
645.50
685.46
726.62
768.98
610.57
649.45
689.53
730.81
773.29
36
37
38
39
40
777.60
821.40
866.40
912.60
960.00
781.93
825.85
870.97
917.29
964.81
786.26
830.30
875.54
921.98
969.62
790.61
834.77
880.13
926.69
974.45
794.98
839.26
884.74
931.42
979.30
799.35
843.75
889.35
936.15
984.15
803.74
848.26
893.98
940.90
989.02
808.13
852.77
898.61
945.65
993.78
812.54
857.30
903.26
950.42
998.78
816.97
861.85
907.93
955.21
1003.69
4-18
4.9
Reference data
Pressure loss factors
An extensive review of pressure loss factors has been
undertaken. Many sources give conflicting information,
much derived from research results of many years ago.
The data presented here are those that are considered
most reliable.
In the light of modern research, much older data, where
values of ζ for ductwork components using air had been
derived from tests using water(23), are now known to be
inappropriate. With few exceptions most published data
on pressure loss factors historically gave just single values
for a component, irrespective of size or of fluid velocity. It
has been known for some time(24) that the values of ζ for
elbows in ductwork vary with the air velocity, but the data
have been so sparse that this has not been considered in
design guides. It is now known that such variation with
velocity exists also for pipework components. More
recently it has been possible to include research data
showing the variation with size.
The pressure loss due to the insertion of a component
such as an elbow is predominantly due to the vortices
created downstream. Practical measurements close to the
component would therefore be highly unrepeatable, and
therefore unreliable. Experimental measurements of pressure are therefore made well upstream and downstream of
the disturbance (i.e. 20 diameters upstream/downstream).
The results are always quoted as the ‘extra pressure drop
due to the insertion of the component’.
The pressure drop calculated for a component is always to
be added to the pressure drop of the full length of the
pipework or ducting (unless otherwise stated).
If the distance between one component and another
(entries and exits included) is less than 20 diameters, there
is an interaction between the components. Thus the
pressure drop could be more or less than the calculated
figure depending on the type of component and the type
of flow disturbances created, especially by the upstream
component.
The predominant source of friction pressure drop has
traditionally been attributed to the flow separation and
vortices downstream of an elbow or bend. However, with
pipework in particular, surface effects play an important
part, the pressure drop being very dependent upon the
surface roughness and shape of the inner surface. Thus it
is found that the values of ζ depend upon the diameter
and the material. Since even a small change in the internal
shape of a pipe fitting can cause an appreciable difference
in friction effects, it is clear that for small diameters, the
pressure loss factor could also be manufacturer-dependent.
This applies principally to elbows of pipework, (see
Miller(25) and Rahmeyer(26,27)) but also to elbows of
ductwork(1,28).
With tees, the predominant friction pressure drop is due
to the turbulence created by the mixing or separation of
flows. In the past it was convenient to consider that
surface effects would not play such an important part with
tees and that therefore the values of ζ might not vary with
diameter. This would appear doubtful in the light of
recent work by Rahmeyer(29,30) on tees in pipework. There
is an indication that larger diameter tees give smaller
values of ζ but the effect is easily swamped by manufacturing details.
It had previously been assumed that any possible variation
with diameter would not apply to ductwork components
due to the larger diameters. Recent work carried out by the
European project(1) and by the United McGill Corporation(28)
on circular ductwork, shows this not to be the case. For
bends in ductwork, ζ is strongly diameter-dependent.
Work done on rectangular bends by Madison and
Parker(31) showed that size effects are appreciable for
square bends of long radius and for those having a low
aspect ratio (h/w).
Smith and Jones(32), testing flat oval tees, found ζ to be
slightly smaller for tees of larger size. Despite the breadth
of work carried out by the European project(1) on ductwork components, and although several combinations of
sizes were tested, no simple test was carried out to confirm
the general assumption that, with tees, the size has no
significant effect. Nevertheless, interpolation to obtain
values of ζ for other tee geometries does permit a direct
comparison. Size is seen to play a part, which is far from
negligible. Larger tees give smaller values of ζ.
With tees, there are three flows and three velocity
pressures. The use of the velocity pressure of the
combined flow is sometimes queried by engineers; one
wonders whether the use of branch velocity pressures for
branch pressure loss might seem clearer (some but not all
texts treat it this way). However, if branch velocity
pressures were used, the value of the appropriate ζ would
result in very large variations. Therefore, to avoid any
confusion, all the pressure loss coefficients are quoted in
relation to the velocity pressure of the combined flow.
Where possible, the most recent research results have been
included in sections 4.10 and 4.11. It is expected that as
more research is carried out, the data and advice given in
this Guide will be amended. Similarly as computational
fluid dynamics (CFD) modelling improves to the point
where it agrees with reliable experimental data, it may one
day be possible to extrapolate its use to those components
which have not yet been physically tested.
4.10
Pressure loss factors for
pipework components
For elbows there is considerable evidence that values of ζ
vary with diameter. Rahmeyer(27) has shown that ζ can
vary appreciably with velocity (Re). For tees there is little
such evidence. Previously it had been considered that with
tees, the predominant friction pressure drop was due to
the turbulence created by the mixing or separation of
flows. It was convenient therefore to consider that surface
effects would not play such an important part with tees
and that therefore their values of ζ might not vary with
diameter. In his tests on PVC -U tees, Rahmeyer(33) found
larger diameter tees to give slightly lower values of ζ but
that the effect could be considerably swamped by the
internal details of the design. He also found considerable
variation in the values of ζ for tees of 100 mm diameter
from five different manufacturers. This confirms that the
internal surface roughness and form play a significant
part, even for tees.
Flow of fluids in pipes and ducts
4-19
The guidance given on ageing allowances when using
water (see section 4.5.3) should be applied to fittings as
well as to straight pipes.
4.10.1
4.10.1.1
Elbows and bends
Laminar flow
As with the friction factor λ for straight pipes, the
pressure loss factor ζ for elbows/bends is found to be much
higher in the laminar flow regime. This fact, generally
overlooked, is important since pipes may often carry fluids
of high viscosity which results in laminar flow.
Using Idelchik(2), to quote a simplistic value of ζ for
laminar flow (Re < 1000), suggests that:
—
ζ = 2.30 could be taken for smooth elbows (laminar)
—
ζ = 2.35 could be taken for rough elbows (laminar).
It is interesting to note that in the laminar flow regime
neither relative roughness nor pipe diameter have any
great effect on the value of ζ.
4.10.1.2
Turbulent flow
Since the primary cause of friction pressure drop around
elbows and tees is internal fluid friction resulting from the
change of direction, it is sometimes considered that
surface roughness will play little part. However, Idelchik(2)
and Miller(25) show that surface roughness, particularly at
the inner wall, does indeed have a very significant effect
on the pressure loss created by bends. The effect is less for
sharp elbows for which flow separation is the greatest
factor. Since surface roughness plays a part, ζ will depend
on the material. However there are no comprehensive data
on this effect. The guidance given on ageing allowances
when using water (see section 4.5.3), should therefore be
applied to fittings as well as to straight pipes
The upstream joint causes a discontinuity equivalent to
increasing the effective roughness substantially. Comparing
values from ASHRAE(4) and Miller(25), the type of
upstream fitting has an effect on the pressure drop: in
descending order of friction, screwed joints give most,
welded and soldered joints less, while smooth joints give
least friction(34).
Miller(25) showed that even a very slight rounding of the
inside part of an elbow has an appreciable effect on the
value of ζ. Thus we can expect that the value of ζ to vary
with the form and thus depend on the manufacturer.
Rahmeyer(26,27,35) included in his tests samples from five,
sometimes six different manufacturers, and several
components from each. The spread of results is considerable.
Recent research by Rahmeyer(27) shows that fluid velocity
also has a considerable effect on the value of ζ . The tests
were all carried out using water at 16 °C, (ν = 0.1208 ×
10–5 m2·s–1). These most recent data are given in Table 4.20
and show the variation of ζ with diameter and velocity.
The PVC-U elbows tested were all proprietary sharp elbows,
except one where the 90° bend was made up of two 45°
elbows glued together. This fabrication results in a bend of
increased r / d, the effect of which is a reduction in the
values of ζ far greater than any adverse effect from the
discontinuity of the glued joint. Table 4.21 gives more
comprehensive data, and shows the variation of ζ with
size.
Table 4.20 Elbows: values of ζ varying with velocity; (a) screwed joint, malleable iron, (b) welded joint, forged steel,
(c) and (d) PVC-U (derived from Rahmeyer(26,27,35))
Type and material
Short radius (r/d = 1.0):
(a) Screwed joint, malleable iron
(b) Welded joint, forged steel
Long radius (r/d = 1.5):
(b) Welded joint, forged steel
Diameter,
d / mm
0.5
1
1.5
2
2.5
3
3.5
4
5
50
100
0.52
0.41
0.58
0.38
0.63
0.36
0.66
0.35
0.68
0.34
0.71
0.33
0.72
0.33
—
—
—
—
100
300*
400
500
600
0.28
0.18
0.15
0.13
0.11
0.26
0.16
0.13
0.12
0.10
0.25
0.15
0.12
0.11
0.10
0.25
0.15
0.12
0.11
0.10
0.24
0.14
0.12
0.12
0.09
0.24
0.14
0.11
0.10
0.09
0.24
0.14
0.11
0.10
0.09
0.23
0.13
0.11
0.10
0.08
0.23
0.13
0.11
0.10
0.08
4
5
6
7.5
Diameter†,
d / mm
Sharp inner edge (r/d = 0.5):
(c) PVC-U
Glued 45° elbows giving
90° bend (r/d ≈ 1.0):
(d) PVC-U
Velocity, c / m·s–1
Velocity, c / m·s–1
0.85
1
1.5
2
3
51
102
153*
204
1.077
0.978
0.887
0.794
1.490
0.955
0.869
0.782
0.990
0.914
0.835
0.759
0.976
0.902
0.826
0.753
0.956
0.886
0.815
0.745
0.938
0.873
0.805
0.738
0.925
0.863
0.797
0.732
0.914
0.855
0.789
0.727
0.901
0.844
—
—
204
0.462
0.448
0.419
0.412
0.402
0.394
0.387
0.382
—
* Experimental readings for this size were unreliable. Figures in italics were obtained by interpolation, and should be considered
as ‘best advice’ only.
† 51 mm = nominal 2-inch, 102 mm = nominal 4-inch, 153 mm = nominal 6-inch, 204 mm = nominal 8-inch.
Note: accuracy: (a) ±22% for d = 50 mm; (b) ±10% for d = 400 mm and 500 mm; (c) ±1.3% for d = 51–204 mm
4-20
Reference data
Table 4.21 Elbows: values of ζ varying with diameter (derived from ASHRAE(4) and Miller(25))
Type
(a)
—
—
—
Diameter, d / mm
Elbows:
screwed fitting(4)*
rough, sharp inner edge(25)
smooth radiussed inner(25)
(b) Bends:
— screwed fitting(4)†
— smooth, r/d > 1.5(25)
10
15
20
25
32
40
50
75
100
2.5
1.56
1.10
2.1
1.45
0.93
1.7
1.35
0.75
1.5
1.3
0.8
1.3
1.24
0.75
1.2
1.18
0.72
1.0
1.15
0.70
0.82
1.10
0.70
0.70
1.10
0.70
—
0.57
—
0.53
0.92
0.49
0.78
0.46
0.65
0.43
0.54
0.42
0.42
0.40
0.33
0.40
0.24
0.40
* Accuracy ± 40% for d < 50 mm, ± 20% for d > 50 mm; † accuracy ± 25%
4.10.2
Elbows in close proximity
For two components:
See Figure 4.3. When components are in close proximity,
the flow disturbance created by the first will interact with
the second. The pressure drop will not then be the same as
for the two components in isolation. Table 4.22 contains
values for a ‘coefficient of close proximity’, Ccp to be used
in the following equations.
Δp = Ccp 2 ζ1 1/2 ρ c2
For three components:
Δp = Ccp 3 ζ1 1/2 ρ c2
(4.25)
where ζ1 is the pressure loss coefficient for one of the
components in isolation.
4.10.3
Expanding and contracting
elbows
See Figure 4.4 and Tables 4.23 and 4.24. Values of ζ are to
be used with the velocity pressure at the smallest
dimension.
l
(a)
(4.24)
(b)
Δp = ζ 1/2 ρ c12
Δp = ζ 1/2 ρ c22
c2
(c)
(d)
c1
Figure 4.3 Elbows in close proximity; configurations for Table 4.22:
(a) two elbows in same plane, (b) two elbows in different planes, (c) two
elbows in same plane (‘U’), (d) three elbows (swing)
(a)
(b)
Figure 4.4 (a) Contracting elbow, (b) expanding elbow
Table 4.22 Elbows in close proximity: values of correction factor Ccp (Rahmeyer(36); ASHRAE Transactions 108 (1) 2002. © American
Society of Heating, Refrigerating and Air-Conditioning Engineers Inc. (www.ashrae.org))
Configuration (see Figure 4.3)
Ratio of separation to diameter, l/d
0
1
2
3
4
5
10
20
Diameter, d = 51 mm (‘2-inch’):
(a) Two elbows in plane
(b) Two elbows out of plane
(c) Two elbows in plane (‘U’)
(d) Three elbows (swing)
0.90
0.87
0.60
0.70
0.88
0.88
0.65
0.72
0.86
0.88
0.70
0.74
0.89
0.85
0.72
0.72
0.88
0.87
0.77
0.75
0.88
0.88
0.83
0.77
1.00
0.97
1.00
0.99
1.01
1.00
1.00
0.99
Diameter, d = 102 mm (‘4-inch’):
(a) Two elbows in plane
(b) Two elbows out of plane
(c) Two elbows in plane (‘U’)
(d) Three elbows (swing)
0.95
0.73
0.82
0.86
0.93
0.79
0.86
0.87
0.90
0.86
0.71
0.87
0.90
0.85
0.85
0.87
0.92
0.88
0.89
0.88
0.94
0.90
0.93
0.90
0.98
0.97
0.97
0.95
1.00
0.99
0.99
0.99
Flow of fluids in pipes and ducts
4-21
Δp = ζ 1/2 ρ c22
Table 4.23 Contracting elbows: values of ζ varying with velocity; the
value of ζ is with reference to the downstream velocity pressure(18)
Type and
diameter, d
Velocity, c2 / m·s–1
Area ratio
A2 /A1
1
2
3
4
5
6
Screwed joint,
50 mm > 37 mm
0.548
0.237 0.250 0.268 0.274 0.280 0.286
welded joint
100 mm > 76 mm
0.578
0.230 0.192 0.173 0.159 0.146 0.137
Area ratio
A2 /A1
not known how much of this is due to the smaller size,
and how much due to the screwed joint, as both are known
to increase the value of ζ .
Velocity, c1 / m·s–1
0.5
1
1.5
2
0.521 0.55
2.5
4.10.4.2
3
3.5
Screwed joint,
1.83
37 mm < 50 mm
0.662 0.61
welded joint
1.73
76 mm < 100 mm
0.285 0.276 0.272 0.269 0.267 0.265 0.263
Expansions
Rahmeyer(26,27,35) tested expansions of two types, the
results of which are reproduced in Table 4.26. The smaller
size, with screwed joints, gave the highest values of ζ . It is
not known how much of this is due to the smaller size,
and how much due to the screwed joint, as both are known
to increase the value of ζ .
0.532 0.521 0.508
Note: the 37 mm fitting is of malleable iron, expanding round the elbow
from 37 mm to 50 mm; the 76 mm fitting is of forged steel, expanding
round the elbow from 76 mm to 100 mm. Both are of long radius.
4.10.5
Abrupt changes of section
See Figure 4.6 and Table 4.27. Values of ζ are to be used
with the velocity pressure at the smallest dimension.
Gradual changes of section
See Figure 4.5 and Tables 4.25 and 4.26. Values of ζ are to
be used with the velocity pressure at the smallest
dimension.
4.10.4.1
Expansion
Figure 4.5 Gradual changes of section
Table 4.24 Expanding elbows: values of ζ varying with velocity; the
value of ζ is with reference to the upstream velocity pressure(26)
4.10.4
c1
c2
Contraction
Note: the 50 mm fitting is of malleable iron, contracting round the elbow
from 50 mm to 37 mm; the 100 mm fitting is of forged steel, contracting
round the elbow from 100 mm to 76 mm. Both are of long radius.
Type and
diameter, d
Δp = ζ 1/2 ρ c12
4.10.5.1
Sudden contractions
There will be a range when flow is in the laminar range
upstream of the contraction, whilst turbulent downstream. In the intermediate zone, it is anticipated that the
disturbance of the sudden contraction will trigger
downstream turbulence at Re2 < 3 × 103, possibly as low as
Re2 = 2 × 103, see Figure 4.1.
Contractions
Rahmeyer(26,27,35) tested contractions of two types, the
results of which are reproduced in Table 4.25. The smaller
size, with screw threads, gave the highest values of ζ . It is
Table 4.25 Contractions: values of ζ (derived from Rahmeyer(26,27,35))
Type and diameters
Velocity, c2 / m·s–1
Area ratio
A2 /A1
0.5
1
2
3
4
5
7
(a) Screwed joint, malleable iron:
— 50 mm > 37 mm
0.548
0.45
0.34
0.20
0.14
0.11
0.09
—
(b) Welded joint, forged steel:
— 100 mm > 75 mm
0.562
0.17
0.14
0.09
0.05
0.04
0.04
—
(c) PVC-U:
— 150 mm > 100 mm
0.444
0.18
0.16
0.13
0.11
0.10
0.10
0.10
Note: spread between items of different manufacturers: (a) Δζ = ± 0.020, ± 22% at c2
(b) Δζ = ± 0.022, ± 55% at c2 = 4 m·s–1; (c) Δζ = ± 0.028, ± 27% at c2 = 5 m·s–1
= 2 m·s–1;
Table 4.26 Expansions: values of ζ (derived from Rahmeyer(26,27,35))
Type and diameters
Area ratio
A2 /A1
Velocity, c1 / m·s–1
0.3
0.5
1
1.5
2
2.5
3
3.7
(a) Screwed joint, malleable iron:
— 37 mm < 50 mm
1.83
0.25
0.21
0.17
0.15
0.14
0.13
0.12
0.12
(b) Welded joint, forged steel:
— 75 mm < 100 mm
1.78
0.14
0.13
0.13
0.12
0.11
0.11
0.11
0.11
(c)
—
—
—
—
1.44
1.78
1.56
1.44
Wrought steel, butt-welded:
254 mm < 305 mm
305 mm < 406 mm
406 mm < 508 mm
508 mm < 610 mm
Note: accuracy: (a) ± 14%; (b) ± 13%
ζ = 0.111 for 0.5 m·s–1 < c < 6 m·s–1
ζ = 0.075 for 0.5 m·s–1 < c < 6 m·s–1
ζ = 0.022 for 0.5 m·s–1 < c < 6 m·s–1
ζ = 0.020 for 0.5 m·s–1 < c < 6 m·s–1
4-22
Reference data
Δp = ζ 1/2 ρ c22
4.10.6
Δp = ζ 1/2 ρ c12
Tees
See Figures 4.7 to 4.9 and Tables 4.28 to 4.34.
c2
c1
Contraction
Expansion
Figure 4.6 (a) Sudden contraction, (b) sudden expansion
For flow in the laminar regime, values of ζ are appreciably
larger than for turbulent flow(2). The value varies
considerably with Reynolds number in a very non-linear
manner; e.g. for a value of Re = 10, ζ < 4.9, referring to
the velocity pressure at the smaller dimension.
For turbulent flow, the Idelchik data suggest that for
Re > 105, variation of ζ with Re is trivial and the
following equation has been found to fit best the available
data for Re > 104:
(
A
ζ = 0.5 1 – –––2
A1
)
0.75
(4.26)
However, this equation takes no account of size effects and
Reynolds number effects, which are in evidence for the
more recent data of Table 4.25 for gradual contractions.
Standard pipe fittings would normally have a more
rounded transition and give a slightly lower pressure drop
than the values given in Table 4.27.
4.10.5.2
Although for elbows there is considerable evidence that
values of ζ vary with diameter, there is no clear evidence
that this is also the case for tees. It once seemed reasonable
to suppose that in tees, the fluid turbulence dominates to
the total exclusion of surface effects and relative roughness
(k / d). Rahmeyer(27) tested equal tees of 50 and 100 mm
diameter, but not of identical form or connection. No firm
data are therefore available on the effect of size.
Note that all values of ζ must be used with the velocity
pressure of the combined flow.
4.10.6.1
Notes on the information as presented
The only recent data are for tees made of PVC-U and steel.
Similarly the only joints mentioned are either screwed or
welded. No data are available concerning either smooth
joints or tees of copper, either of which might be expected
to give lower values of ζ .
The most recently obtained values are those of
Rahmeyer(29,30,33). From analysis of his results the values
given in Tables 4.28 to 4.34 were derived. He tested only
for reduced values of ds / dc = 0.74 and 1.0, and for branch
ratios of db / dc = 0.74 and 1.0. Where identical geometries
permit comparisons, the Rahmeyer data give consistently
lower values of ζ than those of Idelchik(2). Being more
recent, CIBSE is inclined to favour the former values.
Sudden enlargements
The Borda–Carnot equation may be used for Re > 104:
(
A
ζ = 0.5 1 – –––1
A2
)
Converging flow
2
Diverging flow
s
(4.27)
c
c
s
Δp = ζ 1/2 ρ cc2
However this equation takes no account of size effects and
Reynolds Number effects which are in evidence for the
more recent data of Table 4.26 for gradual expansions.
Standard pipe fittings would normally have a more
rounded transition and give a slightly lower pressure drop.
b
Configuration A
Converging flow
b
Diverging flow
b
b
4.10.5.3
Sudden entry/exit of a pipe to/from
a vessel
Δp = ζ 1/2 ρ cc2
For a sudden entry to a pipe from a vessel, ζ = 0.5.
c
For a sudden exit from a pipe into vessel, ζ = 1.0
c
Configuration B
Figure 4.7 Equal tees: configurations (Tables 4.28 to 4.30)
Table 4.27 Abrupt contraction: values of ζ ; for Re2 < 104 (from diagram 4-10 of Idelchik(2))
Area ratio,
A2 / A1
Reynolds number, Re2
40
50
100
200
500
1000
2000
4000
5000
10 000
0.1
0.2
0.3
2.00
1.84
1.70
1.80
1.62
1.50
1.30
1.20
1.10
1.04
0.95
0.85
0.82
0.70
0.60
0.64
0.50
0.44
0.50
0.40
0.30
0.80
0.60
0.55
0.75
0.60
0.55
0.50
0.40
0.35
0.4
0.5
0.6
1.60
1.46
1.35
1.40
1.30
1.20
1.00
0.90
0.80
0.78
0.65
0.56
0.50
0.42
0.35
0.35
0.30
0.24
0.25
0.20
0.15
0.45
0.40
0.35
0.50
0.42
0.35
0.30
0.25
0.20
Note: figures in italics are for conditions where, although turbulent flow occurs downstream of the
contraction, laminar conditions occur upstream.
Flow of fluids in pipes and ducts
4.10.6.2
4-23
Tees: laminar flow
In the laminar region, ζ is sensibly constant for flow to or
from a branch, being rather higher than for turbulent flow.
Summarised from Idelchik(2) it could be said that for
Re < 2000:
—
for laminar flow, converging flow branch: ζ = 2.5
—
laminar flow, diverging flow branch: ζ = 3.4
Surprisingly, compared with turbulent flow, it is the
pressure loss factor for the straight flow across the tee
which is said to be most complex. Idelchik gives very
complex relationships depending on the relative branch
size, the relative flows and the Reynolds number. Carrying
out a sample calculation for Re = 100, and with 50 per
cent of the flow to or from a branch of the same diameter,
revealed that, approximately:
—
for converging flow, straight ζ is four times that
for turbulent flow
—
for diverging flow, straight ζ is four times that for
turbulent flow.
4.10.6.3
Tees: turbulent flow
The value of ζ is seen to vary considerably with the ratio
of the respective flows so no simplistic values can be
given. The friction loss differs considerably between
converging and diverging flows. The effect of branch
diameter relative to the diameter of the part carrying the
combined flow, db / dc , is appreciable and cannot be
ignored but there are few data on this effect.
For flows straight across the tee, the values of ζ do not
vary greatly with the relative flows, qb / qc.
A clear distinction is made between converging and
diverging flows as follows.
Converging flows
There is little information on the effect of the upstream
type of connection. However Idelchik(2) reports that when
the flow from the branch is less than 80% of the combined
flow, screwed branches give losses 10–20% more than for
smooth connections. Conversely it would appear that
when the branch flow is greater than 80% of the total,
screwed branches give losses 10–20% less than for smooth
connections.
It will be observed that in the case of converging flows, it
is possible under certain flow conditions for the flow from
the branch to experience a negative pressure loss factor,
i.e. to experience a pressure gain.
For those who are unfamiliar with the concept of a
negative pressure loss factor, a small explanation follows.
With most of the flow going along the straight, this flow
has the greater momentum. The flow arriving from the
branch must be accelerated by frictional contact with the
straight-flowing fluid, the effect more than counteracting
the bend friction loss effect, and resulting in a pressure
increase.
Diverging flows
For losses round to the branch, there is little difference
between tees of smooth joints and those of screwed joints.
Table 4.28 Equal tees, converging flow, configuration A (see Figure 4.7): values for the straight factor, ζ s-c (derived from
Rahmeyer(29,30,33))
Type and diameter
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.43
0.48
0.51
0.52
0.52
0.50
0.46
0.40
0.32
0.23
(b) Welded joint, forged steel:
— 100 mm
–0.15
≠ –0.07
–0.01
0.05
0.11
0.15
0.17
0.16
0.12
0.06
(c) Butt-welded, wrought steel:
— 300 mm
— 400 mm
–0.05
0.01
0.02
0.09
0.08
0.15
0.14
0.20
0.18
0.22
0.20
0.21
0.21
0.19
0.18
0.14
0.13
0.09
0.07
0.03
(d) PVC-U, moulded:
— 50 mm
— 100 mm
— 150 mm
— 200 mm
0.18
0.22
0.38
0.24
0.24
0.26
0.40
0.27
0.28
0.30
0.41
0.30
0.31
0.32
0.40
0.31
0.34
0.33
0.38
0.30
0.35
0.33
0.35
0.28
0.34
0.31
0.31
0.25
0.31
0.27
0.25
0.21
0.26
0.21
0.17
0.15
0.20
0.13
0.07
0.07
(e) PVC-U, segmented:
— 200 mm
0.64
0.68
0.70
0.67
0.63
0.57
0.48
0.37
0.26
0.14
(a) Screwed joint, malleable iron:
— 50 mm
Note: scatter between different manufacturers: (a) (b) (c) = ± 0.2; (d) (e) = ± 0.1; figures in italics are extrapolated values
4-24
Reference data
Table 4.29 Equal tees, converging flow, configuration A (see Figure 4.7): values for the branch factor, ζ b-c (derived from
Rahmeyer(29,30,33))
Type and diameter
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Screwed joint, malleable iron:
— 50 mm
–0.22
–0.06
0.10
0.27
0.43
0.59
0.74
0.88
1.00
1.10
(b) Welded joint, forged steel:
— 100 mm
–0.65
–0.48
–0.34
–0.20
–0.06
0.08
0.20
0.30
0.42
0.54
(c) Butt–welded, wrought steel:
— 300 mm
— 400 mm
–0.55
–0.49
–0.39
–0.32
–0.23
–0.18
–0.09
–0.02
0.05
0.12
0.19
0.26
0.33
0.39
0.79
0.51
0.60
0.63
0.71
0.75
(d)
—
–0.53
–0.30
–0.09
0.11
0.29
0.42
0.56
0.70
0.85
1.00
PVC–U,
moulded:
50 mm to 200 mm
Note: scatter between different manufacturers: (a) (b) (c) = ± 0.2; (d) = ± 0.1; figures in italics are extrapolated values
Table 4.30 Equal tees, diverging flow, configuration A (see Figure 4.7): values for the straight factor, ζ s-c (derived from
Rahmeyer(29,30,33))
Type and diameter
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Screwed joint, malleable iron:
— 50 mm
0.25
0.18
0.13
0.08
0.04
0.02
0.02
0.05
0.12
0.21
(b) Welded joint, forged steel:
— 100 mm
0.45
0.35
0.26
0.18
0.11
0.06
0.03
0.01
0.02
0.06
(c) Butt-welded, wrought steel:
— 300 mm
0.30
0.21
0.14
0.08
0.04
0.02
0.02
0.03
0.05
0.09
(d) PVC-U, moulded:
— 50 mm
— 100 mm
— 150 mm
— 200 mm
0.22
0.35
0.34
0.32
0.17
0.28
0.27
0.23
0.13
0.22
0.20
0.16
0.09
0.16
0.14
0.10
0.06
0.11
0.09
0.06
0.04
0.07
0.05
0.03
0.04
0.04
0.03
0.02
0.07
0.05
0.03
0.02
0.13
0.08
0.06
0.04
0.21
0.14
0.10
0.07
(e) PVC-U, segmented:
— 200 mm
0.35
0.27
0.21
0.16
0.11
0.07
0.06
0.06
0.09
0.13
Note: scatter between different manufacturers: (a) (b) (c) = ± 0.4; (d) (e) = ± 0.5; figures in italics are extrapolated values
Table 4.31 Equal tees, diverging flow, configuration A (see Figure 4.7): values for the branch factor, ζ c-b (derived from
Rahmeyer(29,30,33))
Type and diameter
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Screwed joint, malleable iron:
— 50 mm
0.74
0.69
0.63
0.62
0.63
0.65
0.70
0.76
0.83
0.90
(b) Welded joint, forged steel:
— 100 mm
0.93
0.82
0.74
0.67
0.62
0.60
0.61
0.64
0.68
0.74
(c) Butt–welded, wrought steel:
— 300 mm
— 400 mm
0.80
0.75
0.72
0.67
0.66
0.60
0.61
0.54
0.57
0.51
0.56
0.50
0.57
0.51
0.59
0.52
0.62
0.53
0.66
0.54
(d) PVC–U, moulded:
— 50 mm
— 100 mm
— 150 mm
0.95
0.95
0.85
0.92
0.87
0.78
0.90
0.82
0.73
0.89
0.79
0.70
0.90
0.79
0.69
0.95
0.81
0.72
1.02
0.85
0.75
1.10
0.89
0.79
1.18
0.95
0.84
1.26
1.02
0.89
(e) PVC–U, segmented:
— 200 mm
1.24
1.18
1.14
1.12
1.12
1.15
1.20
1.27
1.36
1.47
Note: scatter between different manufacturers: (a) (b) (c) = ± 0.15; (d) (e) = ± 0.12; figures in italics are extrapolated values
Table 4.32 Equal tees, converging and diverging flow, configuration B (see Figure 4.7): values of ζ (derived from
Rahmeyer(29))
Type
Flow ratio, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Converging flow (ζb-c)
0.09
0.26
0.45
0.56
0.55
0.47
0.39
0.37
0.49
0.80
Diverging flow (ζc-b)
0.64
0.64
0.63
0.64
0.67
0.71
0.77
0.84
0.95
1.10
Flow of fluids in pipes and ducts
c
37 mm
50 mm
4-25
c
s
s
s
100 mm
37 mm
b
37 mm
50 mm
100 mm
s
c
100 mm
100 mm
37 mm
b
75 mm
b
(a)
c
75 mm
b
(a)
(b)
(b)
Figure 4.9 Unequal tees, converging flow: configurations (Table 4.34)
Figure 4.8 Unequal tees, diverging flow: configurations (Table 4.33)
Table 4.33 Unequal tees, diverging flow: values of ζ ; (a) for dc = 50 mm, ds = 37 mm, db = 37 mm, (b) dc = 100 mm, ds = 100 mm,
db = 75 mm (see Figure 4.8) (derived from Rahmeyer(29))
Type
Flow ratio, qb / qc
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Branch factors, ζc-b:
(a) 50 mm, screwed
(b) 100 mm, welded
—
—
0.78
0.91
0.78
0.89
0.86
0.90
1.04
0.94
1.30
1.11
1.64
1.33
2.05
1.64
2.55
2.06
3.11
2.59
3.75
3.26
Straight factors, ζc-s:
(a) 50 mm, screwed
(b) 100 mm, welded
2.55
0.04
2.02
0
1.56
0.01
1.16
0.01
0.83
0.05
0.57
0.11
0.38
0.17
0.25
0.24
0.20
0.31
0.22
0.39
—
—
Table 4.34 Unequal tees, converging flow: values of ζ ; for (a) dc = 50 mm, ds = 37 mm, db = 37 mm, (b) dc = 100 mm, ds = 100 mm,
db = 75 mm (see Figure 4.9) (derived from Rahmeyer(29))
Type
Flow ratio, qb / qc
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Branch factors, ζb-c:
(a) 50 mm, screwed
(b) 100 mm, welded
—
—
2.26
–1.18
2.54
–0.82
2.73
–0.60
2.86
–0.55
2.98
–0.35
3.08
0.26
3.174
0.55
3.24
1.00
3.30
1.45
3.36
1.60
Straight factors, ζs-c:
(a) 50 mm, screwed
(b) 100 mm, welded
1.59
0.07
1.60
0.21
1.60
0.20
1.61
0.19
1.62
0.17
1.63
0.04
1.64
–0.04
1.68
–0.14
1.73
–0.16
4.10.7
1.66
–0.06
4.10.7.1
Valves
The value of the pressure loss factor for a valve will
depend upon the type of valve and the configuration used
by the manufacturer. The following approximate data are
given to help in initial design calculations. The actual
values, supplied by the manufacturer, should be used as
soon as they are available.
A single value can only be given for the valve in the fully
open position. (The value of ζ will be infinite when the
valve is closed.) For regulating valves therefore, the
manufacturer will generally prefer to give a value of the
valve capacity (K) for the valve fully open, supplemented
by a graph of the variation of the relative capacity with
relative valve opening. (The value of K will be 0 when the
valve is closed.) This is more useful than ζ when establishing the valve authority and overall control characteristic.
The pressure drop due to the valve is easily calculated
from equation 4.13 (see section 4.4.2), i.e:
—
qv = K √Δp
Globe valves
See Table 4.35. As with balancing valves, these are
designed to give a better control characteristic, for use in
either balancing or control. Values of ζ are for the valve
fully open. These vary with the internal design of the
valve so are included here only for guidance and should be
used with care.
4.10.7.2
Gate valves
These should be installed for use in the fully open
position. They are designed to give a clear bore when fully
open. In operation, therefore, the pressure drop through
them should be quite small.
Although designs may vary, the following provides a
rough estimate of the pressure drop:
—
spherical-seal gates: ζ = 0.03
—
plain-parallel gates: ζ = 0.3
Table 4.35 Globe valves: approximate values of ζ (taken from Idelchik(2))
Value of ζ for stated diameter / mm
Type
Standard globe valve,
angular dividing walls
Angle globe valve
—
—
20
40
60
80
100
150
200
300
8
4.9
—
4
4.1
4.4
4.7
5.4
—
—
2.7
2.4
2.2
1.86
1.65
1.4
4-26
Reference data
4.10.7.3
Non-return valves
4.10.8.2
See Tables 4.36 and 4.37. A single value of ζ cannot be
given.
Tubes are likely to be shorter and smaller and the effects of
joints can be significant. All of the values in Table 4.38 are
taken from Idelchik(2) for Re values: 1.8 × 105 < Re < 5 × 105.
For the gravity flap type, the greater the flow, the more the
valve flap opens and the lower becomes the value of ζ .
4.10.9
Spring-loaded non-return valves also behave in a very
non-linear fashion, and so the manufacturer’s characteristic must be used. The data in Table 4.37, taken from part
of the performance characteristic of valves of a single
manufacturer, may be used for the purpose of first
estimates. It does not state what flow would result in these
values of K.
Orifice plates are generally used for flow measurement but
may sometimes be installed to aid the balancing of flow.
Although there is a gradual pressure recovery downstream
of the orifice, they do incur a permanent pressure loss and
permanent pumping costs. Thus if used for balancing
purposes, consideration should be given to reducing the
resistance of the parallel circuit instead.
Angle of opening / degree
Non-return valve
20
30
40
50
60
70
75
1.7
3.2
6.6
14
30
62
90
Idelchik(2) gives data for various shapes of orifice and for
the combination with a sudden contraction. In Table 4.39
the data for only one are given, namely for a thin sharpedged orifice for which Reo (within the orifice) ≥ 105 and
δ /do ≤ 0.0075, where δ is the plate thickness. Note that the
values of ζ are to be used with the velocity pressure in the
main pipe.
Table 4.37 Spring-loaded non-return valves:
approximate values of K
ζ is given by:
Value of K (/ m3·h–1·bar–0.5)
for stated diameter / mm
Type
Spring-loaded
non-return valve
25
38
50
15
38
55
Orifices
See Figure 4.10 and Table 4.39.
Table 4.36 Non-return valves: approximate values of ζ (taken from
Idelchik(2))
Type
Plastic joints
( ) [(
A
ζ= —
Ao
2
)
( ) ]
A
A
1 – —–o + 0.707 1 – —–o
A
A
Δp = ζ 1/2 ρ c2
4.10.8
Pipe joints
4.10.8.1
Welded and screwed metal tubes
d, A, c
The joints do not have a great effect and will generally be
small in relation to the long tube lengths used. Therefore
only brief guidance is given in Table 4.38. Screwed joints
give a greater pressure drop due to the appreciable
discontinuity of the surface at the joint, but no clear data
are available.
do , Ao , co
Diameter = d
Area = A
Velocity = c
δ
Figure 4.10 Orifice
Table 4.38 Pipe joints: values of ζ for 1.8 × 105 < Re < 5 × 105 (from Idelchik(2))
Type
Pipe diameter / mm
Metal pipe,
welded joints
Plastic pipe:
— welded joints
— flanged joints
50
75
100
150
200
250
300
400
500
600
—
—
—
—
0.026
—
0.0135
0.009
0.006
0.004
0.411
0.131
0.224
0.13
0.146
0.114
0.079
0.096
0.037
0.062
0.028
0.045
—
—
—
—
—
—
0.057
0.079
Table 4.39 Sharp-edged orifice: values of ζ calculated from equation 4.28; for Reo > 105 (Idelchik(2), diagram 4-14)
Type
Orifice
Diameter ratio, do / d
0.15
0.2
0.25
0.3
0.35
0.4
0.5
0.6
0.7
0.8
0.9
5565
1714
678
313
160
88.2
30.8
11.8
4.67
1.73
0.49
0.375 2
(4.28)
Flow of fluids in pipes and ducts
4.11
Pressure loss factors for
ductwork components
4.11.1
General
An extensive review of pressure loss factors has been
undertaken. Many sources give conflicting information.
Note has been taken of recommended standard components given by HVCA(22), though in some instances no
experimental data are given for these components. Best
estimates are presented and are identified as such. Much
of the experimental data were obtained long ago and
original source data are therefore difficult to obtain.
Tolerance on the published values is therefore impossible
to estimate.
Technical names for components can vary but, for
consistency, the HVCA labels are used.
Jones(32)
Smith and
found that bends having the seams
against the flow gave rise to an additional 0.06 in the value
of ζ in comparison with the value when the flow is with
the seam. Surface effects associated with manufacture or
installation could alter the values presented for ζ
significantly. For flat-oval elbows the effect could give a
variation of ±25%.
No data are presented for laminar flow (Re < 2 × 103).
The CIBSE is more confident about the data for circular
ductwork than for rectangular ductwork. Only one source
(Madison and Parker(31)) has been found giving evidence
that rectangular ductwork has been tested, and one for
square sections (Miller(37)). Much of the data for
rectangular ductwork appears to have been adapted from
results for circular ductwork.
For tees, ζ for branch losses and for the straight flow
losses are based on use with the velocity pressure of the
combined flow. The formula is included with each item as
a reminder.
For tees, Eschman(24) shows that for diverging flow, the
values of ζ vary very little with the branch area ratio
Ab / Ac , but are very dependent on the velocity ratio cb / cc .
However, since designers usually work with volume flow
rates, much source data have been presented in terms of
the relative branch flow qb / qc, and therefore also of Ab / Ac .
This practice has been continued in this edition of Guide C.
Since publication of the 2001 edition of Guide C, the
CIBSE has been able to obtain a copy of the report of the
European Research Programme conducted in the 1990s(1).
The Programme investigated pressure losses in circular
ductwork of two different sizes, over a considerable range
of air speeds. Where appropriate, data have been amended
in the light of this report. Major points to note are:
—
for most components, ζ varies with diameter
—
Reynolds number effects are significant.
Where data are available for a range of values of Reynolds
number, and the variation of ζ is not large, the values
quoted are for Re = 2 × 105.
4-27
The radius of curvature of bends is standardised as that of
the mean air stream (HVCA being the exception).
The data presented here are those which are considered
most reliable. The CIBSE will continue to amend the data
as more research results become available.
The data are presented as follows:
—
components for circular ductwork: section 4.11.2
—
components for flat-oval ductwork: section 4.11.3
—
components for rectangular ductwork: section 4.11.4
—
transitions between circular and rectangular ductwork:
section 4.11.5.
4.11.2
Pressure loss factors for
ductwork components: circular
Recent work by the United McGill Corporation(28), and by
the European project(1) has shown that for bends, the
value of ζ is dependent on the diameter. Work done on
rectangular elbows by Madison and Parker(31), showed that
size effects are appreciable for square bends of long radius
and for those having a low aspect ratio (h/w).
The data for bends show that there is an optimum relative
bend radius r / d. The phenomenon of the friction factor
increasing with increasing radius may seem strange, but is
explained by the fact that the bend inevitably becomes
longer, for greater radiuses. In principle a sharper bend
will introduce a greater pressure drop than a more gradual
bend having less auxiliary ductwork associated with it.
Although HVCA(22) suggests r/d = 1.0 as standard, the use
of larger radius bends with r / d = 1.5 always results in
appreciably less resistance, and is regarded as standard by
ASHRAE(4). The European Programme(1) confirms much
earlier findings by Miller(25) that for medium size ducts
(i.e. d > 250 mm) for minimum pressure loss, the
optimum radius of a segmented bend is given by r/d = 2.
Values of ζ are now known to vary appreciably with
Reynolds number. The variation is shown by Koch(38) to
be greater than the variation of λ for straight ductwork,
and should not therefore be ignored. Such data are
provided where available.
Generally overlooked is that the direction of installation
of a segmented bend matters. Smith and Jones(32), testing
segmented oval bends, found that when the flow was
‘against’ the lap seam, the value of ζ was 23% higher than
when the flow was ‘with’ the seam. CETIAT(39) tested
segmented elbows from several different manufacturers
and found ζ to vary by ±25%, a variation which could
easily be explained by the different states of projection of
the butt welds on the inside. The condition and intrusion
of joints might account for some of the discrepancy
between certain research results.
The data are presented for the standard sizes recommended by HVCA(22).
The variation of ζ with bend angle (α) has been found by
the European project(2) to be very different depending on
the nature of the elbow/bend. This variation, relative to
the value of ζ at 90° is given by the correction factor Cα
and is shown in Figure 4.11. The rather older data of
4-28
Reference data
1.0
4.11.2.2
Pleated bends
0.9
Correction factor, Cα
0.8
Segmented
0.7
Mitred
0.6
r
0.5
α
0.4
d
Smooth
0.3
The only data available are for 90° bends, see Table 4.43.
For bends of other angles (α) see Figure 4.11.
0.2
0.1
0
0
15
60
45
30
75
90
Bend angle, α / degree
Figure 4.11 Variation of correction factor with bend angle (from Koch(38));
duct diameter d = 250 mm. Valid for 1.0 × 105 < Re < 4.0 × 105; segmented
and smooth bends (r/d = 1.0)
Miller(37) suggests that the curves for circular bends with
r/d > 1.0 would be rather straighter. It is possible that this
variation might be different for different sizes.
4.11.2.1
Table 4.43 Pleated 90° bends: variation of ζ with diameter; for r/d = 1.5,
Reynolds number unknown (adapted from ASHRAE Handbook:
Fundamentals 2005(4), chapter 35. © American Society of Heating,
Refrigerating and Air-Conditioning Engineers Inc. (www.ashrae.org))
Type
100
Pleated
90° bend
200
250
300
350
400
0.57 0.495 0.43 0.375 0.34
125
150
180
0.28
0.26
0.11
0.25
Note: figures in italics were obtained by interpolation
4.11.2.3
Smooth radius round bends
(HVCA 127: ‘pressed bend’)
Diameter, d / mm
Segmented bends (HVCA 128)
r
α
r
d
α
See Tables 4.44 to 4.48. Data from SMACNA(40) shows that
the greater the number of segments, the smoother is the
bend, and the lower is the value of ζ . Five or more
segments are only likely to be used for large radius bends.
d
See Tables 4.40, 4.41 and 4.42.
Table 4.40 Smooth bends: variation of ζ with Reynolds number; for
d = 250 mm, r/d = 1.0 (derived from European Programme Report(1) and
Koch(38))
Bend angle,
α / degree
30
45
60
75
90
4.11.2.4
Mitred elbow (HVCA 128)
Reynolds number, Re (/ 105)
0.5
1
1.5
2
2.5
3
3.5
4
—
0.119
0.221
0.298
0.343
—
0.101
0.187
0.252
0.290
0.048
0.094
0.175
0.238
0.271
0.044
0.087
0.161
0.217
0.250
0.044
0.086
0.160
0.216
0.248
0.043
0.085
0.158
0.213
0.245
0.043
0.084
0.156
0.211
0.242
0.042
0.083
0.155
0.209
0.240
α
d
Note: figures in italics were obtained by interpolation
Table 4.41 Smooth bends of any angle: value of ζ relative to that of a 90°
bend; for d = 250 mm, r/d = 1.0; 1.0 × 105 < Re < 2 × 105 (derived from
the European Programme Report(1) and Koch(38))
Type
Smooth bend
Value of ζ relative to 90˚ bend for stated bend angle, α
30°
45°
60°
75°
90°
0.177
0.347
0.645
0.870
1
See Tables 4.49 to 4.51.
4.11.2.5
Bends and elbows in close proximity,
in same plane (‘gooseneck’)
ζ = Ccp 2 ζ1
Note: figures in italics were obtained by interpolation
l
Table 4.42 Smooth 90° bends: variation of ζ with diameter; for Reynolds
number = 1 × 105 (adapted from UMC (28))
Ratio, r/d
Diameter, d / mm
63
1.5
80
100
(0.35) (0.28) (0.21)
125
150
180
200
250
0.16
0.14
0.115
0.11
0.11
Notes: UMC also provides data for r/d = 1.0, but where a cross reference
with Table 4.41 is possible a large contradiction is evident; these have
therefore been omitted so as to avoid any confusion. Figures in
parentheses were obtained by extrapolation. UMC gives the variation
with diameter but gives no data on the variation with Re.
l
α
See Table 4.52; ζ 1 is the factor for a single bend.
Flow of fluids in pipes and ducts
4-29
Table 4.44 Segmented 90° bends: variation of ζ with diameter; for Re = 1 × 105 (adapted from UMC (28))
Ratio, r/d
Diameter, d / mm
80
1.5 (5-segments)
100
125
150
200
250
300
400
500
800
1200
(0.48) (0.40) (0.325) 0.28
0.23
0.20
0.18
0.16
0.14
0.12
0.12
Note: similar data are also provided for r/d = 2.5 (7-segments) by UMC and for r/d = 1.0 (5-segments) by
ASHRAE but the values contradict those of Table 4.48 for d = 250 mm; to avoid confusion, these are omitted.
Figures in parenthesis are extrapolated values.
Table 4.45 Segmented bends: variation of ζ with Reynolds number; for r/d = 1.0 (derived from European
Programme Report(1) and Koch(38))
Diameter,
d / mm
Reynolds number, Re (/ 105)
Bend angle,
α / degree
0.5
1.0
1.5
2.0
2.5
3.0
4.0
5.0
6.0
250
45
60
75
90
0.159
0.243
0.303
0.340
0.143
0.218
0.272
0.305
0.129
0.197
0.245
0.275
0.122
0.186
0.232
0.260
0.120
0.183
0.228
0.256
0.118
0.180
0.225
0.252
0.114
0.175
0.217
0.244
—
—
—
—
—
—
—
—
400
400
400
45
60
90
0.12
0.21
—
0.105
0.183
—
0.09
0.170
—
0.083
0.160
0.20*
0.078
0.152
—
0.073
0.147
—
0.068
0.142
—
0.064
0.135
—
0.064
0.13
—
* estimated value
Note: figures in italics were obtained by interpolation
Table 4.46 Segmented bends of any angle: value of ζ relative to that of a
90° bend; for d = 250 mm, r/d = 1.0; 1.0 × 105 < Re < 4 × 105 (derived
from the European Programme Report(1) and Koch(38))
Table 4.50 Mitred elbows: variation of ζ with Reynolds number; for
d = 250 mm (derived from European Programme Report(1) and Koch(38))
Diam., Bend angle,
d / mm α / degree
Value of ζ relative to 90˚ bend for
stated bend angle, α
Type
Segmented bend
45°
60°
75°
0.44
0.73
0.90
90°
0.5
1.0
1.5
2.0
2.5
3.0
4.0
250
30
45
60
75
90
0.131
0.269
0.526
0.901
1.38
0.121
0.253
0.488
0.835
1.28
0.115
0.239
0.461
0.790
1.23
0.112
0.233
0.450
0.770
1.18
0.110
0.229
0.448
0.757
1.16
0.109
0.227
0.432
0.750
1.15
0.107
0.223
0.431
0.737
1.13
400
30
0.08
0.061 0.045 0.039 0.035 0.034 0.032
1
Note: figure in italics was obtained by interpolation
Table 4.47 Segmented bends (4 segments): variation of ζ with relative
bend ratio (r/d); for α = 90°, d = 250 mm; Re = 2 × 105 (adapted from
the European Programme Report(1))
Type
Note: figures in italics were obtained by interpolation
Table 4.51 Mitred elbows of any angle: values of ζ relative to that of a
90° elbow; for d = 250 mm; 1.0 × 105 < Re < 4 × 105 (derived from
European Programme Report(1) and Koch(38))
Relative bend ratio, r/d
Segmented bend
(4 segments)
0.7
1.0
1.5
2.0
2.5
3.0
5.0
0.44
0.26
0.20
0.195
0.21
0.23
0.31
0.7
1.0
1.5
≥ 2.0
Value of ζ relative to that of a 90° elbow,
for stated elbow angle, α / degree
Type
Mitred elbow
Table 4.48 Segmented bends: variation of ζ with Reynolds number, in
terms of a multiplying factor CRe to be applied to the values of Table
4.45; for α = 90°, d = 250 mm (adapted from the European Programme
Report(1))
Aspect
ratio, r/d
Reynolds number, Re (/ 105)
22.5
30
45
60
75
90
0.05
0.095
0.197
0.381
0.653
1
Note: figures in italics were obtained by interpolation
Multiplying factor, CRe , for stated Reynolds number, Re / 105
0.5
1.0
1.5
2.0
2.5
3.0
4.0
1.30
1.31
1.44
1.51
1.15
1.17
1.24
1.24
1.05
1.08
1.10
1.08
1.0
1.0
1.0
1.0
0.95
0.93
0.92
0.92
0.95
0.92
0.87
0.86
0.95
0.93
0.84
0.87
Table 4.49 Mitred elbows: variation of ζ with diameter; Re unknown (derived from UMC(28))
Bend angle,
α / degree
90
Diameter, d / mm
80
100
125
150
200
250
300
400
500
800
1200
(1.44)
(1.4)
(1.36)
1.31
1.26
1.23
1.20
1.17
1.15
1.14
1.12
Note: figures in parentheses were obtained by extrapolation
4-30
Reference data
4.11.2.7
Table 4.52 Two bends in close proximity in the same plane; values of
interaction factor Ccp; for d = 250 mm, r/d = 1 (from European
Programme Report(1) and Koch(38))
Bend angle, α ,
and type
Ratio, l/d
Value of Ccp for stated
Reynolds number, Re / 105
30° mitred
1< l/d <5
0.83 0.82 0.82 0.82 0.82 0.81 0.80
30° smooth
l/d = 1
3< l/d <5
45° segmented
1< l/d <5
1.45 1.16 1.10 1.07 1.04 1.02 0.96
45° smooth
1< l/d <5
0.96 0.99 0.97 0.92 0.88 0.84 0.85
60° segmented
1< l/d <5
1.03 1.11 1.10 1.07 1.08 1.09 1.09
60° smooth
1< l/d <5
1.05 0.94 0.93 0.87 0.86 0.84 0.83
75° segmented
l/d = 1
1< l/d <5
1.11 1.11 1.04 1.02 1.04 0.99 1.01
1.10 0.97 0.93 0.93 0.95 0.93 0.81
75° smooth
1< l/d <5
1.07 1.00 0.96 0.92 0.92 0.91 0.89
90° smooth and
segmented
1< l/d <5
1.07 0.96 0.95 1.02 1.04 1.02 1.10
0.5
—
—
1.0
—
—
1.5
2.0
2.5
3.0
A2
γ
4.0
A1
Δp = ζ 1/2 ρ c12
c1
0.95 0.88 0.84 0.73 0.73
1.12 1.02 0.93 0.87 0.79
Laminar flow
For laminar flow through expansions of circular cross
section, Idelchik(2) gives the following relationship, valid
for ζ ≤ 40°:
A
ζ = —–
Re
(4.29)
20 (A2 / A1) 0.33
A = ——————
(tan γ) 0.75
(4.30)
where:
Note: factors for close proximity Ccp are applied to the values of ζ 1
obtained from Tables 4.40 to 4.51, as appropriate.
The data given in Table 4.52 do not include the pressure
drop of the length of separation. The separation ( l) should
be added to the length of straight ductwork of the same
size.
4.11.2.6
Symmetrical expansion
(HVCA taper 132)
Bends and elbows in close proximity,
through perpendicular plane
ζ = Ccp 2 ζ1
l
Turbulent flow
See Tables 4.54 and 4.55.
For turbulent flow, Idelchik(2) reports that values of ζ are
very dependent on flow separation which in turn is
dependent on upstream flow conditions giving a velocity
profile which may be symmetrical or asymmetrical. For
small angles of divergence (γ ) the length of travel of an
unseparated core of flow will depend very much on the
degree of asymmetry. Thus for small values of γ , prediction of the pressure drop becomes more difficult. Table
4.54 shows that even small values of γ result in appreciable
pressure drop, and that abrupt expansions (γ = 180°) do
not cause the pressure drop to be as great as might have
been expected.
Contrary to the data of Idelchik(2), reproduced in other
publications, the European Programme(1) shows that ζ
See Table 4.53; ζ 1 is the factor for a single bend.
The data given in Table 4.53 do not include the pressure
drop of the length of separation. The separation l should
be added to the length of straight ductwork of the same
size.
Table 4.53 Two 90° bends in close proximity, out of plane: values of
interaction factor Ccp; for d = 250 mm, r/d = 1 (derived from European
Programme Report(1))
Type
Smooth
Segmented
Ratio, l/d
Value of Ccp for stated
Reynolds number, Re (/ 105)
Table 4.54 Symmetrical expansion: values of ζ with no variation with
Re; for A2 / A1 = 2.44, d1 = 160 mm, d2 = 250 mm (derived from
European Programme Report(1))
Divergence angle, γ
Type
Symmetrical
expansion
30°
60°
90°
120°
150°
180°
0.168
0.280
0.353
0.40
0.45
0.49
Note: values in italics were obtained by interpolation
Table 4.55 Symmetrical expansion: values of ζ for various divergence
angles (derived from Miller(37))
0.5
1.0
1.5
2.0
2.5
3.0
4.0
1
3
5
1.14
1.04
1.16
0.91
0.95
0.96
0.83
0.90
0.90
0.82
0.89
0.89
0.83
0.89
0.89
0.83
0.88
0.89
0.84
0.87
0.89
1
3
5
0.87
0.94
0.98
0.93
0.99
1.05
0.98
1.04
1.08
1.04
1.09
1.14
1.10
1.15
1.19
1.09
1.15
1.20
1.01
1.02
1.08
Divergence
angle, γ
Area ratio, A2 / A1
1.2
40°
30°
20°
0.058 0.095 0.13 0.17
0.055 0.082 0.104 0.14
0.050 0.072 0.091 0.11
1.4
1.6
1.8
3.0
4.0
0.20
—
0.38
0.17 0.168* 0.31
0.125 —
0.21
2.0
2.44
0.55
0.49
0.40
* value from the European Programme Report(1), see Table 4.54
Flow of fluids in pipes and ducts
4-31
does not vary with Reynolds number. The close agreement
between the values Miller(37) and those of the European
Programme enable Miller’s data to be used for other
expansion ratios, see Table 4.55.
4.11.2.9
Offset tapers (HVCA 131), contractions
and expansions
A1
γ /2
The European Programme also tested abrupt expansions
of different offsets. Even the maximum possible offset did
not make a significant difference.
4.11.2.8
A2
c2
c2
A1
Δp = ζ 1/2 ρ c22
See Tables 4.56 and 4.57. It is clear from Table 4.56 that for
contractions the values of ζ are small, but their relative
variation with Re is appreciable. For other values of A1 /A2
the only available data are from ASHRAE, but of unknown
Reynolds number, see Table 4.57. There is an unresolved
conflict between these two sets of data, especially evident
for γ = 90°.
The angle γ to be used should be twice the angle of the
part deviating most.
4.11.2.10
Bend coupled to short symmetrical
expansion
The European project carried out no tests on bends
coupled to contractions; only on bends close-coupled to
expansions as shown below.
Δptot = ζ tot 1/2 ρ c12
Table 4.56 Symmetrical contraction: values of ζ for various convergence
angles; for A1 / A2 = 2.44, d1 = 250 mm, d2 = 160 mm (derived from
European Programme Report(1))
Convergence
angle, γ
90°
60°
30°
c1
The European Programme(1) tested several different
offsets for sudden expansions, γ = 180°, but found only a
trivial difference from a symmetrical expansion. It is
reasonable to suppose that there would not have been a
significant difference for offset sudden contractions. In
the absence of other specific data concerning offset tapers,
it seems reasonable to suppose no significant differences
in the value of ζ from those given in Tables 4.54 to 4.57.
c2
γ
A1
A2
Symmetrical contractions, short
tapers (HVCA 132 and 133)
A2
γ /2
Reynolds number, Re (/ 105)
1.2
1.5
0.084
0.084
0.084
0.075
0.072
0.073
2.0
2.5
0.059 0.048
0.051 0.036
0.054 0.039
3.0
4.0
5.0
6.0
0.042
0.029
0.033
0.040
0.027
0.030
0.044
0.031
0.034
0.051
0.040
0.045
α
d1
Table 4.57 Symmetrical contraction: values of ζ ; Reynolds number
unknown (adapted from ASHRAE Handbook: Fundamentals 2005(4),
chapter 35. © American Society of Heating, Refrigerating and AirConditioning Engineers Inc. (www.ashrae.org))
Convergence angle, γ
Ratio,
A1 /A2
15°
30°
45°
60°
90°
120°
150°
180°
2
4
6
10
0.05
0.04
0.04
0.05
0.05
0.04
0.04
0.05
0.06
0.06
0.06
0.07
0.06
0.07
0.07
0.08
0.12
0.17
0.18
0.19
0.18
0.27
0.28
0.29
0.24
0.35
0.36
0.37
0.26
0.41
0.42
0.43
See Table 4.58. The values of ζ tot for the combined
assembly of bend plus expansion, always exceeds the sum
of the values of ζ for the two individual components.
Although the individual value of ζ for a bend varies
considerably with Re, with the close-coupling, it is the
effect of the expansion which dominates. ζ tot is found to
vary very little with Re.
Values for 90° bends were deemed unreliable. The figures
in italics, are ‘best advice’ only.
Table 4.58 Segmented bend coupled to a symmetrical expansion: values
of ζ tot; for d1 = 250 mm, d2 = 400 mm, A2 / A1 = 2.44, r / d = 1.0, Re / 105
(from the European Programme Report(1))
Bend angle,
and type
30° mitred
45°
60°
90°
Included angle of taper, γ
30°
60°
90°
180°
0.805
0.645
0.670
0.85
0.824
0.815
0.888
1.09
0.872
0.834
0.990
1.18
0.925
0.925
1.081
1.25
4-32
Reference data
4.11.2.11
Two bends coupled by a short
symmetrical contraction, in same plane
4.11.2.12
Two bends coupled by a short
symmetrical expansion, in same plane
Δptot = ζ tot 1/2 ρ c22
Δptot = ζ tot 1/2 ρ c12
c1
γ
γ
c2
α
α
See Table 4.59. γ is the total included angle of the taper.
See Table 4.60. γ is the total included angle of the taper.
Table 4.59 Two bends coupled by a symmetrical contraction in same plane; values of ζ tot; for r / d = 1.0 (derived from the European Programme
Report(1))
Type
Taper angle, γ
Bend angle, α , and Reynolds number, Re
2 × 30°
1×
105
2 × 45°
2×
105
1×
105
2 × 60°
2×
105
1×
105
2 × 75°
2×
105
1×
105
2 × 90°
2×
105
1×
105
2 × 105
(a) Contraction from d1 = 250 mm, to d2 = 160 mm; A1 / A2 = 2.44
Smooth*
30°
60°
90°
0.115
0.115
0.116
0.096
0.097
0.098
0.160
0.163
0.189
0.134
0.138
0.143
0.206
0.208
0.208
0.199
0.199
0.200
0.286
0.289
0.295
0.273
0.277
0.281
0.347
0.349
0.367
0.333
0.338
0.342
Segmented
30°
60°
90°
—
—
—
—
—
—
—
—
—
—
—
—
0.250
0.257
0.271
0.263
0.271
0.288
—
—
—
—
—
—
0.455
0.263
0.473
0.465
0.475
0.483
(b) Contraction from d1 = 400 mm, to d2 = 250 mm; A1 / A2 = 2.56
Mitred
30°
60°
90°
0.184
0.188
0.188
0.136
0.148
0.150
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
Segmented
30°
60°
90°
—
—
—
—
—
—
0.172
0.192
0.212
0.135
0.140
0.166
0.300
0.306
0.324
0.239
0.248
0.260
0.298
0.335
0.353
0.260
0.277
0.283
0.426
0.432
0.452
0.376
0.393
0.409
Note: figures in italics are ‘best advice’ figures, replacing experimental values which were much out of step, reflecting experimental problems.
Table 4.60 Two bends coupled by a symmetrical expansion in same plane; values of ζ tot; for r / d = 1.0 (derived from the European Programme
Report(1))
Type
Taper angle, γ
Bend angle, α , and Reynolds number, Re
2 × 30°
1 × 105
2 × 45°
2 × 105
1 × 105
2 × 60°
2 × 75°
2 × 90°
2 × 105
1 × 105
2 × 105
1 × 105
2 × 105
1 × 105
2 × 105
(a) Expansion from d1 = 160 mm, to d2 = 250 mm; A2 / A1 = 2.44
Smooth*
30°
60°
90°
0.513
0.547
0.562
0.495
0.503
0.529
0.503
0.717
0.761
0.482
0.685
0.743
0.417
0.654
0.755
0.373
0.588
0.758
0.475
0.634
0.743
0.436
0.582
0.687
0.465
0.589
0.717
0.420
0.590
0.671
Segmented
30°
60°
90°
—
—
—
—
—
—
—
—
—
—
—
—
0.916
—
0.849
0.854
—
0.819
—
—
—
—
—
—
0.742
0.830
0.889
0.748
0.475
0.876
(b) Expansion from d1 = 250 mm, to d2 = 400 mm; A2 / A1 = 2.56
Mitred
30°
60°
90°
0.727
0.746
0.760
0.731
0.735
0.739
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
Segmented
30°
60°
90°
—
—
—
—
—
—
0.722
0.855
1.154
0.730
0.844
1.120
0.750
1.072
1.145
0.740
1.010
1.106
0.580
0.805
0.856
0.538
0.769
0.816
0.625
0.890
1.012
0.624
0.870
0.921
Note: figures in italics are ‘best advice’ figures, replacing experimental values which were much out of step, reflecting experimental problems.
Flow of fluids in pipes and ducts
4.11.2.13
4-33
Two 90° bends coupled by a short
symmetrical contraction, out of plane
4.11.2.15
90° branch tees, circular from circular
(HVCA 139) and pressed equal tee
(HVCA 130)
c2
Δptot = ζ tot 1/2 ρ c22
(a) Converging flows (Ac = As)
As
qs
cs
γ
Δp = ζ 1/2 ρ cc2
See Table 4.61. γ is the total included angle of the taper.
Ab
qb
cb
Table 4.61 Two 90° bends coupled by a symmetrical contraction, out of
plane; values of ζ tot for r / d = 1.0 (derived from the European
Programme Report(1))
Taper
angle, γ
Type and Reynolds number, Re
Smooth
1 × 105
See Tables 4.63 and 4.64. Rec is based on the value for the
combined flow.
Segmented
2 × 105
1 × 105
2 × 105
(a) Contraction from d1 = 250 mm, to d2 = 160 mm; A2 / A1 = 2.44
30°
60°
90°
0.309
0.304
0.323
0.308
0.303
0.303
0.460
0.441
0.450
0.466
0.454
0.458
(b) Contraction from d1 = 400 mm, to d2 = 250 mm; A2 / A1 = 2.56
30°
60°
90°
—
—
—
4.11.2.14
—
—
—
Ac
qc
cc
0.461
0.428
0.460
0.406
0.380
0.403
Two 90° bends coupled by a short
symmetrical expansion, out of plane
Δptot = ζ tot 1/2 ρ c12
It is now evident that the value of both the straight factor
and the branch factor vary with the size of the tee (i.e.
with the diameters of the main parts of the tee: Ac , As ),
and with Reynolds number. Values of the straight factor
ζ s-c appear generally to vary little with Re and not in a
regular manner. In the interests of simplicity, the values of
ζ s-c given in Table 4.63 are mean values over the range
1 × 105 < Rec < 5 × 105. Values for Rec = 0.5 × 105 can be as
much as 25% greater.
It is now evident that the value of the branch factor ζ b-c
varies with the size of the tee (i.e. with the diameters of
the main parts of the tee: ds , dc ), and with Reynolds
number. For Re > 1 × 105, the variation is not very great.
In the interests of simplicity, the values of ζb-c given in
Table 4.64 are mean values over the range 1 × 105 < Rec
< 2 × 105. Values for Rec = 0.5 × 105 are generally about
8% greater(33).
γ
(b) Diverging flows (Ac = As)
Ac
qc
cc
c1
Δp = ζ 1/2 ρ cc2
See Table 4.62. γ is the total included angle of the taper.
Table 4.62 Two 90° bends coupled by a symmetrical expansion, out of
plane; values of ζ tot for r / d = 1.0 (derived from the European
Programme Report(1))
Taper
angle, γ
Smooth
Segmented
2 × 105
1 × 105
2 × 105
(a) Expansion from d1 = 160 mm, to d2 = 250 mm; A2 / A1 = 2.44
0.454
0.560
0.715
0.423
0.544
0.673
0.702
0.783
0.834
0.721
0.771
0.817
(b) Expansion from d1 = 250 mm, to d2 = 400 mm; A2 / A1 = 2.56
30°
60°
90°
As
qs
cs
Type and Reynolds number, Re
1 × 105
30°
60°
90°
Ab
qb
cb
—
—
—
—
—
—
0.616
0.793
0.946
0.604
0.807
0.948
See Tables 4.65 and 4.66. Values of the straight factor ζs-c
appear generally to vary little with Reynolds number, and
not in a regular manner. Mean values are therefore given
below. Any possible variation with diameter is inconclusive at present.
It is now evident that the value of the branch factor ζ s-b
varies with the size of the tee (i.e. with the diameters of
the main parts of the tee: dc , ds), and with Reynolds
number. Re is based on the value for the combined flow.
For Rec > 1 × 105, the variation is not very great. In the
interests of simplicity, the values of ζ given in Table 4.66
are mean values over the range 1.0 × 105 < Rec < 5 × 105.
Values for Rec = 0.5 × 105 are generally about 8% greater.
4-34
Reference data
Table 4.63 90° tees, converging flow: values for the straight factor ζ s-c (derived from the European Programme
Report(1) and Koch(38))
Area ratio,
Ab / Ac
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.10
0.1406*
0.20
0.45
1.2
1.65
1.4
0.60
1.1
1.5
1.3
0.80
1.15
1.25
1.10
1.1
1.08
1.0
0.83
1.4
1.0
0.74
0.62
0.85
0.60
0.50
0.43
0.55
0.35
0.31
0.285
0.25
0.22
0.20
0.19
0.04
0.10
0.09
0.10
0
0
0
0
0.25*
0.30
0.3906*
1.0
0.80
0.56
1.0
0.75
0.54
0.86
0.70
0.47
0.72
0.60
0.42
0.55
0.47
0.34
0.41
0.38
0.30
0.27
0.26
0.24
0.18
0.175
0.17
0.10
0.10
0.10
0
0
0
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
1.55
1.50
1.3
1.7
1.5
1.2
1.6
1.4
1.05
1.53
1.2
0.90
1.09
1.0
0.75
0.87
0.75
0.60
0.56
0.55
0.47
0.4
0.39
0.36
0.2
0.21
0.22
0.02
0.02
0.03
0.36†
0.4
0.5
1.18
1.12
0.98
1.08
1.02
0.90
0.93
0.9
0.80
0.78
0.79
0.73
0.67
0.66
0.62
0.55
0.53
0.52
0.47
0.43
0.415
0.60
0.335
0.32
0.30
0.215
0.21
0.04
0.04
0.05
0.6
0.64†
0.7
0.87
0.84
0.81
0.80
0.78
0.75
0.74
0.68
0.71
0.68
0.66
0.66
0.59
0.58
0.58
0.51
0.49
0.50
0.405
0.43
0.40
0.305
0.31
0.30
0.20
0.19
0.17
0.05
0.05
0.05
0.8
1.00†
0.78
0.74
0.74
0.72
0.70
0.70
0.65
0.64
0.58
0.58
0.50
0.49
0.40
0.41
0.30
0.30
0.14
0.19
0.06
0.07
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.64 90° tees, converging flow: values for the branch factor ζ b-c; for 1 × 105 < Re < 2 × 105 (derived from
the European Programme Report(1) and Koch(38))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
40
15
6.5
3.3
69
25
10.5
5.0
100
42
16
7.5
2.0
1.3
0.73
3.3
2.0
1.3
5.1
3.0
2.0
10.4
6.1
2.8
15.5
9.6
4.0
0.7
0.8
0.9
1.0
180
80
30.4
15
230
102
39.7
19
283
125
49.4
24
12.2
8.0
4.8
14.7
10
6.0
39
23
8.2
46.7
30
9.8
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
1.5
1.0
0.10
0
10
3.5
1.0
0.50
0.25*
0.30
0.3906*
0
0.10
–0.20
0.43
0.30
0
22
7.5
3.3
1.8
1.1
0.70
0.30
140
60
22.6
11
7.2
4.4
2.85
9.5
6.1
3.76
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.05
0.40
0.40
1.2
0.85
0.30
3.24
2.0
0.90
6.1
3.5
1.8
22.5
13
5.2
30.3
17
6.8
0.36†
0.4
0.5
0
–0.20
0
0.21
0.17
0.13
0.65
0.55
0.40
1.20
1.0
0.78
1.91
1.6
1.15
2.83
2.3
1.6
3.89
3.2
2.3
5.22
4.35
3.0
6.61
5.2
3.8
7.74
6.3
4.5
0.6
0.64†
0.7
0
–0.12
–0.10
0.85
0.07
0.05
0.30
0.27
0.25
0.61
0.55
0.50
0.9
0.82
0.72
1.2
1.10
1.0
1.7
1.43
1.3
2.2
1.87
1.7
2.6
2.26
2.0
3.0
2.61
2.3
0.8
1.00†
0
–0.59
0.05
-0.24
0.20
0.15
0.42
0.36
0.63
0.56
0.9
0.76
1.2
0.95
1.5
1.07
1.72
1.19
1.93
1.26
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.65 90° tees, diverging flow; values for the straight factor ζ c-s (derived
from the European Programme Report(1) and Koch(38))
Diam. dc ,
(= ds) / mm
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
0.03
0.11
250
0.24
0.20
0.14
0.08
0.04
0.01 –0.01
400
0.29
0.22
0.15
0.09
0.04
0.01 –0.01 –0.03 –0.02
0
Flow of fluids in pipes and ducts
4-35
Table 4.66 90° tees, diverging flow: values for the branch factor ζ c-b (derived from the European Programme
Report(1) and Koch(38))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
2.0
1.5
1.25
1.1
3.0
1.8
1.3
1.2
3.6
2.4
1.7
1.4
4.2
3.0
2.2
1.65
4.5
3.4
2.7
2.0
6.0
4.5
3.4
2.3
9.0
6.0
4.3
2.7
12.0
8.1
5.4
3.3
16
10.4
6.6
3.75
21
12.5
7.8
4.5
0.25*
0.30
0.3906*
1.08
1.05
0.99
1.2
1.1
0.99
1.3
1.18
1.0
1.4
1.25
1.02
1.65
1.37
1.05
1.75
1.48
1.1
2.0
1.6
1.18
2.3
1.8
1.3
2.65
2.05
1.45
3.1
2.4
1.6
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
1.6
1.45
1.25
2.3
2.0
1.5
3.0
2.5
1.8
4.0
3.3
2.2
5.7
4.4
2.7
7.9
6.5
3.3
10
7.6
4.1
13
9.0
5.0
16.8
10.5
6.0
21.5
14
7.0
0.36†
0.4
0.5
1.18
1.14
1.06
1.3
1.2
1.05
1.48
1.35
1.15
1.8
1.6
1.2
2.16
1.9
1.4
2.6
2.2
1.7
3.1
2.6
1.9
3.7
3.1
2.2
4.4
3.8
2.5
5.0
4.4
3.0
0.6
0.64†
0.7
1.01
1.0
0.98
1.01
1.0
0.98
1.05
1.0
0.98
1.04
1.0
0.98
1.15
1.1
1.05
1.3
1.2
1.1
1.5
1.35
1.2
1.65
1.5
1.3
1.8
1.7
1.5
2.2
2.0
1.7
0.8
1.00†
0.97
0.97
0.97
0.95
0.97
0.95
0.97
0.95
1.0
0.95
1.0
0.95
1.1
1.0
1.15
1.08
1.3
1.15
1.4
1.24
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
4.11.2.16
For the straight factor, ζ s-c ,:
Angle branch tees (HVCA 138)
(a) Converging flows
Ab
qb
cb
As
qs
cs
—
for β = 60°, use Table 4.77
—
for β = 45°, use Table 4.79
—
for β = 30°, use Table 4.81
—
for β = 15°, use Table 4.83.
Δp = ζ 1/2 ρ cc2
For the branch factor, see Table 4.67.
β
(b) Diverging flows
Ac
qc
cc
Ac
qc
cc
There are few data available for this simple component.
Ab
qb
cb
β
For the straight factor ζ s-c , the values given in section
4.11.2.21 may be used. These data are for an angle tee with
a bend on the branch, but the bend on the branch is not
expected to greatly affect the values of the straight factor.
Table 4.67 Angle branch tee, converging flow: values for branch factor
ζ b–c (derived from SMACNA(40) and partially confirmed by CETIAT(39))
Ratio,
Ab / Ac
0.1
0.2
0.3
0.4
0.6
0.8
1
Relative branch flow, qb / qc
0.1 0.2
0.22 3.1
–0.37 0.31
— –0.12
— –0.21
—
—
—
—
—
—
As
qs
cs
For the straight factor, ζ s-c , the values in section 4.11.2.22
may be used. These data are for an angle tee with a bend
on the branch, but the bend on the branch is not expected
to greatly affect the values of the straight factor.
For the straight factor:
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
8
1.5
0.38
0.08
—
3.2
1.11
0.44
—
5.3
2.1
1.02
—
—
3.2
1.6
—
—
4.6
2.4
—
—
6.2
3.2
—
—
8
4.3
—
—
—
5.4
–0.09
—
—
0.07
0.02
0.05
0.28
0.13
0.11
0.53
0.26
0.18
0.93
0.43
0.28
1.3
0.62
0.4
1.7
0.9
0.53
2.2
1.1
0.69
—
for β = 60°, use Table 4.85
—
for β = 45°, use Table 4.87
—
for β = 30°, use Table 4.89
—
for β = 15°, use Table 4.91.
See Table 4.68 for the branch factor ζ c-b.
4-36
Reference data
Table 4.68 Angle branch tee, diverging flow: values for branch factor
ζ c-b (derived from SMACNA(40))
Angle,
α
30°
45°
60°
Ratio,
Ab /Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.1
0.2
0.4
0.6
0.8
0.28
0.4
0.59
0.69
0.75
1.5
0.26
0.33
0.46
0.55
—
0.58
0.21
0.31
0.4
—
1.3
0.20
0.21
0.28
0.1
0.2
0.4
0.6
0.8
0.6
0.56
0.66
0.74
0.78
2.1
0.56
0.47
0.56
0.62
—
1
0.4
0.44
0.49
— — — — — —
1.8
— — — — —
0.43 0.54 0.69 0.95 1.3 1.7
0.37 0.35 0.36 0.43 0.54 0.68
0.4 0.34 0.31 0.32 0.35 0.4
0.1
0.2
0.4
0.6
0.8
1
0.77
0.76
0.81
0.83
2.9
0.96
0.65
0.68
0.71
—
1.6
0.65
0.6
0.62
— — — — — —
2.5
— — — — —
0.74 0.89 1.1 1.4 1.8 2.3
0.58 0.58 0.61 0.72 0.87 1.1
0.56 0.52 0.50 0.53 0.60 0.68
0.5
0.6
0.7
0.8
0.9
— — — — —
2.5
— — — —
0.27 0.40 0.62 0.92 1.3
0.17 0.16 0.2 0.28 0.39
0.21 0.16 0.15 0.16 0.19
Table 4.69 90° tees with expansion taper, converging flow: values for the
straight factor ζ s-c; for Rec = 2 × 105 and correction for Reynolds number
(derived from the European Programme Report(1))
Taper
angle, γ
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2.7
3.8
4.3
1.4
2.2
2.8
2.8
3.4
3.8
1.7
2.2
2.5
3.0
3.9
4.6
1.4
2.1
2.8
2.6
3.4
3.7
1.4
1.9
2.3
(a) Equal tees: 250/250/250 mm with expansion to 400 mm
30°
60°
90°
5.4
7.4
8.0
5.4
7.2
8.0
5.2
7.1
7.9
5.0
6.9
7.7
4.8
6.5
7.2
4.4
5.8
6.4
3.7
4.9
5.5
(b) Equal tees: 160/160/160 mm with expansion to 250 mm
30°
60°
90°
5.0
6.1
7.0
5.0
6.1
6.9
5.0
6.0
6.8
4.9
5.9
6.6
4.8
5.7
6.2
4.5
5.3
5.7
3.8
4.4
4.8
(c) Unequal tees: 250/200/250 mm with expansion to 400 mm
30°
60°
90°
5.0
6.6
7.6
5.5
7.2
8.1
5.8
7.4
8.3
5.8
7.4
8.2
5.4
7.0
7.8
5.0
6.4
7.0
4.2
5.3
6.0
(d) Unequal tees: 160/100/160 mm with expansion to 250 mm
4.11.2.17
90° tees, with enlargement taper for
combined flow; converging flow
γ
5.6
6.3
7.5
Diam.
/ mm
Δp = ζ 1/2 ρ cc2
As
qs
cs
30°
60°
90°
Ac
qc
cc
Ab
qb
cb
See Tables 4.69 and 4.70. Unusually these tables show
lower values of ζ for the smaller tee than for the larger,
even when taking into account the slightly different
enlargement ratios. The two sizes were investigated by
different research establishments. The data for the smaller
size was contributed to the European Programme(1) by the
National Engineering Laboratory (NEL) whose results
were frequently found to give lower values than those of
other contributors where a component had also been
tested by another contributor. There is thus a strong
possibility that the values listed below, for the smaller tee,
may be on the low side.
5.6
6.3
7.5
5.3
6.3
7.2
5.0
6.2
6.8
4.6
5.8
6.4
4.0
5.2
5.7
3.4
4.4
4.8
Correction factor for stated Reynolds number, Rec
0.8 × 105
250/250
160/160
160/100
1.0 × 105
1.06
1.06
1.5 × 105
2.0 × 105
2.5 × 105
1.05
1.03
1.0
1.06
1.03
1.0
No correction required
0.94
0.95
Note: area ratios as follows:
(a) Ab / Ac = 1.0, Ac / As = 2.56
(b) Ab / Ac = 1.0, Ac / As = 2.44
(c) Ab / Ac = 0.64, Ac / As = 2.56
(d) Ab / Ac = 0.391, Ac / As = 2.44
Figures in italics were obtained by extrapolation
Table 4.70 90° tees with expansion taper, converging flow: values for the
branch factor ζ b-c; for Rec = 2 × 105 and correction for Reynolds number
(derived from the European Programme Report(1))
Angle, γ
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
8.2
10.2
10.6
8.8
10.7
11.0
8.2
9.2
9.8
8.8
9.6
10.0
—
—
—
—
—
—
(a) Equal tees: 250/250/250 mm with expansion to 400 mm
30°
60°
90°
–1.5
0.0
1.0
0.4
1.4
2.4
2.0
3.0
3.9
3.3
4.5
5.2
4.8
5.8
6.6
5.8
7.4
8.0
6.8
8.7
9.4
7.6
9.5
10.0
(b) Equal tees: 160/160/160 mm with expansion to 250 mm
30°
60°
90°
–1.0
–0.4
–0.1
0.5
1.2
1.5
2.0
2.8
3.5
3.6
4.4
5.0
4.8
5.8
6.5
5.9
6.9
7.6
6.7
7.7
8.5
7.6
8.5
9.3
(c) Unequal tees: 250/200/250 mm with expansion to 400 mm
30°
60°
90°
Diam.
/ mm
250/250
160/160
0.2
1.0
1.2
1.8
2.9
3.2
3.4
4.6
5.3
5.0
6.4
7.2
6.8
8.2
9.2
8.4
10
11
10
12
13
11.7
14
15
Correction factor for stated Reynolds number, Rec
0.8 × 105
1.0 × 105
1.5 × 105
1.24
1.16
1.11
1.12
1.05
1.05
Note: area ratios as follows:
(a) Ab / Ac = 1.0, Ac / As = 2.56
(b) Ab / Ac = 1.0, Ac / As = 2.44
(c) Ab / Ac = 0.64, Ac / As = 2.56
Figures in italics were obtained by extrapolation
2.0 × 105
1
1
2.5 × 105
0.92
0.96
Flow of fluids in pipes and ducts
4.11.2.18
4-37
90° tees, with contraction taper for
combined flow; diverging
Δp = ζ 1/2 ρ cc2
Ac
qc
cc
As
qs
cs
γ
Ab
qb
cb
See Tables 4.71 and 4.72.
Table 4.71 90° tees with contraction taper, diverging flow: values for the
straight factor ζ c-s; for Rec = 2 × 105 and correction for Reynolds number
(derived from the European Programme Report(1))
Table 4.72 90° tees with contraction taper, diverging flow: values for the
branch factor ζ c-b; for Rec = 2 × 105 (derived from the European
Programme Report(1)) and correction for Reynolds number
Taper
angle, γ
1.0
Taper
angle, γ
0.50
30–90°
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(a) For dc = 400 mm; db = 250 mm; ds = 250 mm (Ac / As = 1.6)
30–90°
2.1
1.4
1.0
0.60
0.40
0.20
0.20
1.9
Type
/mm
Equal
Unequal
1.4
0.95
0.63
0.43
0.28
0.20
1.07
4.11.2.19
1.0 × 105
1.5 × 105
2.0 × 105
1.05
1.03
1
No correction required
0.27
0.42
2.5 × 105
0.94
Angle branch tees, with enlargement
taper for combined flow; converging
Ac
qc
cc
γ
30–90°
Type
/mm
Equal
Unequal
0.4
0.5
0.6
0.7
0.8
0.9
1.0
6.1
6.0
5.8
5.6
5.6
5.7
5.9
6.1
6.3
6.7
6.9
7.0
7.8
8.4
9.1
9.9
Correction factor for stated Reynolds number, Rec
0.8 × 105
1.0 × 105
1.03
1.5 × 105
2.0 × 105
2.5 × 105
1.01
1.0
1.0
No correction required
1.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
30°
30°
60°
90°
0.8
1.6
2.5
1.7
2.6
3.4
2.4
3.4
4.2
3.0
3.9
4.5
3.4
4.1
4.5
3.5
4.1
4.4
3.4
3.9
4.2
2.8 1.8
3.45 2.7
3.8 3.3
45°
30°
60°
90°
2.5
4.2
4.6
3.2
4.9
5.2
3.6
5.2
5.6
3.9
5.4
5.8
3.9
5.2
5.7
3.7
4.9
5.4
3.3
4.3
4.9
2.6
3.4
4.1
1.8
2.3
2.9
60°
30°
60°
90°
5.8
7.0
7.2
6.8
7.7
8.0
7.0
8.2
8.3
7.1
8.1
8.4
6.8
7.8
8.0
6.1
7.0
7.3
5.0
5.8
6.2
3.6
4.2
4.8
1.7
2.3
2.9
See Tables 4.73 and 4.74.
Data for the variation of ζ with Reynolds number were
available only for full straight flow and full branch flow.
The variation was sometimes found to be significant, so
values of the correction factor CRe are given in the tables.
However, analysis for 90° tees(38) has shown that this is not
necessarily an indication of what will occur for other flow
rates.
6.8
Taper
angle, γ
β
Ab
qb
cb
7.0
Table 4.73 Angle tees with expansion taper, converging flow: values for
the straight factor ζ s-c; for Rec = 2 × 105 and correction for Reynolds
number (derived from the European Programme Report(1))
Branch
angle, β
Δp = ζ 1/2 ρ cc2
As
qs
cs
0.3
(b) For dc = 400 mm; db = 200 mm; ds = 250 mm (Ac / As = 1.6)
Correction factor for stated Reynolds number, Rec
0.8 × 105
0.2
(a) For dc = 400 mm; db = 250 mm; ds = 250 mm (Ac / As = 1.6)
0.30
(b) For dc = 400 mm; db = 200 mm; ds = 250 mm (Ac / As = 1.6)
30–90°
Relative branch flow, qb / qc
Branch
angle, β
Relative straight flow, qs / qc
Taper
angle, γ
1.0
Correction factor for stated
Reynolds number, Rec
0.8 × 105 1.0 × 105 1.5 × 105 2.0 × 105 2.5 × 105
30°
30°
60°
90°
1.02
1.15
1.11
1.01
1.10
1.05
1.00
1.01
1.00
1.00
1.00
1.00
1.00
1.03
1.01
45°
30–90°
1.02
1.01
1.01
1.00
0.99
60°
30–90°
No correction required
Note: using a size of ds = db = 250 mm, dc = 400 mm (Ac / As = 2.56).
The figures in italics are extrapolations.
4-38
Reference data
Table 4.74 Angle tees with expansion taper, converging flow: values for
the branch factor ζ b-c; for Rec = 2 × 105 and correction for Reynolds
number (derived from the European Programme Report(1))
Branch
angle, β
Taper
angle, γ
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
30°
30°
60°
90°
–0.4
0
–0.2
1.0
1.5
1.6
2.1
2.7
3.0
3.0
3.8
4.2
3.8
4.7
6.3
4.4
5.4
6.1
4.9
6.0
6.6
5.15 5.4
6.35 6.4
6.9 6.9
45°
30°
60°
90°
–1.0
0.3
0.9
1.2
2.4
2.8
2.7
4.0
4.5
4.0
5.6
5.9
5.0
6.6
7.1
5.8
7.6
7.9
6.2
8.0
8.6
6.4
8.1
9.0
60°
30°
60°
90°
1.9
3.0
3.0
3.8
5.0
5.0
5.5
6.6
6.7
6.9
7.9
9.0
8.0 8.8 9.4 9.7 9.6
9.2 10.1 11.0 11.4 11.5
9.2 10.5 11.2 11.8 12.2
Branch
angle, β
Relative branch flow, qb / qc
Taper
angle, γ
1.0
6.3
8.0
9.1
Correction factor for stated
Reynolds number, Rec
0.8 × 105 1.0 × 105 1.5 × 105 2.0 × 105 2.5 × 105
30°
30°
60°
90°
1.13
1.22
1.26
1.10
1.14
1.14
1.01
0.99
0.99
1.00
1.00
1.00
1.00
1.01
1.01
45°
30–90°
1.07
1.04
1.02
1.00
0.99
60°
30–90°
No correction required
Note: using a size of ds = db = 250 mm, dc = 400 mm (Ac / As = 2.56).
Figures in italics were obtained by extrapolation
4.11.2.20
Angle branch tees, with contraction
taper for combined flow; diverging
Δp = ζ 1/2 ρ cc2
Ac
qc
cc
As
qs
cs
γ
β
Ab
qb
cb
See Tables 4.75 and 4.76.
Table 4.75 Angle tees with contraction taper, diverging flow: values for
the straight factor ζ c-s (derived from the European Programme Report(1))
Branch
angle, β
Taper
angle, γ
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Equal tees: using dc = 400 mm; ds = db = 250 mm (Ac / As = 2.56)
Table 4.76 Angle tees with contraction taper, diverging flow: values for
the branch factor ζ c-b (derived from the European Programme Report(1))
30–60°
90°
1.85 1.26 0.85 0.55 0.43 0.38 0.49 0.70 1.02
1.85 1.30 0.85 0.56 0.45 0.40 0.55 0.81 1.18
Branch
angle, β
45°
30–90°
1.96 1.43 1.02 0.68 0.46 0.33 0.37 0.45 0.66
(a) Equal tees: using dc = 400 mm; ds = db = 250 mm (Ac / As = 2.56)
60°
30°
60–90°
2.10 1.50 1.00 0.60 0.40 0.20 0.10 0.15 0.30
2.15 1.51 1.15 0.65 0.40 0.23 0.15 0.30 0.40
30°
45°
60°
30°
(b) Unequal tees: using dc = 400 mm; ds = 250 mm, db = 200 mm
(Ac / As = 2.56)
30°
30–90°
1.78 1.33 0.98 0.70 0.51 0.44 0.43 0.53 0.70
45°
30–90°
2.02 1.47 1.07 0.73 0.50 0.36 0.32 0.40 0.56
60°
30–90°
1.94 1.41 0.97 0.61 0.39 0.24 0.21 0.29 0.48
Note: figures in italics were obtained by extrapolation
Taper
angle, γ
30–60°
30–90°
30–90°
Relative branch flow, qb / qc
0.2
5.6
5.9
6.3
0.3
4.4
4.8
5.6
0.4
3.5
3.9
5.0
0.5
2.8
3.2
4.4
0.6
2.4
2.8
4.0
0.7
2.3
2.5
3.8
0.8
2.3
2.5
3.8
0.9
2.7
2.7
3.9
1.0
3.2
3.1
4.1
(b) Unequal tees: using dc = 400 mm; ds = 250 mm, db = 200 mm
(Ac / As = 2.56)
30°
45°
60°
30–90°
30–90°
30–90°
4.5
5.1
6.4
3.1
3.8
5.2
2.2
3.0
4.4
1.9
2.6
4.0
2.0
2.6
3.8
2.6
3.0
4.0
Note: figures in italics were obtained by extrapolation
3.7
4.0
4.6
5.4
5.2
5.5
7.0
6.8
6.5
Flow of fluids in pipes and ducts
4.11.2.21
4-39
Angle branch tees, with bend
on branch; converging flows
Δp = ζ 1/2 ρ cc2
As
qs
cs
Ac
qc
cc
β
α
Ab
qb
cb
All branch and bend pieces in same
plane, always giving: α + β = 90°
See Tables 4.77 to 4.84.
Table 4.77 Angle tee‚ branch angle β = 60°, with bend on branch, α = 30°, converging flow: values for the
straight factor ζ s-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
0.25*
0.30
0.3906*
0.4
–12
–7.5
–4.5
–2.4
–1.7
–1.4
–1.07
–1.04
–9.2
–5.5
–3.4
–1.6
–6.9
–4.0
–2.5
–1.1
–5.0
–2.8
–1.76
–0.75
–3.3
–1.9
–1.04
–0.50
–1.8
–1.1
–0.5
–0.30
–0.8
–0.4
–0.2
–0.12
–0.3
–0.1
0
–0.05
–0.05
–0.04
0.05
–0.06
0
0
0
0
–1.1
–0.90
–0.64
–0.61
–0.75
–0.60
–0.43
–0.41
–0.50
–0.40
–0.23
–0.21
–0.35
–0.25
–0.10
–0.08
–0.20
–0.11
0
0.01
–0.06
0
0.09
0.10
0.07
0.08
0.10
0.10
0.06
0.09
0.08
0.08
0
0
0
0
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–3.0
–2.5
–1.6
–1.16
–2.3
–1.8
–1.1
–0.82
–1.65
–1.32
–0.80
–0.53
–1.15
–0.90
–0.48
–0.27
–0.75
–0.54
–0.25
–0.13
–0.35
–0.26
–0.1
0
–0.15
–0.10
0
0.07
–0.03
–0.02
0.02
0.05
0
0.01
0.03
0.04
0.03
0.03
0.04
0.04
0.4
0.5
0.6
0.64†
–0.96
–0.58
–0.40
–0.34
–0.66
–0.40
–0.23
–0.18
–0.40
–0.22
–0.10
–0.04
–0.17
–0.03
–0.08
0.12
–0.05
0.10
0.20
0.23
0.05
0.18
0.27
0.29
0.10
0.21
0.29
0.30
0.08
0.16
0.22
0.24
0.06
0.11
0.15
0.16
0.05
0.05
0.06
0.06
0.8
1.00†
–0.23
–0.12
–0.07
0.04
0.07
0.18
0.20
0.28
0.29
0.34
0.32
0.36
0.32
0.34
0.26
0.28
0.18
0.20
0.07
0.08
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
4-40
Reference data
Table 4.78 Angle tee‚ branch angle β = 60°, with bend on branch, α = 30°, converging flow: values for the
branch factor ζ b-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
70
30
9.0
3.8
108
43
15
6.0
155
60
23
9.5
2.2
1.3
0.60
0.60
3.6
2.2
1.1
1.0
5.6
3.5
1.8
1.7
8.1
5.1
2.6
2.4
11
7.0
3.5
3.3
14
9.0
4.6
4.3
18
11
5.9
5.6
11.0
7.5
3.0
1.8
16.0
11.2
4.6
2.8
22
16
6.5
3.9
29
21
9
5.3
37
26
12
7.0
45
32
15
9.6
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
5.0
3.3
2.0
0.50
0.25*
0.30
0.3906*
0.4
–0.20
–0.30
–0.20
–0.18
20
8.0
3.0
1.0
0.30
0.10
0
0
40
17
5.0
2.1
1.1
0.60
0.25
0.22
210
84
32
14
276
110
42
19
350
140
52
24
430
180
65
30
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–2.0
–1.5
–0.80
–0.50
0.01
0
0
0
3.3
2.0
1.0
0.54
6.5
4.5
1.8
1.1
0.4
0.5
0.6
0.64†
–0.40
0.22
–0.14
–0.10
0
0
0
0
0.35
0.20
0.15
0.14
0.8
0.52
0.40
0.36
1.35
0.85
0.62
0.56
2.1
1.25
0.85
0.77
2.9
1.7
1.15
1.06
3.8
2.3
1.5
1.33
5.0
3.0
1.9
1.67
7.0
4.0
2.4
2.0
0.8
1.00†
–0.18
–0.40
0.10
0
0.25
0.16
0.40
0.32
0.55
0.46
0.70
0.56
0.90
0.64
1.1
0.73
1.2
0.80
–0.05
–0.20
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.79 Angle tee‚ branch angle β = 45°, with bend on branch, α = 45°, converging flow: values for the
straight factor ζ s-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
–16
–10.5
–6.6
–3.7
–12
–8.0
5.0
–2.8
–8.8
–6.0
–3.8
–2.1
–6.0
–4.1
–2.6
–1.5
–3.9
–2.5
–1.7
–1.0
–2.0
–1.4
–1.0
–0.6
–1.0
–0.7
–0.5
–0.3
–0.5
–0.35
0.2
–0.1
–0.2
–0.08
0
0
0
0
0
0
0.25*
0.30
0.3906*
0.4
–2.6
–2.3
–2.1
–2.0
–2.1
–1.8
–1.5
–1.4
–1.5
–1.2
–1.0
–0.98
–1.1
–0.85
–0.61
–0.59
–0.7
–0.5
–0.29
–0.27
–0.4
–0.25
–0.10
–0.08
–0.2
–0.1
0
–0.01
–0.05
0.01
0.07
0.08
0
0.03
0.06
0.06
0
0
0
0
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–4.6
–3.8
–2.5
–2.1
–3.7
–3.0
–1.9
–1.5
–2.8
–2.2
–1.4
–1.05
–2.0
–1.6
–0.90
–0.68
–1.4
–1.05
–0.55
–0.39
–0.90
–0.65
–0.28
–0.16
–0.44
–0.30
–0.10
0
–0.15
–0.09
0
0.05
–0.02
0.01
0.03
0.05
0.03
0.03
0.04
0.04
0.4
0.5
0.6
0.64†
–1.8
–1.4
–1.0
–0.92
–1.3
–0.95
–0.70
–0.61
–0.90
–0.60
–0.42
–0.36
–0.55
–0.32
–0.18
–0.12
–0.32
–0.10
0
0.04
–0.10
0.02
0.10
0.15
0.04
0.12
0.20
0.22
0.07
0.12
0.17
0.20
0.06
0.09
0.11
0.13
0.04
0.05
0.06
0.06
0.8
1.00†
–0.65
–0.46
–0.40
–0.24
–0.18
–0.04
0
0.11
0.14
0.22
0.22
0.28
0.26
0.28
0.23
0.25
0.16
0.18
0.07
0.09
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Flow of fluids in pipes and ducts
4-41
Table 4.80 Angle tee‚ branch angle β = 45°, with bend on branch, α = 45°, converging flow: values for the
branch factor ζ b-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
62
26
9.3
3.7
99
40
15
6.4
144
55
22
9.7
2.2
1.4
0.5
0.4
3.8
2.3
1.0
0.9
5.5
3.6
1.7
1.5
7.7
5
2.5
2.3
10
6.8
3.4
3.1
13
9.0
4.4
4.0
17
12
5.5
5.2
13
7.5
3.0
1.7
18
11
4.5
2.5
24
16
6.0
3.4
31
21
8.0
4.6
39
27
11
5.9
49
34
15
7.4
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
17
5.0
1.0
–0.50
23
8.0
2.0
0.35
0.25*
0.30
0.3906*
0.4
–0.70
–0.60
–0.25
–0.18
0
–0.1
–0.06
0
35
15
4.6
1.9
1.0
0.60
0.20
0.18
193
72
30
13
248
95
39
17
310
120
51
22
380
150
70
30
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–1.0
–0.50
–0.05
0
0.80
0.60
0.30
0.20
4.0
2.5
1.0
0.50
8.0
4.5
1.8
1.0
0.4
0.5
0.6
0.64†
0
0.
0
–0.05
0.15
0.05
0
–0.04
0.35
0.15
0.06
0.03
0.80
0.44
0.24
0.20
1.3
0.75
0.50
0.45
1.9
1.2
0.83
0.76
2.8
1.7
1.2
1.0
3.7
2.3
1.5
1.2
4.5
2.8
1.7
1.4
5.0
3.0
1.8
1.6
0.8
1.00†
–0.12
–0.25
–0.08
–0.18
0
–0.17
0.16
0.10
0.40
0.22
0.50
0.32
0.60
0.40
0.70
0.46
0.85
0.51
1.0
0.56
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.81 Angle tee‚ branch angle β = 30°, with bend on branch, α = 60°, converging flow: values for the
straight factor ζ s-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
–19
–13.5
–8.5
–5.5
–15
–10.5
–6.7
–4.3
–11
–8.0
–5.0
–3.2
–7.5
–5.5
–3.6
–2.3
–4.7
–3.3
–2.3
–1.5
–2.5
–1.6
–1.1
–0.75
–0.9
–0.7
–0.5
–0.3
–0.2
–0.12
–0.10
–0.09
0
–0.05
–0.07
–0.06
0
0
0
0
0.25*
0.30
0.3906*
0.4
–4.4
–3.6
–2.8
–2.7
–3.4
–2.7
–2.1
–2.0
–2.5
–2.0
–1.5
–1.4
–1.8
–1.40
–0.97
–0.93
–1.1
–0.80
–0.52
–0.49
–0.54
–0.37
–0.20
0.18
–0.18
–0.11
–0.05
0.04
–0.07
–0.04
0
0
–0.05
0.02
0
0
0
0
0
0
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–7.0
–5.7
–3.9
–3.1
–5.0
–4.2
–2.8
–2.3
–3.6
–2.9
–2.0
–1.6
–2.6
–2.1
–1.4
–1.0
–1.8
–1.4
–0.83
–0.59
–1.05
–0.80
–0.38
–0.25
–0.56
–0.37
–0.09
0
–0.20
–0.14
–0.04
0.02
0
0.01
0.02
0.04
0.05
0.05
0.06
0.06
0.4
0.5
0.6
0.64†
–2.8
–2.1
–1.6
–1.4
–2.0
–1.5
–1.1
–0.98
–1.4
–1.0
–0.70
–0.60
–0.90
–0.60
–0.40
–0.33
–0.50
–0.27
–0.12
–0.08
–0.19
–0.06
0.02
0.05
0.03
0.11
0.16
0.17
0.04
0.13
0.19
0.20
0.06
0.09
0.14
0.15
0.06
0.06
0.07
0.07
0.8
1.00†
–1.0
–0.8
–0.70
–0.50
–0.04
–0.25
–0.15
–0.05
0.04
0.11
0.12
0.18
0.21
0.23
0.24
0.25
0.19
0.20
0.09
0.12
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
4-42
Reference data
Table 4.82 Angle tee‚ branch angle β = 30°, with bend on branch, α = 60°, converging flow: values for the
branch factor ζ b-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
65
25
10
5.0
98
37
16
8.0
0.6
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
7.0
1.5
–0.20
–0.35
20
8
2.0
0.45
0.25*
0.30
0.3906*
0.4
–0.4
–0.45
–0.47
–0.47
0.2
0.10
–0.12
–0.13
40
15
6.0
2.6
1.1
0.60
0.28
0.25
140
50
23
11
2.3
1.2
0.77
0.75
3.8
1.8
1.3
1.3
5.6
2.6
2.0
1.9
12
7.8
2.9
1.7
17
10.5
4.0
2.4
190
88
31
15
7.7
3.6
2.65
2.6
250
87
40
19
320
110
50
24
400
140
60
28
10
4.8
3.45
3.4
13
6.5
4.35
4.3
16
8.7
5.4
5.1
30
19
7.0
4.2
38
24
9.3
5.3
47
30
12
6.4
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–1.0
–0.80
–0.50
–0.40
1.0
0.70
0.20
0
4.1
2.5
0.85
0.50
7.7
5.0
1.85
1.1
23
14
5.4
3.2
0.4
0.5
0.6
0.64†
–0.38
–0.43
–0.46
–0.48
–0.08
–0.18
–0.23
–0.24
0.37
0.18
0.05
0
0.85
0.47
0.30
0.25
1.35
0.80
0.55
0.48
1.9
1.2
0.80
0.71
2.6
1.65
1.05
0.92
3.4
2.1
1.3
1.1
4.2
2.5
1.5
1.3
4.8
2.9
1.7
1.5
0.8
1.00†
–0.54
–0.56
–0.30
–0.35
–0.08
–0.16
0.11
0
0.26
0.15
0.40
0.27
0.55
0.37
0.65
0.42
0.75
0.45
0.85
0.46
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.83 Angle tee‚ branch angle β = 15°, with bend on branch, α = 75°, converging flow: values for the
straight factor ζ s-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative straight flow, qs / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
–11
–6.5
–4.2
–2.7
–7.1
–4.3
–2.9
–1.8
–4.0
–2.6
–1.7
–0.90
–2.0
–1.25
–0.70
–0.30
–0.8
–0.45
–0.20
–0.13
–0.3
–0.17
–0.05
–0.04
0
0
0
0
–2.0
–1.5
–1.05
–1.00
–1.2
–0.90
–0.60
–0.57
–0.60
–0.40
–0.20
–0.18
–0.18
–0.10
–0.05
–0.04
–0.07
–0.05
–0.03
–0.03
–0.04
–0.03
–0.02
–0.02
0
0
0
0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
–27
–17
–10.5
–7.0
–21
–12
–8.0
–5.3
0.25*
0.30
0.3906*
0.4
–5.3
–4.0
–3.1
–3.0
–4.1
–3.2
–2.3
–2.2
–16
–9
–6.0
–3.8
–2.9
–2.3
–1.65
–1.6
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
–9
–6.8
–4.3
–3.5
–7
–5.5
–3.3
–2.6
–5
–3.9
–2.3
–1.8
–3.1
–2.45
–1.5
–1.15
–1.75
–1.44
–0.85
–0.59
–1.0
–0.80
–0.37
–0.20
–0.46
–0.32
–0.09
0
–0.15
–0.10
0.01
0.06
–0.02
0.01
0.05
0.08
0.07
0.08
0.08
0.09
0.4
0.5
0.6
0.64†
–3.1
–2.3
–1.7
–1.5
–2.3
–1.64
–1.15
–1.03
–1.55
–1.05
–0.75
–0.66
–0.95
–0.60
–0.40
–0.33
–0.45
–0.25
–0.12
–0.08
–0.13
0
0.06
0.08
0.04
0.11
0.16
0.18
0.08
0.14
0.18
0.20
0.09
0.13
0.16
0.18
0.10
0.11
0.12
0.13
0.8
1.00†
–1.05
–0.76
–0.70
–0.49
–0.40
–0.26
–0.18
–0.06
0.04
0.10
0.13
0.19
0.22
0.24
0.24
0.26
0.23
0.25
0.16
0.20
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Flow of fluids in pipes and ducts
4-43
Table 4.84 Angle tee‚ branch angle β = 15°, with bend on branch, α = 75°, converging flow: values for the
branch factor ζ b-c (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0625*
0.1
0.1406*
0.20
20
5.0
–3.0
–1.0
35
15
0.20
0
55
20
4.2
1.7
78
27
9.0
4.0
108
35
14.5
6.5
146
47
21
9.5
192
65
28.5
13
0.25*
0.30
0.3906*
0.4
0.10
–0.20
–0.60
–0.62
0.60
0.20
–0.20
–0.22
1.3
0.80
0.30
0.28
2.4
1.5
0.80
0.70
3.9
2.3
1.3
1.2
5.6
3.3
1.9
1.8
7.6
4.4
2.5
2.4
9.8
5.5
3.1
3.0
12
7.0
3.8
3.6
14.5
9.0
4.5
4.0
0.16†
0.2
0.3
0.36†
–1.3
–1.1
–0.80
–0.7
1.4
0.80
0.10
0
4.6
3.0
1.0
0.52
8.6
5.0
2.0
1.2
13
7.0
3.0
1.9
18
9.0
4.0
2.7
25
11
5.0
3.5
32
14
6.3
4.4
41
18
8.0
5.3
50
24
10
6.3
0.4
0.5
0.6
0.64†
–0.65
0.55
–0.50
–0.50
–0.12
–0.15
–0.20
–0.20
0.38
0.22
0.13
0.10
1.0
0.65
0.43
0.35
1.6
1.05
0.69
0.60
2.2
1.5
1.0
0.88
2.9
1.9
1.3
1.1
3.7
2.3
1.6
1.3
4.5
2.8
1.8
1.5
5.1
3.2
2.0
1.7
0.8
1.00†
–0.50
–0.52
–0.25
–0.30
0
–0.11
0.15
0.06
0.32
0.19
0.50
0.28
0.62
0.36
0.80
0.44
0.90
0.49
1.0
0.52
247
90
37
17
0.9
1.0
310
120
46
21
380
150
57
25
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
4.11.2.22
Angle branch tees, with bend on
branch; diverging flow
Δp = ζ 1/2 ρ cc2
Ac
qc
cc
As
qs
cs
β
α
Ab
qb
cb
All branch and bend pieces in same
plane, always giving: α + β = 90°
See Tables 4.85 to 4.92.
Values of ζ are found to vary little with Reynolds number.
Values of the straight factors, ζ c-s , do not vary with Ab / Ac.
Table 4.85 Angle tee‚ branch angle β = 60°, with bend on branch,
α = 30°, diverging flow: values for the straight factor ζ c-s (derived from
the European Programme Report(1))
Diam. dc ,
(= ds) / mm
Relative straight flow, qs / qc
0.1
250*
0.26 0.20 0.14 0.09 0.04 0.02 0.00 0.02 0.05 0.12
400†
0.30 0.23 0.16 0.10 0.05 0.02 –0.01 –0.02 –0.01 0.01
0.2
0.3
0.4
0.5
* mean of values for 0.16 < Ab / Ac < 1.00
† mean of values for 0.062 < Ab / Ac < 0.39
0.6
0.7
0.8
0.9
1.0
4-44
Reference data
Table 4.86 Angle tee‚ branch angle β = 60°, with bend on branch, α = 30°, diverging flow: values for the branch
factor ζ c-b (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
30
14
6.0
2.5
46
24
9.6
4.0
65
33
14
6.0
88
44
20
8.8
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
0.48
0.48
0.48
0.48
6.0
3.0
0.90
0.55
0.25*
0.30
0.3906*
0.4
0.48
0.48
0.48
0.48
0.50
0.50
0.50
0.50
16
7.0
3.0
1.2
0.67
0.61
0.53
0.52
1.0
0.80
0.60
0.58
1.6
1.1
0.76
0.72
2.7
1.7
1.12
1.06
4.0
2.5
1.54
1.44
110
59
28
12
5.5
3.5
2.1
1.95
136
79
36
16
7.5
5.0
2.8
2.57
160
92
44
21
9.6
6.5
3.5
3.19
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
1
1
1
1
1.3
1.0
0.80
0.70
2.0
1.5
0.90
0.70
4.0
2.8
1.3
0.80
6.4
4.5
1.8
1.2
10.0
7
2.5
1.6
14.7
10.5
4.0
2.3
21
15
6.5
3.4
28
20
9
4.5
38
26
11
5.8
0.4
0.5
0.6
0.64†
1
1.05
1.09
1.10
0.70
0.80
0.89
0.90
0.68
0.69
0.75
0.76
0.72
0.67
0.65
0.65
1.0
0.75
0.65
0.64
1.3
0.90
0.68
0.65
1.8
1.15
0.81
0.76
2.4
1.5
1.05
0.95
3.5
2.0
1.35
1.2
4.5
2.9
1.85
1.6
0.8
1.00†
1.10
1.10
0.91
0.92
0.79
0.80
0.66
0.70
0.63
0.64
0.63
0.60
0.66
0.58
0.74
0.60
0.85
0.63
1.05
0.66
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.87 Angle tee‚ branch angle β = 45°, with bend on branch,
α = 45°, diverging flow: values for the straight factor ζ c-s (derived from
the European Programme Report(1))
Diam., dc
(= ds) / mm
0.1
Relative straight flow, qb / qc
250*
0.29 0.22 0.15 0.10 0.04 0.02 0
400†
0.28 0.21 0.14 0.09 0.04 0.01 –0.01 –0.03 –0.03 0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.02 0.05 0.13
* Mean of values for 0.16 < Ab / Ac < 1.00
† Mean of values for 0.062 < Ab / Ac < 0.39
Table 4.88 Angle tee‚ branch angle β = 45°, with bend on branch, α = 45°, diverging flow: values for the branch
factor ζ c-b (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
30
15
5.8
2.5
45
23
10
4.2
65
32
14.5
7.0
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
2.0
1.0
0.64
0.40
10
3.5
1.2
0.60
0.25*
0.30
0.3906*
0.4
0.30
0.30
0.50
–0.18
0.56
0.40
0.50
0
20
8.0
3.0
1.2
0.74
0.65
0.50
0.22
90
45
21
10
120
62
27
14
150
80
35
18
160
100
43
22
1.4
1.0
0.60
0.60
2.3
1.5
0.80
1.0
3.8
2.4
1.1
1.7
5.6
3.5
1.6
2.4
8.0
5.0
2.2
3.3
10.5
6.8
3.0
4.3
13.3
8.5
3.8
5.6
11
7.5
3.0
1.8
16
11
4.2
2.6
23
16
6.0
3.8
31
22
9.0
5.0
42
30
13
6.6
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
1.0
0.90
0.70
0.70
1.5
1.2
0.65
0.50
2.3
1.7
0.80
0.53
4.0
2.9
1.2
0.80
7.0
5.0
2.0
1.15
0.4
0.5
0.6
0.64†
0.72
0.80
0.88
0.90
0.51
0.59
0.67
0.70
0.49
0.51
0.57
0.60
0.70
0.55
0.51
0.50
0.90
0.60
0.45
0.42
1.35
0.85
0.55
0.50
2.0
1.2
0.75
0.65
2.9
1.8
1.1
0.90
3.9
2.5
1.6
1.3
5.0
3.2
2.0
1.7
0.8
1.00†
0.95
0.90
0.78
0.80
0.65
0.70
0.50
0.60
0.42
0.48
0.40
0.38
0.45
0.38
0.55
0.40
0.70
0.45
0.90
0.52
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Flow of fluids in pipes and ducts
4-45
Table 4.89 Angle tee‚ branch angle β = 30°, with bend on branch,
α = 60°, diverging flow: values for the straight factor ζ c-s (derived from
the European Programme Report(1))
Table 4.91 Angle tee‚ branch angle β = 15°, with bend on branch,
α = 75°, diverging flow: values for the straight factor ζ c-s (derived from
the European Programme Report(1))
Diam., dc
(= ds) / mm
0.1
Diam., dc
(= ds) / mm
0.1
250*
0.25 0.18 0.12 0.07 0.04 0.02 0.02 0.03 0.06 0.12
250*
0.23 0.17 0.11 0.06 0.02 0
400†
0.27 0.19 0.13 0.07 0.03 0
400†
0.24 0.17 0.11 0.06 0.02 0
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
–0.01 –0.02 –0.02 0
* Mean of values for 0.16 < Ab / Ac < 1.00
† Mean of values for 0.062 < Ab / Ac < 0.39
Relative straight flow, qs / qc
0.2
0.3
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
40
19
8.0
3.0
60
30
13
4.8
85
42
20
7.5
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
0.60
0.55
0.50
0.43
10
4.0
2.0
0.90
0.25*
0.30
0.3906*
0.4
0.40
0.37
0.35
0.35
0.55
0.48
0.40
0.39
24
10
4.0
1.8
0.90
0.60
0.50
0.49
110
60
28
11
138
80
37
16
170
100
47
21
200
120
58
27
1.5
0.90
0.70
0.69
2.5
1.5
1.0
0.97
4
2.3
1.6
1.5
6
3.5
2.3
2.2
8.2
5
3.1
3.0
11
7
4.0
3.8
15
9
4.9
4.6
15
10
4.0
2.3
22
14
5.6
3.2
30
20
8.0
4.7
40
29
11
6.3
54
38
15
8.0
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
1.5
1.0
0.50
0.30
2.0
1.4
0.55
0.30
2.8
2.0
0.70
0.41
5.6
3.8
1.5
0.80
9.6
6.5
2.7
1.4
0.4
0.5
0.6
0.64†
0.32
0.42
0.51
0.55
0.33
0.41
0.48
0.51
0.41
0.43
0.48
0.47
0.65
0.48
0.46
0.45
1.1
0.62
0.45
0.50
1.8
1.0
0.70
0.60
2.6
1.4
0.95
0.75
3.7
1.9
1.3
1.1
4.8
2.6
1.8
1.5
6.5
4.0
2.5
2.1
0.8
1.00†
0.75
1.0
0.64
0.82
0.54
0.63
0.47
0.50
0.40
0.39
0.49
0.34
0.50
0.34
0.60
0.40
0.80
0.50
1.3
0.61
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
Table 4.92 Angle tee‚ branch angle β = 15°, with bend on branch, α = 60°, diverging flow: values for the branch
factor ζ c-b (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
36
15
6.8
3.0
54
22
13
5.3
78
35
20
8.0
0.7
0.8
0.9
1.0
(a) Main duct size: ds = dc = 400 mm
0.0625*
0.1
0.1406*
0.20
2.0
0.80
0.50
0.32
12
5.0
1.6
0.60
0.25*
0.30
0.3906*
0.4
0.27
0.24
0.15
0.14
0.40
0.30
0.20
0.19
24
10
3.6
1.4
0.76
0.50
0.30
0.28
0.5
* Mean of values for 0.16 < Ab / Ac < 1.00
† Mean of values for 0.062 < Ab / Ac < 0.39
Table 4.90 Angle tee‚ branch angle β = 30°, with bend on branch, α = 60°, diverging flow: values for the branch
factor ζ c-b (derived from the European Programme Report(1))
Area ratio,
Ab / Ac
0.4
1.6
1.0
0.60
0.56
2.8
1.6
1.0
0.92
107
52
28
12
145
75
36
17
190
100
47
22
250
130
59
27
4.5
2.9
1.5
1.4
6.5
4.2
2.2
2.0
9.0
5.8
3.0
2.7
12
7.5
4.0
3.6
15
9.5
5.0
4.5
20
13
5.0
2.4
28
19
7.5
3.6
39
28
11
5.2
52
38
16
7.0
66
47
21
9.1
(b) Main duct size: ds = dc = 250 mm
0.16†
0.2
0.3
0.36†
1.4
1.0
0.55
0.30
2.0
1.5
0.60
0.30
3.9
2.5
0.78
0.37
7.6
5.0
1.5
0.80
12.5
8.5
3.0
1.4
0.4
0.5
0.6
0.64†
0.21
0.20
0.20
0.20
0.22
0.20
0.20
0.20
0.30
0.25
0.24
0.25
0.60
0.40
0.31
0.30
1.0
0.60
0.50
0.45
1.7
1.0
0.80
0.70
2.6
1.6
1.1
1.0
3.8
2.2
1.6
1.4
5.0
3.0
2.2
1.9
6.5
4.2
3.1
2.6
0.8
1.00†
0.41
0.68
0.30
0.50
0.29
0.35
0.28
0.26
0.27
0.20
0.40
0.19
0.60
0.23
0.85
0.36
1.2
0.50
1.7
0.65
* Values obtained using a main duct size: ds = dc = 400 mm; other values obtained by interpolation
† Values obtained using a main duct size: ds = dc = 250 mm; other values obtained by interpolation
0.6
0.7
0.8
0
0.02 0.05 0.11
0.9
1.0
–0.02 –0.02 –0.01 0.01
4-46
Reference data
4.11.2.23
Angle branch tees, with bend on
branch and expansion taper;
converging flow
Δp = ζ 1/2 ρ cc2
As
qs
cs
Ac
qc
cc
γ
β
α
Ab
qb
cb
See Tables 4.93 and 4.94.
Table 4.93 Angle tees with bend on branch and expansion taper,
converging flow: values for the straight factor ζ s-c (derived from the
European Programme Report(1))
Table 4.94 Angle tees with bend on branch and expansion taper,
converging flow: values for the branch factor ζ b-c (derived from the
European Programme Report(1))
Tee
angle, β
Tee
angle, β
Taper
angle, γ
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Equal tees: 250/250/250 mm with expansion to 400 mm
Taper
angle, γ
Relative branch flow, qb / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Equal tees: 250/250/250 mm with expansion to 400 mm
30°
30°
60–90°
—
—
0.9
1.7
1.9
2.7
2.7
3.5
3.3
4.0
3.6
4.3
3.5
4.2
3.0
3.7
1.8
2.8
30°
30°
60–90°
–0.2
0.4
1.0
1.5
1.9
2.5
2.7
3.5
3.5
4.3
4.1
5.0
4.6
5.6
5.0
6.2
5.3
6.6
45°
30°
60–90°*
—
—
1.9
3.9
2.5
4.5
2.9
4.9
3.3
4.9
3.4
4.7
3.2
4.3
2.6
3.5
1.6
2.4
45°
30°
60–90°
–0.4
0.2
0.9
1.9
2.0
3.4
3.0
4.7
3.9
5.8
4.6
6.6
5.2
7.1
5.5
7.4
5.7
7.3
60°
30°
60–90°
—
—
6.0
7.6
6.5
8.1
6.6
8.1
6.4
7.8
5.8
7.2
4.8
6.2
3.4
4.6
1.5
2.6
60°
30°
60–90°
1.6
3.3
3.4
5.0
5.0
6.2
6.4
7.5
7.5
8.9
8.3 8.9 9.2 9.3
9.9 10.7 11.7 11.5
(b) Equal tees: 160/160/160 mm with expansion to 250 mm
(b) Equal tees: 160/160/160 mm with expansion to 250 mm
30°
30°
60–90°
–0.8
–0.4
0.2
0.8
1.2
1.8
1.9
2.6
2.6
3.1
3.0
3.4
3.0
3.5
2.8
3.2
1.9
2.6
30°
30°
60–90°
–0.4
–0.2
0.7
1.0
1.6
2.1
2.3
2.9
2.9
3.6
3.4
4.0
3.7
4.4
4.0
4.7
4.3
4.8
45°
30°
60–90°
0
0.9
1.2
1.9
2.0
2.7
2.7
3.2
3.1
3.6
3.4
3.8
3.4
3.7
3.0
3.4
2.2
2.8
45°
30°
60–90°
0
0.2
1.0
1.3
1.9
2.4
2.7
3.3
3.2
3.9
3.7
4.4
4.1
4.9
4.5
5.5
4.8
5.6
60°
30°
60–90°
1.4
2.6
2.1
3.2
2.6
3.5
3.0
3.7
3.1
3.8
3.1
3.8
2.8
3.6
2.3
3.2
1.7
2.4
60°
30°
60–90°
–0.2
0.2
0.9
1.5
2.0
2.7
3.0
3.8
3.9
4.7
4.7
5.5
5.4
6.3
6.0
7.0
6.5
7.4
(c) Unequal tees: 250/200/250 mm with expansion to 400 mm
(c) Unequal tees: 250/200/250 mm with expansion to 400 mm
30°
30°
60–90°
— –2.5 –0.9
— –1.7 0
0.4
1.3
1.4
2.3
2.0
3.0
2.2
3.4
2.0
3.3
1.6
2.6
30°
30°
60–90°
–0.7
0.1
0.8
1.7
2.2
3.4
3.8
4.9
5.4
6.5
7.1
8.1
—
—
—
—
—
—
45°
30°
60–90°
— –2.5 –0.6
— –0.4 1.1
0.8
2.3
1.8
3.1
2.5
3.7
2.7
3.8
2.4
3.4
1.4
2.5
45°
30°
60–90°
–0.1
0.7
1.0
2.1
2.4
3.7
3.7
5.2
5.2
6.8
6.6
8.5
—
—
—
—
—
—
60°
30°
60–90°
—
—
3.8
6.3
4.25 4.2
6.4 6.1
3.8
5.4
2.8
4.2
1.4
2.5
60°
30°
60–90°
1.0
2.7
2.5
4.7
4.2
6.6
5.8 7.4 9.0
8.9 10.2 11.9
—
—
—
—
—
—
2.1
4.8
3.1
5.7
(d) Unequal tees: 160/100/160 mm with expansion to 250 mm
(d) Unequal tees: 160/100/160 mm with expansion to 250 mm
30°
30°
60–90°
–8.0 –5.7 –3.1 –1.2
–7.5 –5.0 –2.4 –0.5
0.2
0.9
1.1
1.9
1.6
2.5
1.8
2.7
1.8
2.4
30°
30°
60–90°
1.0
1.8
3.3
4.1
7.0 11
7.8 12
16
17
21
23
29
31
37
39
45
48
45°
30°
60–90°
–6.8 –3.9 –1.8 –0.2
–6.1 –3.4 –1.2 0.4
1.0
1.6
1.6
2.5
1.8
2.9
1.4
2.9
0.5
2.4
45°
30–90°
2.0
4.0
8.0 12
18
24
32
42
52
60°
30°
4.0
6.0
8.5 13
19
26
35
45
56
60°
30°
60–90°
–1.4
–0.4
3.0
4.1
3.3
4.3
3.2
4.1
2.6
3.4
1.7
2.3
0.1
1.1
1.4
2.4
2.4
3.5
* Experimental results for β = 45°, γ = 90° were rejected as unreliable;
estimated values were assumed to be close to those for γ = 60° as was the
case for all the other results.
Note: area ratios as follows: (a) (c) Ac /As = 2.56; (b) (d) Ac /As = 2.44
Figures in italics were obtained by extrapolation
Note: area ratios as follows: (a) (c) Ac /As = 2.56; (b) (d) Ac /As = 2.44
Figures in italics were obtained by extrapolation
Flow of fluids in pipes and ducts
4.11.2.24
4-47
Angle branch tees, with bend on
branch and contraction taper;
diverging flow
4.11.2.25
90° ‘Y’ tees
(a) Converging flow:
Δp = ζb-c 1/2 ρ cc2
Δp = ζ 1/2 ρ cc2
Ac
qc
cc
db
qb
cb
As
qs
cs
γ
β
dc
qc
cc
α
Ab
qb
cb
See Table 4.97.
All branch and bend pieces in same
plane, always giving: α + β = 90°
Table 4.97 90° ‘Y’ tees, converging flow: values for the branch factor ζ b-c
(derived from the European Programme Report(1))
See Tables 4.95 and 4.96.
Diameter
/ mm
Table 4.95 Angle tees with bend on branch and contraction taper,
diverging flow: values for the straight factor ζ c-s (derived from the
European Programme Report(1))
100/250/100
160/250/160
100/250/100
Tee
angle, β
Note: values determined at Reynolds numbers as follows:
100/250/100: Rec = 1.6 × 105
160/250/160: Rec = 2.0 × 105
100/250/100: Rec = 2.0 × 105
Taper
angle, γ
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) Equal tees: 250/250/250 mm with contraction from 400 mm
30°
45°
60°
30–90°
30–90°
30–90°
2.10
1.91
2.17
1.46 0.96 0.61 0.47 0.42 0.51 0.75 1.13
1.38 0.99 0.64 0.45 0.37 0.34 0.43 0.65
1.48 1.00 0.65 0.42 0.29 0.23 0.28 0.48
Ratio,
Ab / Ac
0.2
0.3
Relative branch flow, qb / qc
0.16
0.41
0.64
7.6
0.35
0.23
7.75 8.0 9.1 12.7 17.4 23 31 38
0.50 0.75 1.07 1.50 2.10 2.85 3.76 4.86
0.28 0.36 0.47 0.65 0.87 1.17 1.47 1.81
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figures in italics were obtained by extrapolation
(c) Unequal tees: 250/200/250 mm with contraction from 400 mm
30°
45°
60°
30–90°
30–90°
30–90°
1.83
1.86
1.97
1.35 0.97 0.66 0.47 0.38 0.41 0.50 0.72
1.34 0.95 0.63 0.43 0.33 0.30 0.39 0.58
1.41 0.98 0.63 0.43 0.35 0.32 0.38 0.52
(b) Diverging flow:
Δp = ζc-b 1/2 ρ cc2
db
qb
cb
Note: area ratio: Ac /As = 2.56
Figures in italics were obtained by extrapolation
Table 4.96 Angle tees with bend on branch and contraction taper,
diverging flow: values for the branch factor ζ c-b (derived from the
European Programme Report(1))
Tee
angle, β
Taper
angle, γ
dc
qc
cc
Relative branch flow, qb / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
See Table 4.98.
(a) Equal tees: 250/250/250 mm with contraction from 400 mm
30°
45°
60°
30–90°
30–90°
30–90°
5.53
5.67
6.07
4.55 3.81 3.33 3.23 3.35 3.72 4.45 5.31
4.63 3.83 3.28 2.87 2.78 2.93 3.32 3.93
5.31 4.75 4.36 4.44 3.96 4.03 4.23 4.54
(c) Unequal tees: 250/200/250 mm with contraction from 400 mm
30°
45°
60°
30–90°
30–90°
30–90°
4.53
5.00
6.13
3.47 3.00 2.85 3.40 4.90 6.70 9.03 12.2
3.87 3.15 2.97 3.30 4.43 6.00 8.13 10.3
4.98 4.17 3.80 3.83 4.33 5.27 6.67 8.07
Note: area ratio: Ac /As = 2.56
Figures in italics were obtained by extrapolation
Table 4.98 90° ‘Y’ tees, diverging flow: values for the branch factor ζ c-b:
for Rec = 2.0 × 105 (derived from the European Programme Report(1))
Diameter
/ mm
100/250/100
160/250/160
100/250/100
Ratio,
Ab / Ac
Relative branch flow, qb / qc
0.2
0.3
0.16
0.41
0.64
0.80
0.37
0.43
1.31 2.05 3.11 4.25 5.6 7.05 9.00 11.6
0.50 0.68 0.87 1.15 1.51 2.00 2.52 3.17
0.48 0.55 0.66 0.80 1.00 1.23 1.55 2.00
0.4
0.5
0.6
Figures in italics were obtained by extrapolation
0.7
0.8
0.9
1.0
4-48
Reference data
4.11.2.26
Angle ‘Y’ tees with bend on branch
(b)
(a) Converging flow
Δp = ζ b-c 1/2 ρ cc2
Diverging flow
Δp = ζ c-b 1/2 ρ cc2
db
cb
qb
α
2β
α
2β
α + β = 90°
dc
cc
qc
db
cb
qb
α + β = 90°
dc
cc
qc
See Table 4.99.
See Table 4.100.
Table 4.99 Angle ‘Y’ tees with bend on branch, converging flow: values
for the branch factor ζ b-c (derived from the European Programme
Report(1))
Table 4.100 Angle ‘Y’ tees with bend on branch, diverging flow: values
for the branch factor ζ c-b (derived from the European Programme
Report(1))
Bend
angle, α
Bend
angle, α
Branch,
angle, β
Relative branch flow, qb / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Branch,
angle, β
Relative branch flow, qb / qc
0.2
0.3
0.4
(a) 100/250/100 mm; Ab / Ac = 0.16
(a) 100/250/100 mm; Ab / Ac = 0.16
30°
45°
60°
30°
45°
60°
60°
45°
30°
2.80 3.80 5.40 8.05 12.2 17.8 24.2 32.4 40.8
1.50 3.00 5.45 9.00 13.6 18.3 23.5 29.5 36.6
0
1.90 4.35 7.69 12.0 16.5 21.5 27.0 32.7
60°
45°
30°
(b) 160/250/160 mm; Ab / Ac = 0.41
30°
45°
60°
30°
45°
60°
0
0.16 0.40 0.80 1.33 1.87 2.55 3.30 4.44
–0.20 –0.03 0.25 0.63 1.16 1.84 2.73 3.66 4.67
–0.50 –0.25 0.08 0.48 1.05 1.66 2.56 3.11 3.97
60°
45°
30°
(c) 200/250/200 mm; Ab / Ac = 0.64
30°
45°
60°
30°
45°
60°
0.04 0.10 0.21 0.36 0.53 0.70 0.88 1.05 1.22
–0.08 0
0.10 0.23 0.39 0.60 0.85 1.13 1.41
–0.22 –0.12 0
0.16 0.35 0.56 0.80 1.08 1.30
60°
45°
30°
(d) 200/400/200 mm; Ab / Ac = 0.25
30°
45°
60°
45°
60°
1.20 1.27 1.50 2.10 3.75 5.95 8.60 12.0 15.5
0.30 0.55 1.10 2.09 4.00 6.40 9.55 13.0 16.4
–1.30 –0.60 0.54 0.246 4.84 7.61 10.9 14.2 18.1
(e) 250/400/250 mm; Ab / Ac = 0.39
30°
45°
60°
60°
45°
30°
0.05 0.10 0.23 0.40 0.83 1.55 2.47 3.61 5.03
–0.60 –0.47 –0.15 0.38 1.00 1.90 2.97 4.31 5.92
–0.80 –0.60 –0.20 0.46 1.13 2.00 3.00 4.13 5.59
45°
30°
45°
60°
45°
30°
0.19 0.17 0.18 0.22 0.30 0.40 0.52 0.66 0.81
0.22 0.21 0.23 0.27 0.34 0.43 0.59 0.79 1.10
(f) 315/400/315 mm; Ab / Ac = 0.62
30°
45°
60°
Note: values determined at Reynolds numbers as follows:
(a) (b) (c) (e) (f): Rec = 2.0 × 105; (d): Rec = 1.6 × 105
Note: values determined at Reynolds numbers as follows:
(a) (d): Rec = 1.6 × 105; (b) (c) (e) (f): Rec = 2.0 × 105
Figures in italics were obtained by extrapolation
1.0
(e) 250/400/250 mm; Ab / Ac = 0.39
45°
60°
–0.05 0
0.10 0.25 0.42 0.65 0.89 1.14 1.41
–0.24 –0.19 –0.09 0.01 0.15 0.35 0.57 0.77 0.99
–0.20 –0.17 –0.07 0.06 0.21 0.43 0.64 0.84 1.10
0.9
0.10 0.13 0.18 0.27 0.37 0.49 0.64 0.83 1.06
0.10 0.18 0.30 0.44 0.61 0.80 1.01 1.26 1.5
(f) 315/400/315 mm; Ab / Ac = 0.62
60°
45°
30°
0.8
0.46 0.42 0.41 0.41 0.42 0.47 0.57 0.71 0.90
0.49 0.39 0.32 0.30 0.31 0.38 0.49 0.64 0.85
0.40 0.30 0.24 0.23 0.28 0.39 0.53 0.74 1.00
(d) 200/400/200 mm; Ab / Ac = 0.25
60°
45°
30°
0.7
0.41 0.42 0.45 0.50 0.55 0.64 0.78 0.94 1.16
0.35 0.31 0.30 0.30 0.38 0.51 0.66 0.88 1.16
0.25 0.24 0.27 0.33 0.48 0.67 0.87 1.13 1.48
(c) 200/250/200 mm; Ab / Ac = 0.64
60°
45°
30°
0.6
0.60 0.87 1.35 2.05 2.80 3.87 5.30 6.80 8.44
0.80 1.20 1.80 2.54 3.50 4.70 6.10 7.90 10.0
0.70 1.13 1.72 2.66 3.70 5.18 6.90 8.80 11.2
(b) 160/250/160 mm; Ab / Ac = 0.41
60°
45°
30°
0.5
45°
30°
0.37 0.29 0.24 0.22 0.21 0.24 0.31 0.41 0.53
0.39 0.27 0.20 0.17 0.20 0.26 0.36 0.55 0.76
Figures in italics were obtained by extrapolation
Flow of fluids in pipes and ducts
4.11.2.27
4-49
‘Y’ breech pieces, symmetrical
(HVCA 150); converging and
diverging flow
4.11.2.29
90° shoe branch tees, circular from
circular (HVCA 139)
(a) Converging flows (Ac = As)
db
cb
qb
Δp = ζ
/ ρ cc
1
b-c 2
2
db
cb
qb
As
qs
cs
2β
Ab
qb
cb
dc
cc
qc
The preferred angle 2 β is 60° to 90°, with manufacturers
preferring 90°. No data are available for this item by itself.
The nearest data available are that of item 4.11.2.26 above,
where there is a bend on each branch. Thus values of ζ b-c
and ζ c-b for the ‘Y’ breech alone can be expected to be less
than those of Tables 4.99 and 4.100.
4.11.2.28
90° conical branch tees, circular from
circular (HVCA 137 and 141)
Ab
qb
cb
Ac
qc
cc
No data are available for a shoe on a circular branch.
However, Miller(25) shows that a reduction of approximately 40% occurs for a trailing bevel on a circular branch
on a rectangular duct and that a similar reduction occurs
when a small radius (r / d = 0.09) is placed at the junction
of a circular branch on a circular main duct. However it is
not known over what range of Ab / Ac such reductions
would apply. Nevertheless, the indication is that values
less than those of Tables 4.63 and 4.64 may be used.
(b) Diverging flows (Ac = As)
Ac
qc
cc
Ac
qc
cc
Ab
qb
cb
As
qs
cs
(a) Converging flows (Ac = As)
Miller(25) shows that, compared with a sharp tee, the
slightest radius at the junction causes a reduction of at
least 40% in the values of ζ s-c and ζ b-c over a range of
normal flows 0.3 < qb / qc < 0.7. The value of Ab / Ac was
not given. Nevertheless the indication is that values less
than those of Tables 4.63 and 4.64 may be used.
As
qs
cs
No data are available for a shoe on a circular branch.
However, Miller(25) shows that a reduction of approximately 10% occurs for a leading bevel on a circular branch
from a rectangular duct and that a 25% reduction occurs
when a small radius (r / d = 0.09) is placed at the junction
of a circular branch from a circular main duct. However it
is not known over what range of Ab / Ac such reductions
would apply. Nevertheless, the indication is that values
less than those of Tables 4.65 and 4.66 may be used.
4.11.2.30
Angled off-sets, circular (HVCA 134)
(b) Diverging flows (Ac = As)
Miller(25) shows that, compared with a sharp tee, the
slightest radius at the junction causes a reduction of
between 11% and 24% in the values of the branch factor
ζ b-c over a range of normal flows 0.3 < qb / qc < 0.7. No
data are given concerning the straight factor. The value of
Ab / Ac was not given. Nevertheless the indication is that
values less than those of Tables 4.65 and 4.66 may be used.
30° max
l
There are no specific data on mitred elbows in close
proximity. A good approximation would be to use the sum
of two mitres, and the length of straight duct between
them. The value of ζ for mitre elbows of small angles can
be obtained from Table 4.51 and Figure 4.11.
4-50
Reference data
4.11.2.31
Exhaust vents with hood
4.11.2.33
Mesh screens; grids of circular
metal wire
Chinaman’s hat
Δp = ζ mesh 1/2 ρ c 2
2d
c
0.3 d
A
h
c
See Table 4.103. The value of ζ mesh depends very much on
the closeness of the mesh, or rather on the free or clear
area ratio, being Ac / A.
Δp = ζ 1/2 ρ c 2
For turbulent flow (Re > 1000) through the mesh, defined
in this instance by:
d
Re = ρ cm d / η
See Table 4.101.
(4.32)
Table 4.101 Exhaust vent with hood (Chinaman’s hat): values of ζ (from
Idelchik(2))
where cm is the mean velocity of air through the mesh and
d is the diameter of the wire.
Item
Idelchik(2) gives the following formula as a reasonable
curve-fit for low values of Ac / A:
Ratio, h/d
0.1
Exhaust vent
(Chinaman’s
hat)
0.2 0.25 0.3
4
0.35 0.4
0.5
0.6
0.8
1.0
2.3 1.90 1.60 1.40 1.30 1.15 1.10 1.00 1.00
2
A
Ac
ζ mesh = 1.3 1 – —–
+ —– – 1
A
Ac
(
) (
)
(4.33)
Table 4.103 Mesh screen: values of (from Idelchik(2))
Plane baffle
Item
Free area ratio, Ac / A
2d
Mesh screen
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
82
17
6.4
3.03
1.65
0.97
0.58
0.32
h
c
4.11.2.34
Δp = ζ 1/2 ρ c 2
Plain duct entries
d
c
See Table 4.102.
Δp = ζ tot 1/2 ρ c 2
Table 4.102 Exhaust vent with hood (plane baffle): values of ζ (from
Idelchik(2))
Item
From Idelchik(2):
Ratio, h/d
Exhaust vent
(plane baffle)
0.25
0.3
0.35
0.4
0.5
0.6
0.8
1
3.4
2.6
2.10
1.70
1.40
1.20
1.10
1.00
ζ tot = 0.5 + ζ mesh
4.11.2.35
(4.34)
Inlet vents with hood
Chinaman’s hat
4.11.2.32
2d
Plain extract
0.3 d
h
c
c
Δp = ζ 1/2 ρ c 2
Δp = ζ tot 1/2 ρ c 2
d
From Idelchik(2):
ζ tot = 1.0 + ζ mesh
(4.31)
See Table 4.104.
Flow of fluids in pipes and ducts
4-51
Table 4.104 Inlet vent with hood (Chinaman’s hat): values of ζ (from
Idelchik(2))
Item
Ratio, h/d
0.1
Inlet vent
(Chinaman’s
hat)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2.63 1.83 1.53 1.39 1.31 1.19 1.15 1.08 1.07 1.06
is with the seam (approximately 23% extra). The values in
Table 4.106 are for flow ‘with the seam’. The values of ζ
are greater than for a bend of circular cross section (see
Table 4.47). It is to be expected that values of ζ for other
values of r / w will be similarly greater than the circular
equivalent.
For bends having the same aspect ratio h / w, the larger
ducts have a slightly lower value of ζ .
Plain baffle
4.11.3.2
Tees, flow diverging
2d
All tees are circular off the oval duct, with branch
diameter equal to the height of the oval duct (db = h). No
data are available for the straight factor ζ c-s , nor for
converging flow.
h
c
Δp = ζ 1/2 ρ c 2
(a) 90° tee
Ac qc cc
db qb cb
d
See Table 4.105.
h
Table 4.105 Inlet vent with hood (plane baffle): values of ζ (from
Idelchik(2))
Item
Δp = ζ 1/2 ρ c c2
Ratio, h/d
Inlet vent
(plane baffle)
w
As qs cs
0.25
0.3
0.35
0.4
0.5
0.6
0.8
1.0
4.4
2.15
1.78
1.57
1.35
1.23
1.10
1.06
See Table 4.107 (page 4-52).
(b) 45° tee
4.11.3
Ac qc cc
Pressure loss factors for
ductwork components:
flat -oval
4.11.3.1
db
qb
cb
45°
h
90° segmented bends
Δp = ζ 1/2 ρ c c2
w
As qs cs
h
See Table 4.108 (page 4-52).
r
w
Flow with the seam
See Table 4.106. Smith and Jones(32) found that having the
seams against the flow gave rise to an additional 0.06 in
the value of ζ in comparison with the value when the flow
Table 4.106 90° segmented bends, flat-oval (r/w = 1.5): values of ζ ; for 4 × 105 < Re < 29 × 105 and
419 mm < de < 794 mm (derived from Smith and Jones(32))
Item
Ratio, h/w
‘Hard’ (w>h)
Seg. bend
(flat-oval)
‘Easy’ (w<h)
0.25
0.33
0.4
0.5
0.75
1
2
3
4
5
0.239
0.220
0.204
0.192
0.171
0.170
0.171
0.182
0.197
0.214
The figures in italics were obtained by interpolation
4-52
Reference data
Table 4.107 90° tee, flat-oval, diverging: values of the branch factor, ζ c-b; for 4 × 105 < Rec < 29 × 105, and 255 mm < dec < 550 mm
(derived from Smith and Jones(32))
Aspect,
ratio, w/h
Equivalent
diameter,
dec / mm
Branch
diameter,
db / mm
Area ratio,
Ab /Ac
2.0
3.2
4.1
255
300
550
150
150
150
2.0
2.9
4.1
423
484
550
250
250
250
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.279
0.196
0.157
0.921
0.958
1.00
1.05
1.17
1.37
1.21
1.64
2.11
1.53
2.26
3.12
1.95
3.12
—
2.42
—
—
3.03
—
—
—
—
—
0.282
0.210
0.159
0.937
0.947
1.00
1.04
1.16
1.37
1.26
1.53
2.05
1.53
2.11
3.03
1.90
2.84
—
2.37
3.69
—
3.00
—
—
3.69
—
—
Table 4.108 45° tee, flat-oval, diverging: values of the branch factor, ζ c-b; for 4 × 105 < Rec < 29 × 105, and 255 mm < dec < 550 mm
(derived from Smith and Jones(32))
Aspect,
ratio, w/h
Equivalent
diameter,
dec / mm
Branch
diameter,
db / mm
Area ratio,
Ab /Ac
2.0
3.2
4.1
255
300
550
150
150
150
2.0
2.9
4.1
423
484
550
250
250
250
4.11.4
Relative branch flow, qb / qc
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.279
0.196
0.157
0.684
0.579
0.505
0.505
0.526
0.658
0.542
0.921
1.42
0.789
1.59
2.79
1.48
2.82
—
3.32
—
—
—
—
—
—
—
—
0.282
0.210
0.159
0.658
0.526
0.484
0.484
0.421
0.431
0.432
0.553
1.00
0.553
0.980
2.05
0.916
1.79
3.66
1.42
3.65
—
2.1
—
—
2.97
—
—
Pressure loss factors for
ductwork components :
rectangular
4.11.4.1
90° radius bends without vanes
(HVCA 86, 87)
When Reynolds number is required for rectangular ducts,
the hydraulic diameter (dh ) is to be used, being four times
the hydraulic radius:
2wh
dh = ———
(w + h)
(4.35)
ρ c dh
Re = ——–
η
(4.36)
w
r
where w and h are the width (mm) and height (mm) of the
duct section.
Original source data are difficult to find. The primary
source, Idelchik(2), is rather all-embracing and frequently
too closely linked to data for circular ducts. Such data may
have been derived using the hydraulic mean diameter. His
original sources, generally in Russian, are neither readily
available nor recent. Nevertheless, in the absence of other
reliable data, we propose some of his data for guidance
only and to be treated with circumspection.
h
w
See Tables 4.109 and 4.110. The values in Table 4.109 are
for Re = 2 × 105.
For values of Re other than 2 × 105 the tabulated values
should be multiplied by the correction factor CRe given in
Table 4.110. These data were obtained from the report of
the European Programme on circular bends (see Table
4.48). It is expected to be similar for square bends
(r/d = 1), but may well be different for other values of h/w
and r/w.
Appreciable savings in pressure drop are obtained by
employing a radius r / d of 1.5 or greater. For ‘tight’ bends
where r / d ≤ 1, consideration should be given to using a
guide vane (see section 4.11.4.2). It should be noted that
for the same duct area (w × h) and for the same radius of
the inner part of the bend, ‘easy’ bends (h > w) give values
of ζ which are appreciably less than for ‘hard’ bends
(h < w).
For bends of angles (α ) other than 90°, Table 4.111 gives
the angle factor, Cα , relative to the values of ζ for 90°
bends. Miller(37) was not precise about the sizes used but
the inference is that w = 300 mm.
Flow of fluids in pipes and ducts
4-53
Table 4.109 90° bends, rectangular: values of ζ ; for Re = 2 × 105 (derived
from Miller(37))
Ratio, r/w
Aspect ratio, h/w
0.5
0.75
1.0
1.5
2.0
0.8
1.0
1.5
—
0.232
0.180
—
0.248
0.177
—
0.254
0.174
—
0.253
0.164
0.359
0.243
0.137
2.0
2.5
3
0.164
0.166
0.170
0.160
0.158
0.158
0.155
0.151
0.150
0.142
0.137
0.137
0.121
0.124
0.128
—
—
—
—
—
—
—
—
0.135
0.153
4
6
Note: w is believed to be approximately 300 mm.
Figures in italics obtained by interpolation
Value of CRe for stated Reynolds number, Re /
90° bend, rect.
105
0.5
1.0
1.5
2.0
3
4
10
1.37
1.16
1.084
1.0
0.98
0.96
0.948
Table 4.111 Radius bends, rectangular: values of angle factor Cα; for
Re = 2 × 105 (derived from Miller(37))
Aspect
ratio, h/w
Ratio,
r/w
0.5
Aspect ratio, h/w
0.25 0.5
1.0
1.5
2.0
3.0
4.0
5.0
6.0
7.0
8.0
(a) 1 turning vane
0.55
0.60
0.65
0.70
0.52
0.36
0.28
0.22
0.40
0.27
0.21
0.16
0.43
0.25
0.18
0.14
0.49
0.28
0.19
0.14
0.55
0.30
0.20
0.15
0.66
0.35
0.22
0.16
0.75
0.39
0.25
0.17
0.84
0.42
0.26
0.18
0.93
0.46
0.28
0.19
1.01
0.49
0.30
0.20
1.09
0.52
0.32
0.21
0.75
0.80
0.90
1.00
0.18
0.15
0.11
0.09
0.13
0.11
0.08
0.06
0.11
0.09
0.07
0.05
0.11
0.09
0.06
0.05
0.11
0.09
0.06
0.04
0.12
0.09
0.06
0.04
0.13
0.10
0.06
0.04
0.14
0.10
0.07
0.05
0.14
0.11
0.07
0.05
0.15
0.11
0.07
0.05
0.15
0.12
0.07
0.05
0.55
0.60
0.65
0.70
0.26
0.17
0.12
0.09
0.20
0.13
0.09
0.07
0.22
0.11
0.08
0.06
0.25
0.12
0.08
0.05
0.28
0.13
0.08
0.06
0.33
0.15
0.09
0.06
0.37
0.16
0.10
0.06
0.41
0.17
0.10
0.06
0.45
0.19
0.11
0.07
0.48
0.20
0.11
0.07
0.51
0.21
0.11
0.07
0.75
0.80
0.90
1.00
0.08
0.06
0.05
0.03
0.05
0.04
0.03
0.02
0.04
0.03
0.03
0.02
0.04
0.03
0.02
0.02
0.04
0.03
0.02
0.02
0.04
0.03
0.02
0.01
0.05
0.03
0.02
0.01
0.05
0.03
0.02
0.01
0.05
0.04
0.02
0.01
0.05
0.04
0.02
0.01
0.05
0.04
0.02
0.01
(c) 3 turning vanes
Value of Cα for stated bend angle, α
15°
30°
45°
60°
75°
90°
1
2
3
0.150
0.219
0.224
0.264
0.400
0.422
0.395
0.568
0.609
0.636
0.742
0.776
0.873
0.897
0.908
1
1
1
1.0
1
2
3
0.124
0.170
0.204
0.237
0.367
0.430
0.328
0.531
0.613
0.498
0.701
0.775
0.784
0.857
0.880
1
1
1
2.0
1
2
3
0.088
0.183
0.182
0.189
0.391
0.388
0.357
0.583
0.554
0.617
0.722
0.711
0.877
0.852
0.860
1
1
1
Figures in italics are interpolated values
4.11.4.2
Ratio,
r/w
(b) 2 turning vanes
Table 4.110 90° bends, rectangular: values of CRe (derived from the
European Programme Report(1))
Item
Table 4.112 Short radius 90° bends, rectangular, with vanes: values of ζ
(reproduced from HVAC Systems Duct Design(40) by permission of the
Sheet Metal and Air-Conditioning Contractors’ National Association
(SMACNA), Chantilly, Virginia, USA)
0.55
0.60
0.65
0.70
0.11
0.07
0.05
0.03
0.10
0.05
0.04
0.03
0.12
0.06
0.04
0.03
0.13
0.06
0.04
0.03
0.14
0.06
0.04
0.03
0.16
0.07
0.04
0.03
0.18
0.07
0.04
0.03
0.19
0.08
0.04
0.03
0.21
0.08
0.04
0.03
0.22
0.08
0.05
0.03
0.23
0.09
0.05
0.03
0.75
0.80
0.90
1.00
0.03
0.03
0.02
0.01
0.02
0.02
0.01
0.01
0.02
0.02
0.01
0.01
0.02
0.02
0.01
0.01
0.02
0.02
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.01
0.01
0.01
Table 4.113 Short radius 90° bends, rectangular: recommended
positions for splitters (from HVCA DW/144(22))
Dimension,
w / mm
No. of
splitters
400–800
801–1600
1601–2000
1
2
3
Splitter position
1
2
3
w/3
w/4
w/8
—
w/2
w/3
—
—
w/2
Short radius bends with vanes
(splitters): rectangular (HVCA 88)
4.11.4.3
90º mitred throat bend (up to
400 mm wide) (HVCA 85)
w
r
h
w
α
ro
l
h
See Table 4.112. These data were published before size
and Re were known to have an effect. Preferred positions
for splitters are given in Table 4.113.
For bends of other angles, it is suggested that the angle
factors given in Table 4.111 be used.
w
See Table 4.114. The figures have been based on an
assumption of l/w = 0.5, where l is the length of the bevel,
and ro /w = 1.5, where ro is the radius of the outer surface.
4-54
Reference data
Table 4.114 90° mitred throat bend: values for ζ
Item
Aspect ratio, h/w
0.25 0.5 0.75
1
1.5
2
3
4
5
6
8
90° bend, 0.31 0.29 0.27 0.26 0.24 0.23 0.22 0.22 0.22 0.23 0.23
mitred
throat
Note: all values are estimates. No experimental values exist to justify
them. They are based on the value of ζ lying between that for a mitred
elbow with bevel inner, and that for a normal round bend. A confidence
tolerance of +
– 30% would seem appropriate.
4.11.4.4
Elbow, mitred, rectangular, any angle
α
h
h
w
w
See Table 4.115. This table has been derived from data of
Idelchik(2). These data were published before size and Re
were known to have an effect.
is the case, but there are a few contradictions. Although
both sets of data have been derived from Idelchik, his
information is derived from many other sources so some
discrepancies may be expected. Comparing the values for
the sharpest inner corner in Table 4.116 (ri /w = 0.05) with
those of a sharp mitre corner in Table 4.115 shows that for
the slightest radius there is an optimum value of h / w,
whereas for the sharp mitre elbow there is not. There is
therefore some doubt about the validity of the values in
Table 4.116 but they are the only data available.
Table 4.116 90° elbow, rectangular, with rounded inner corner: values of ζ
(from Idelchik(2))
Ratio,
ri / w
0.5
0.75
1
Aspect ratio, h/w
2
3
4
6
0.05
0.1
0.2
1.31
1.05
0.85
1.22
0.98
0.79
1.12
0.90
0.73
0.95
0.77
0.62
0.95
0.77
0.62
1.01
0.81
0.66
1.10
0.88
0.72
0.3
0.5
0.7
0.67
0.60
0.65
0.64
0.56
0.51
0.59
0.52
0.47
0.51
0.45
0.41
0.51
0.45
0.41
0.53
0.47
0.43
0.58
0.51
0.46
4.11.4.6
90° rectangular mitred elbows of
unequal areas
With the exception of small angles, similar values of ζ may
be obtained using the following algorithm, being adapted
from curve-fits by Idelchik(2):
h
(
h
ζ = 0.97 – 0.13 ln —
w
(
)(
)
40
0.89 + —– cos2 (α – 45)
α
( ))
α
α
× 0.95 sin2 — + 2.05 sin4 ––
2
2
( )
h
w2
w1
(4.37)
See Table 4.117. This table is a modification of that given
in Idelchik’s diagram 6–6(2).
Note that the value of ζ must be applied to the upstream
velocity pressure, i.e.:
Table 4.115 Mitred elbow, rectangular: values of ζ (from Idelchik(2))
Bend
angle, α
0.25 0.5 0.75
Aspect ratio, h/w
20°
30°
45°
0.14 0.13 0.13 0.12 0.12 0.11 0.10 0.10 0.09 0.09 0.09
0.17 0.17 0.16 0.16 0.15 0.14 0.13 0.12 0.12 0.11 0.11
0.35 0.34 0.33 0.32 0.3 0.29 0.26 0.25 0.24 0.23 0.22
60°
75°
90°
0.61 0.59 0.58 0.56 0.53 0.50 0.46 0.43 0.42 0.40 0.39
0.89 0.86 0.84 0.81 0.77 0.73 0.67 0.63 0.60 0.58 0.56
1.31 1.27 1.24 1.19 1.13 1.07 0.99 0.93 0.89 0.86 0.83
4.11.4.5
1
1.5
2
3
4
5
6
Elbow, 90° rectangular, rounded
inner corner
h
h
w
ri
Δp = ζ 1/2 ρ c12
8
w
See table 4.116. This table has been derived from data of
Idelchik(2). It is to be expected that the values of ζ for the
rounded inner corner should be lower than for a 90°
mitred corner (see section 4.11.4.4). In most instances this
(4.38)
Note that in the case of equal areas (w1 / w2 = 1), there are
slight discrepancies compared with the 90° mitred elbow
(section 4.11.4.4).
Table 4.117 Mitred elbow, rectangular, of unequal areas: values of ζ
(from Idelchik(2))
Ratio,
h/w1
Ratio, w1 /w2
0.6
0.8
1
1.2
1.4
1.6
2
0.25
1
4
∞
1.76
1.70
1.46
1.50
1.43
1.36
1.10
1.04
1.24
1.15
0.90
0.79
1.14
1.02
0.81
0.69
1.09
0.95
0.76
0.63
1.06
0.90
0.72
0.60
1.06
0.84
0.66
0.60
Flow of fluids in pipes and ducts
4.11.4.7
4-55
Rectangular mitred elbows with vanes
4.11.4.9
Bends in close proximity, rectangular,
through perpendicular plane
h
w1
l
w
h
No reliable data are available. As an interim measure it is
suggested that the values of Table 4.115 might be halved.
4.11.4.8
Bends in close proximity, rectangular
(‘gooseneck’)
l
Since bends of this type involve one bend which is ‘easy’
and the other ‘difficult’, it is difficult to see which bend
should be used for ζ. Use of ζ for a ‘difficult’ bend could
give a conservative value.
No data are available for the interaction factor Ccp of
rectangular ductwork installed in close proximity. It is to
be expected that Ccp would depend upon r/w, r/h and h/w
of each bend as well as the separation l / w. It is also
expected that it will vary with Reynolds number, and
possibly also with size w.
Data for bends in close proximity for circular ductwork are
given in section 4.11.2.6 for bends with d = 250 mm, and
r/d = 1.0. Thus for close coupling of square bends of sides
approximately 250 mm and having r / d = 1.0, it would
seem reasonable to use the values of Ccp given in Table
4.53, and use it in conjunction with values of ζ1 from Table
4.109 in equation 4.39.
w
h
No data are available for the interaction factor Ccp of
rectangular ductwork installed in close proximity. It is to
be expected that Ccp would depend upon r / w and h / w of
each bend as well as the separation l/w. We can also expect
that it will vary with Reynolds number, and possibly also
with size w.
Note that the above does not include the pressure drop of
the length of separation. The separation ( l ) should be
added to the length of straight ductwork of the same size.
4.11.4.10
Elbows in close proximity, rectangular,
in plane
Data for ‘gooseneck’ bends for circular ductwork are given in
section 4.11.2.5 for close coupling of bends with d = 250 mm,
and r/d = 1.0. Thus for close coupling of square bends of
sides approximately 250 mm and with r/d = 1.0, it would
seem reasonable to use the values of Ccp given in Table
4.52, in conjunction with values of ζ1 from Table 4.109 in
the equation:
Δp = 2 Ccp ζ1 1/2 ρ c2
(4.39)
Note that the above does not include for the pressure drop
of the length of separation. The separation ( l ) should be
added to the length of straight ductwork of the same size.
l
w
h
No recent data are available. Some tentative data are
presented in Table 4.118. However, it is expected that ζ
should vary with Reynolds number and with size.
4-56
Reference data
Table 4.118 Combined double elbow, rectangular: values of ζ for the
whole, including the separating length (derived from Idelchik(2), diagram
6–13)
4.11.4.12
Offset
step, l/w
The only data available are from Miller(25,37). For both the
straight and branch factors, his values of ζ are consistently
higher than his values for circular tees of the same area
ratio Ab / Ac. However his values of ζ for rectangular tees
were all a little lower than the more recently obtained data
of the European Programme(1) for circular tees (see Tables
4.63 to 4.66). Therefore, for consistency, the original
values produced by Miller have been increased so as to
show, as he found, the increase in ζ compared to circular
tees. The values printed in Tables 4.120 to 4.123, therefore,
should be treated as ‘best advice’. In the rectangular tees
tested, w of the main duct remained constant (w = hc =
hs ), whereas hc ≥ hb. Miller tested for various sizes of the
shoe, b. The greater the size of the shoe the greater the
reduction in ζ . The reduction in the values of ζ due to the
installation of a trailing or leading bevel (Δζ) is shown in
the tables.
Aspect ratio, h/w
0.25
0.5
1
1.5
2
3
5
8
0.6
0.8
1
1.8
2
1.0
1.8
2.9
4.8
4.6
0.98
1.7
2.8
4.6
4.5
0.91
1.6
2.7
4.3
4.2
0.87
1.5
2.5
4.0
4.0
0.82
1.5
2.4
3.8
3.8
0.79
1.3
2.2
3.5
3.5
0.69
1.22
2.0
3.2
3.2
0.64
1.14
1.9
3.0
3.0
2.4
3
4
6
10
4.1
3.7
3.5
3.3
2.9
4.0
3.6
3.4
3.2
2.8
3.7
3.4
3.2
3.0
2.7
3.5
3.2
3.0
2.9
2.5
3.3
3.0
2.9
2.7
2.4
3.1
2.8
2.6
2.5
2.2
2.8
2.5
2.4
2.3
2.0
2.6
2.3
2.2
2.2
1.9
Notes:
(1) The maximum friction pressure loss occurs when the offset is
around l/w = 1.8.
(2) In this instance l is defined as the step and not the separation.
4.11.4.11
Elbows in close proximity, rectangular,
through perpendicular plane
h1
w1
90° rectangular tees (HVCA 104
and 106)
It is to be expected that values of ζ will vary considerably
with Ab / Ac , as occurs for circular tees. It is expected that ζ
will depend on the aspect ratios of both the main duct
(hc /w) and of the branch (hb/wb), and a little upon size but
no experimental data are available.
(a) Converging flow
w
Δp = ζ 1/2 ρ cc2
As qs cs
l
Ab qb cb
hc
hb
wb
Ac qc cc
See Table 4.119.
Plain
No recent data are available. The data presented in Table
4.119 should be regarded as tentative. It is expected that ζ
should vary with Reynolds number and with size.
w
Δp = ζ 1/2 ρ cc2
As qs cs
b
Table 4.119 Double elbow, rectangular, through perpendicular plane:
values of ζ for the whole, including the separating length (derived from
Idelchik(2), diagram 6–13)
Offset
step, l/w1
hc
Ab qb cb
Aspect ratio, h1 /w1
0.25
0.5
1
1.5
2
3
5
8
hb
wb
Ac qc cc
Trailing bevel
0
0.6
1
1.5
1.26
2.7
3.8
3.6
1.23
2.6
2.6
3.5
1.15
2.4
3.5
3.2
1.09
2.3
2.3
3.0
1.04
2.2
2.2
2.9
0.95
2.0
2.0
2.7
0.86
1.8
1.8
2.4
0.81
1.7
1.7
2.3
See Tables 4.120 and 4.121.
2
3
5
7
3.5
3.5
3.3
3.1
3.4
3.5
3.2
3.0
3.2
3.2
3.0
2.8
3
3.1
2.8
2.7
2.8
2.9
2.6
2.6
2.6
2.7
2.5
2.4
2.4
2.4
2.3
2.2
2.2
2.3
2.1
2.0
Table 4.120 90° rectangular tees, converging flow: values for the straight
factor ζ s-c and reduction in ζ obtained by inclusion of trailing bevel; for
w = hc = hs = 300 mm, Rec > 105 (derived from Miller(25,37))
10
2.9
2.8
2.6
2.5
2.4
2.2
2.0
1.9
Area ratio,
Ab / Ac
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.79
1.00
0.75
0.74
0.71
0.70
0.66
0.65
0.60
0.59
0.53
0.52
0.44
0.43
0.35
0.33
Notes:
(1) In this instance l is defined as the step and not the separation.
(2) The outlet has the same dimensions h and w, but ζ is given in terms
of w1 and h1.
(3) Although the data available are for any aspect ratio h/w, it is perhaps
surprising that high values, implying that the second elbow is
‘difficult’, do not result in higher values of ζ . It is easier to have
confidence in the values for a square or almost square duct.
Relative straight flow, qs / qc
Reduction in straight factor, Δζ s-c ,
due to trailing bevel
Bevel
length, b
0.79
1.00
1.00
w/8
w/8
w/2
0.26
0.26
0.54
0.24
0.24
0.45
0.22
0.25
0.35
0.20
0.26
0.27
0.17
0.19
0.19
0.15
0.11
0.11
0.11
0.06
0.06
Flow of fluids in pipes and ducts
4-57
Table 4.121 90° rectangular tees, converging flow: values for the branch
factor ζ b-c and reduction in ζ obtained by inclusion of trailing bevel; for
w = hc = hs = 300 mm, Rec > 105 (derived from Miller(25,37))
Area ratio,
Ab / Ac
Relative branch flow, qb / qc
0.79
1.00
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.18
–0.10
0.34
0.19
0.51
0.42
0.71
0.62
0.94
0.83
1.23
1.01
1.52
1.13
—
—
—
0.23
0.15
0.19
0.21
0.22
0.26
0.23
0.25
0.32
0.25
0.27
0.40
0.27
0.25
0.49
w
Ab
qb
cb
Δp = ζ 1/2 ρ cc2
β
hc
hb
wb
Converging
0.30
0.26
0.57
* Raw data is out of step with other data
(b)
Angled branch tees: rectangular from
rectangular (HVCA 105)
As
qs
cs
Reduction in branch factor, Δζ b-c ,
due to trailing bevel
Bevel
length, b
0.79 w/8
1.00* w/8
1.00 w/2
4.11.4.13
Ac
qc
cc
w
Diverging flow
Ac qc cc
Δp = ζ 1/2 ρ cc2
hb
w
Δp = ζ 1/2 ρ cc2
Ac qc cc
hc
β
As qs cs
wb
hc
Ab qb cb
hb
Ab qb cb
Diverging
wb
As qs cs
The all-embracing data provided by Idelchik(2) is too
simple to be true. For angle circular tees (cf Tables 4.77
and 4.78 for example) it is clear that, for the same value of
Ab / Ac , size matters. From the limited data on flat-oval
tees, (cf Tables 4.107 and 4.108) it is also clear that values
of the branch factor depend upon hc / wc . We can also
expect the branch factors in particular to depend upon
wb / wc and hb / hc . In the absence of any data which takes
account of these factors, it is impossible to present even
simplified guidance. The data in this Guide which might
point the designer towards an estimate of likely values of ζ
are the data for angle branch tees, circular (section
4.11.2.16), 90° tees, flat-oval (section 4.11.3.2) and 90° tees,
rectangular (section 4.11.4.12).
Plain
w
Ac qc cc
Δp = ζ 1/2 ρ cc2
b
hc
hb
Ab qb cb
wb
As qs cs
Leading bevel
See Tables 4.122 and 4.123.
Table 4.122 90° rectangular tees, diverging flow: values for the straight
factor ζ c-s and reduction in ζ obtained by inclusion of leading bevel; for
w = hc = hs = 300 mm, Rec > 105 (derived from Miller(37))
Area ratio,
Ab / Ac
Relative straight flow, qs / qc
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.00
0.31
0.21
0.13
0.07
0.025
0
0
No noticeable effect
No noticeable effect
w/8
w/2
Area ratio,
Ab / Ac
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.00*
0.87
0.82
0.82
0.84
0.89
0.94
1.02
Relative branch flow, qb / qc
Reduction in branch factor, Δζ b-c ,
due to leading bevel
Bevel
length, b
w/8
w/2
Δp = ζ 1/2 ρ cc2
As
qs
cs
Ab qb cb
Table 4.123 90° rectangular tees, diverging flow: values for the branch
factor ζ c-b and reduction in ζ obtained by inclusion of leading bevel; for
w = hc = hs = 300 mm, Rec > 105 (derived from Miller(25,37))
1.00
1.00
90° Tees: rectangular from
rectangular; bell-mouth branch
(HVCA 107)
Reduction in straight factor, Δζ s-c ,
due to leading bevel
Bevel
length, b
1.00
1.00
4.11.4.14
0.04
0.095
0.04
0.16
0.07
0.23
0.09
0.31
0.13
0.39
0.16
0.48
0.21
0.58
* Figures in italics are Miller’s readings. They would be expected to be
greater than for a circular tee (Table 4.66), but he did not make this
comparison. The values as presented conflict with those for circular tees,
thus there is possibly some doubt about these values.
Ac
qc
cc
Converging and diverging flows (Ac = As)
No data can be found for this component. There is no
reason to believe that the values of ζ will be any less than
that for a shoe branch (section 4.11.4.12).
4-58
Reference data
4.11.4.15
90° radiussed twin bend: rectangular
(HVCA 91)
1
The values of the branch factor ζc-b ought to depend on
the aspect ratio hb / wb . The only available data are from
ASHRAE(4).
4.11.4.17
Angled offsets (HVCA 96, 97, 98)
α
r
2
Ac qc cc
w
Δp = ζ 1/2 ρ cc2
Little information is available. Even for a symmetrical tee
with an equal division of flow, values of ζ will depend
upon A1 / Ac , r / w, hb / wb , hc / wc and size. Guidance should
be taken from section 4.11.2.26 (Angle ‘Y’ tees with bend
on branch, circular).
4.11.4.16
90° swept branch tee
wc
Ac qc cc
Δp = ζ 1/2 ρ cc2
There are no specific data on rectangular elbows and
bends in close proximity. A good approximation would be
to use the sum of two bends or elbows, and the length of
clear duct between. Values of ζ are given in Tables 4.109 to
4.111 for bends, and Table 4.115 for mitred elbows.
r
As qs cs
ws
wb
r / wb = 1.5
4.11.4.18
Ab qb cb
Opposed blade dampers
See Tables 4.124 and 4.125.
Table 4.124 90° swept tees, rectangular, diverging flow: values for the
straight factor ζ c-s; for hb = hc = hs , Ab + As >
– Ac (from ASHRAE
Handbook: Fundamentals 2005(4), ch. 35. © American Society of Heating,
Refrigerating and Air-Conditioning Engineers Inc. (www.ashrae.org))
As / Ac
Ab / Ac
Relative straight flow, qs / qc
0.1
0.3
0.4
0.5
0.6
0.25
0.50
1.00
8.75 1.62 0.50
7.50 1.12 0.25
5.00 0.62 0.17
0.17
0.06
0.08
0.05
0.05
0.08
0.00 –0.02 –0.02
0.09 0.14 0.19
0.09 0.12 0.15
0.00
0.22
0.19
0.75
0.25
0.50
1.00
19.13 3.38 1.00
20.81 3.23 0.75
16.88 2.81 0.63
0.28 0.05 –0.02 –0.02 0.00
0.14 –0.02 –0.05 –0.05 –0.02
0.11 –0.02 –0.05 0.01 0.00
0.06
0.03
0.07
1.00
0.25
0.50
1.00
46.00 9.50 3.22
35.00 6.75 2.11
38.00 7.50 2.44
1.31
0.75
0.81
0.50
0.2
0.7
0.8
0.52 0.14 –0.02 –0.05 –0.01
0.24 0.00 –0.10 –0.09 –0.04
0.24 –0.03 –0.08 –0.06 –0.02
Ab / Ac
Relative branch flow, qb / qc
0.1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.25
0.50
1.00
3.44 0.70 0.30
11.00 2.37 1.06
60.00 13.00 4.78
0.20
0.64
2.06
0.17
0.52
0.96
0.16
0.47
0.47
0.16
0.47
0.31
0.17
0.47
0.27
0.18
0.48
0.26
0.75
0.25
0.50
1.00
2.19 0.55 0.35
13.00 2.50 0.89
70.00 15.00 5.67
0.31
0.47
2.62
0.33
0.34
1.36
0.35
0.31
0.78
0.36
0.32
0.53
0.37
0.36
0.41
0.39
0.43
0.36
1.00
0.25
0.50
1.00
3.44 0.78 0.42
15.50 3.00 1.11
67.00 13.75 5.11
0.33
0.62
2.31
0.30
0.48
1.28
0.31
0.42
0.81
0.40
0.40
0.59
0.42
0.42
0.47
0.46
0.46
0.46
0.50
0.2
w
α
0.9
Table 4.125 90° swept tees, rectangular, converging flow: values for the
branch factor ζ c-b; for hw = hc = hs , Ab + As >
– Ac (from ASHRAE
Handbook: Fundamentals 2005(4), ch. 35. © American Society of Heating,
Refrigerating and Air-Conditioning Engineers Inc. (www.ashrae.org))
As / Ac
h
Crimped leaf edges
See Table 4.126. The parameter x is determined from:
nw
x = ————
2 (h + w)
(4.40)
where n is the number of blades.
Table 4.126 Opposed blade damper: values of from ASHRAE
Handbook: Fundamentals 2005(4), ch. 35. © American Society of Heating,
Refrigerating and Air-Conditioning Engineers Inc. (www.ashrae.org))
Value
of x
Value of ζ for stated blade angle, α
0°
10°
20°
30°
40°
50°
60°
70°
80°
0.3
0.4
0.5
0.6
0.52
0.52
0.52
0.52
0.79
0.85
0.93
1.00
1.91
2.07
2.25
2.46
3.77
4.61
5.44
5.99
8.55
10.4
12.3
14.1
19.5
26.7
34.0
41.3
70.1
92.9
119
144
295
346
393
440
807
926
1045
1163
0.8
1.0
1.5
0.52
0.52
0.52
1.08
1.17
1.38
2.66
2.91
3.16
6.96
7.31
9.51
18.2
20.2
27.6
56.5
71.7
104.4
194
245
361
520
576
717
1325
1521
1804
Flow of fluids in pipes and ducts
4.11.4.19
4-59
Exhaust vents; lateral openings with
and without side louvers
z
c
Table 4.128 Inlet vents, lateral openings: values of (from Idelchik(2))
Number of
openings
Layout
Value of ζ
w/z
Without
louvres
30°
louvres
45°
louvres
One
1.5
12.6
17.5
—
Two
1.5
3.6
5.4
—
Three
1.5
1.8
3.2
—
Four
1.5
1.0
0.5
1.2
2.0
8.0
2.5
3.6
13.7
3.8
6.0
21.5
w1
w
Δp = ζ 1/2 ρ cc2
z / w = 0.5
The pressure drop through such exhaust vents will depend
strongly on the geometry of the louvres so manufacturer’s
guidance should be sought. Table 4.127, taken from
Idelchik(2), is intended for initial guidance only, when
doing initial feasibility calculations.
4.11.4.21
Louvred duct entries
Table 4.127 Exhaust vents, lateral openings: values of (from Idelchik(2))
Number of
openings
Layout
Value of ζ
w/z
Without
louvres
30°
louvres
45°
louvres
One
1.5
15.5
22.0
—
Two
1.5
5.0
7.2
—
Three
1.5
3.5
5
—
c
h
h1
x1 x
l
(a)
Four
1.5
1.0
0.5
2.2
5.3
15.6
2.6
7.0
19.6
3.5
10.0
29
(b)
Table 4.129 gives values of ζ for the two idealised shapes of
louvre blade, for values of l / x1 > 2.2. Note that the angle
of the blades would appear not to play a part, except
insofar as it affects the value of h1 / h.
Table 4.129 Louvred duct entries: values of (from Idelchik(2))
Louvre
4.11.4.20
Inlet vents; lateral openings with and
without side louvres
z
x / x1
0.7
0.8
0.9
0.95
1.0
Type (a)
0.8
0.9
7.9
6.7
5.7
4.8
4.3
3.7
3.3
2.9
3.0
2.6
2.7
2.3
Type (b)
0.8
0.9
4.8
4.0
3.4
2.9
2.6
2.2
2.0
1.7
1.8
1.5
1.6
1.4
4.11.4.22
c
Ratio, h1 / h
0.6
Plain outlets
w1
w
z / w = 0.5
c
Δp = ζ 1/2 ρ cc2
The pressure drop through such exhaust vents will depend
strongly on the geometry of the louvres so manufacturer’s
guidance should be sought. Table 4.128, derived from
Idelchik(2), is intended for initial guidance only, when
doing initial feasibility calculations.
Δp = ζ tot 1/2 ρ c 2
From Idelchik(2):
ζ tot = 1.0 + ζ mesh
(4.41)
4-60
Reference data
4.11.4.23
Mesh screens; grids of circular
metal wire
No recent experimental data can be found. ASHRAE
reports that the same values of ζ apply for transitions
circular-to-rectangular and rectangular-to-circular, and
that for taper angles γ > 30° these are very similar to those
for circular-to-circular tapers. However the influence of
aspect ratio h / w is not reported and has perhaps not been
investigated. In the light of this, values of ζ should be
taken from section 4.11.2.7.
Δp = ζ mesh 1/2 ρ c 2
c
A
See Table 4.130. The value of ζ mesh depends very much on
the closeness of the mesh, or rather on the free or clear
area ratio, Ac / A.
For turbulent flow (Re > 1000) through the mesh, defined
in this instance by:
Re = ρ cm d / η
(4.42)
where cm is the mean velocity of air through the mesh and
d is the diameter of the wire.
For non-symmetrical expansions, vertical and horizontal
projections will give two different taper angles, γ1 and γ2.
The greater of these should be used when using the data of
section 4.11.2.7.
It is expected that the expansion of rectangular sections,
whether symmetrical or non-symmetrical, might have
greater values of ζ than for circular-to-circular tapers.
4.11.5.2
Contractions, transitions
Idelchik(2) gives the following formula as a reasonable
curve-fit for low values of Ac / A:
) (
A2
c1
2
A
Ac
ζ mesh = 1.3 1 – —–
+ —– – 1
A
Ac
(
c2
)
(4.43)
A1
Table 4.130 Mesh screen: values of (from Idelchik(2))
Item
Free area ratio, Ac / A
Mesh screen
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
82
17
6.4
3.03
1.65
0.97
0.58
0.32
4.11.4.24
Plain duct entries
c1
Δp = ζ tot 1/2 ρ c 2
For non-symmetrical contractions, vertical and horizontal
projections will give two different taper angles, γ1 and γ2.
The greater of these should be used when using the data of
section 4.11.2.8.
From Idelchik(2):
ζ tot = 0.5 + ζ mesh
(4.44)
4.11.5
Transitions between circular and
rectangular ductwork
4.11.5.1
Expansions, transitions
Δp = ζ 1/2 ρ c12
It is expected that the contraction of rectangular sections,
whether symmetrical or unsymmetrical, might have
greater values of ζ than for circular-to-circular tapers.
References
1
Energy loss coefficients of components used in air distribution systems
EEC Programme Report No. 3401/1/0/110/90/8-BCR-D(30)
(Brussels: Commission of the European Communities
Directorate-General for Science, Research and Development)
(1992) (obtainable from Eurovent, 62 Boulevard de Sébastopol,
75003 Paris) (www.eurovent-certification.com)
2
Idelchik I E Handbook of hydraulic resistance 3rd edn. (New
York, NY: Begell House) (1996)
3
Lamont P ‘The reduction with age of the carrying capacity of
pipelines’ J. Inst. Water Engineers 8 53–92 (1954)
4
Fundamentals 2005 ASHRAE Handbook (Atlanta, GA:
American Society of Heating, Refrigerating and AirConditioning Engineers) (2005)
c2
A2
c1
A1
l
γ
c2
No recent experimental data can be found. ASHRAE
reports that the same values of ζ apply for transitions
circular-to-rectangular and rectangular-to-circular. However
the influence of aspect ratio h / w is not reported and has
perhaps not been investigated. In the light of this, values of
ζ should be taken from section 4.11.2.8.
c
c1
γ
c2
Flow of fluids in pipes and ducts
4-61
5
Schneider K J Bautabellen (9th edn.) (Dusseldorf, Germany:
Werner Verlag) (1990)
25
Miller D S Internal flow systems (Cranfield:
Hydromechanics Research Association) (1990)
6
BS EN 10255: 2004: Non-alloy steel tubes suitable for welding or
threading. Technical delivery conditions (London: British
Standards Institution) (2004)
26
Rahmeyer W J ‘Pressure loss coefficients of pipe fittings for
threaded and forged weld pipe fittings for ells, reducing ells,
and pipe reducers’ ASHRAE Trans. 105 (2) 334–354 (1999)
7
BS EN 10220: 2002: Seamless and welded steel tubes. Dimensions
and masses per unit length (London: British Standards
Institution) (2002)
27
Rahmeyer W J ‘Pressure loss data for large pipe ells, reducers
and expansions’ ASHRAE Trans. 108 (1) 360–375 (2002)
28
8
BS 1211: 1958: Specification for centrifugally cast (spun) iron
pressure pipes for water, gas and sewage (London: British
Standards Institution) (1958)
An experimental study of the performance characteristics of 90° elbow
UMC Reports SRF 785 (1985) and 1285 (1986) (Westerville,
OH: United McGill Corporation) (dates as indicated)
29
9
BS EN 1057: 2006: Copper and copper alloys. Seamless, round
copper tubes for water and gas in sanitary and heating applications
(London: British Standards Institution) (2006)
Rahmeyer W J ‘Pressure loss coefficients of pipe fittings for
threaded and forged weld pipe tees’ ASHRAE Trans. 105 (2)
355–385 (1999)
30
10
BS EN 1452-2: 2000: Plastics piping systems for water supply.
Unplasticized poly(vinyl chloride) (PVC-U). Pipes (London:
British Standards Institution) (2000)
Rahmeyer W J ‘Pressure loss data for large pipe tees’
ASHRAE Trans. 108 (1) 376–389 (2002)
31
Madison R D and Parker J R ‘Pressure loss in rectangular
elbows’ ASHRAE Trans. 58 (1936)
32
Smith J R and Jones J W ‘Pressure loss in high velocity flat
oval duct fittings’ ASHRAE Trans. 82 157–176 (1976)
33
Rahmeyer W J ‘Pressure loss data for
Trans. 109 (2) 230–251 (2003)
34
Koch P and Pierson P ‘Et si le calcul des pertes de charge
singulières n’était pas si juste qu’on pouvait le croire?’ Chaud
Froid Plomberie (661) 65–74 (2003)
35
Rahmeyer W J ‘Pressure loss data for PVC pipe elbows, reducers
and expansions’ ASHRAE Trans. 109 (2) 230–251 (2003)
36
Rahmeyer W J ‘Pressure loss coefficients for close-coupled
pipe ell’ ASHRAE Trans. 108 (1) 390–406 (2002)
37
Miller D S Internal flow: A guide to losses in pipe and duct systems.
(Cranfield: British Hydromechanics Research Association)
(1971)
11
BS 7291: Thermoplastics pipes and associated fittings for hot and
cold water for domestic purposes and heating installations in
buildings: Part 1: 2006: General requirements; Part 2: 2006:
Specification for polybutylene (PB) pipes and associated fittings; Part
3: 2006: Specification for cross-linked polyethylene (PE-X) pipes
and associated fittings; Part 4: 1990: Specification for chlorinated
polyvinyl chloride (PVC-C) pipes and associated fittings and solvent
cement (London: British Standards Institution) (dates as
indicated)
12
BS ISO 4065: 1996: Thermoplastics pipes. Universal wall thickness
table (London: British Standards Institution) (1996)
13
BS 2782-11: Method 1121B: 1997 (ISO 161-1: 1996): Methods of
testing plastics. Thermoplastics pipes, fittings and valves.
Thermoplastics pipes for the conveyance of fluids. Nominal outside
diameters and nominal pressures. Metric series (London: British
Standards Institution) (1997)
PVC
British
pipe tees’ ASHRAE
14
Haaland S E ‘Simple and explicit formulas for the friction
factor in turbulent flow’ ASME J. of Fluids Eng. 105 (3) 89–90
(March 1983)
38
Koch P ‘ The influence of Reynolds number and size effects on
pressure loss factors of ductwork components’ Building Serv.
Eng. Res. Technol. 27 (4) 261–300 (2006)
15
Rules of thumb UK/France BSRIA TN 18/1995 (Bracknell:
Building Services Research and Information Association)
(1995)
39
Bersisparic S and Dagonnot J Catalogue des coefficients de
perte d’énergie mécanique (Pressure loss coefficients)
CETIAT NTO 90.307 (Villeurbanne, France: Centre Technique
des Industries Aéraulique et Thermiques) (1990)
16
Ball E F and Webster C ‘Some measurements of water-flow
noise in copper and ABS pipes’ Building Services Engineer 44 (5)
33–40 (May 1976)
40
HVAC
17
Rogers W L ‘Noise and vibration in water piping systems’
ASHRAE J. 1 (3) 83–86 (1959)
41
Rogers G F C and Mayhew Y R Thermodynamic and transport
properties of fluids (London: Blackwell) (1980)
18
BS EN ISO 5167-1: 2003: Measurement of fluid flow by means of
pressure differential devices inserted in circular cross-section conduits
running full. General principles and requirements (London: British
Standards Institution)
42
Eckert E R and Drake R M Analysis of heat and mass transfer
(New York, NY: McGraw-Hill) (1972)
43
National Engineering Laboratory Viscosity of gases in metric
units (London: Her Majesty’s Stationary Office) (1972)
44
The Engineering Toolbox Ethylene glycol heat-transfer fluid
(available at http://www.engineeringtoolbox.com) (accessed 21
November 2006)
19
Noise and vibration control for HVAC ch. 5 in CIBSE Guide B:
Heating, ventilating, air conditioning and refrigeration (London:
Chartered Institution of Building Services Engineers) (2001–2)
20
Huebscher R G ‘Friction equivalents for round square and
rectangular ducts’ ASHVE Trans. 54 101–118 (1948)
21
Heyt J W and Diaz M J ‘Pressure drop in flat oval spiral air
duct’ ASHRAE Trans. 81 (2) 221–232 (1975)
22
Specification for sheet metal ductwork HVCA DW/144 (London:
Heating and Ventilating Contractors Association) (1998)
23
Pressure losses in three-leg pipe junctions: combining flows
Engineering Sciences Data Unit Item 73023 (London: IHS
ESDU International) (1973)
24
Eschman R and Lang W E ‘A critical assessment of high
velocity duct design information’ ASHRAE Trans. 76 157–176
(1970)
systems duct design (3rd edn.) (Chantilly, VA: Sheet Metal
and Air Conditioning Contractors' National Association
(SMACNA)) (1990)
Bibliography
AiCVF Aéraulique: Principes de l’aéraulique appliqués au génie climatique
(Paris: Association d’Ingénieurs de Climatisation Ventilation, et Froid)
(1991)
ASHRAE Duct Fitting Database (Atlanta, GA: American Society of
Heating, Refrigerating and Air-Conditioning Engineers) (2002)
BS EN 1505: 1998: Ventilation for buildings. Sheet metal air ducts and fittings
with rectangular cross-section. Dimensions (London: British Standards
Institution) (1998)
4-62
Reference data
BS EN 1506: 1998: Ventilation for buildings. Sheet metal air ducts and fittings
with circular cross section. Dimensions (London: British Standards
Institution) (1998)
BS ISO 4065: 1996: Thermoplastics pipes. Universal wall thickness table
(London: British Standards Institution) (1996)
Carlson L W and Irvine T F ‘Fully developed pressure drop in
triangular shaped ducts’ ASME J. Heat Transfer 83 441–444 (1961)
Carrier Piping design in Carrier System Design Manual (Syracuse, NY:
Carrier Air Conditioning Company) (1960)
Crowder D Calculation of pipework and ductwork friction loss from first
principles MRC Submission Report (September 2000)
Engineering Toolbox Ethylene glycol based
http://www.engineeringtoolbox.com (March 2004)
heat-transfer
fluids.
Eurovent Catalogue of energy loss coefficients of air handling components
(Paris: Eurovent) (1996) (This report is a simplified summary of the
contents of the European Programme Report(1))
Hydraulic Institute Engineering Data Book (Parsippany, NJ: Hydraulic
Institute) (1979)
Jones C D Friction factor and roughness of United Sheet Metal Company
spiral duct (Westerville, OH: United McGill Corporation) (1979)
Koch P ‘A survey of available data for pressure loss coefficients, ζ , for
elbows and tees of pipework’ Building Serv. Eng. Res. Technol. 153–160
(2000)
Koch P ‘Comparisons and choice of pressure loss coefficients, ζ , for
ductwork components’ Building Serv. Eng. Res. Technol. 22 (3) 167–183
(2001)
Lamont P ‘A review of pipe-friction data and formulae, with a proposed
set of exponential formulae based on the theory of roughness’ Proc. Inst.
Civil Eng. III 248–255 (1954)
Moody L F ‘Friction factors for pipe flow’ ASME Trans. 66 671 (1944)
Plastic Pipe Institute Water flow characteristics of thermoplastic pipe (Irving,
TX: The Plastic Pipe Institute) (1971)
Griggs E I ‘Resistance to flow of round galvanised ducts’ ASHRAE
Trans. 98 (1) (1987)
Sprenger F Friction pressure drops in ducts and pipes Undergraduate thesis
(Coventry: Coventry University School of the Built Environment) (1995)
Hegberg R A ‘Where did the k-factors for pressure loss in pipe fittings
come from?’ ASHRAE Trans. 101 (1) 1264–1278 (1995)
Townsend B S et al. ‘Equivalent round diameter of spiral flat oval ducts’
ASHRAE Trans. 100 (2) 389–395 (1994)
Hennington, Durham and Richardson Design Guide (Omaha, NE:
Hennington, Durham and Richardson) (1981)
4-63
Appendix 4.A1 : Properties of various fluids
4.A1.1
Although the preferred units of dynamic viscosity (η) are
kg·m–1·s–1, the Poise still persists in some sources of data,
for which the following conversion may be useful:
Air and water
See Tables 4.A1.1 and 4.A1.2.
Note that values of density, being the reciprocal of the
specific volume, are best obtained from the psychrometric
data in chapter 1, which cover all values of humidity.
The variation of density with pressure can be obtained
using a value ρ0 from Table 4.A1.1 or the psychrometric
data, and ideal gas equation, namely:
(
p
ρ = ρ0 ———–
1.01325
)
(4.A1.1)
Values of viscosity and specific thermal capacity do not
vary significantly with pressure.
Table 4.A1.1 Some properties of water
1 cP = 0.01 Pa·s = 10–2 kg·m–1·s–1
Similarly, although the preferred units of dynamic
viscosity (ν) are m2·s–1, the Stoke still persists in some
sources of data, for which the following conversion may be
useful:
1 cSt = 0.01 cm2·s–1 = 10–6 m2·s–1
4.A1.2
Water–glycol mixtures
See Tables 4.A1.3 to 4.A1.6. The primary source for this
data has been provided by Shell Chemicals. For low values
of temperature this is supplemented in Tables 4.A1.4 and
4.A1.5 by some sparse internet data(44), the original source
of which is not known, and which required interpolation
from Imperial values.
θ
/ °C
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
ν
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
0.01
4
10
20
999.8
1000.0
999.7
999.8
1752
1551
1300
1002
1.7524
1.5510
1.3004
1.0022
4.210
4.205
4.193
4.183
30
40
50
60
995.6
992.2
988.0
983.2
797
651
544
463
0.8005
0.6561
0.5506
0.4709
4.179
4.179
4.182
4.185
Note: the figure in italics was obtained by extrapolation.
70
80
90
100
977.8
971.8
965.3
958.4
400
351
311
279
0.4091
0.3612
0.3222
0.2911
4.191
4.198
4.201
4.219
Table 4.A1.4 Density of ethylene-glycol–water mixture
110
120
130
140
950.6
943.4
934.6
925.9
252
230
216
195
0.2651
0.2438
0.2258
0.2106
4.233
4.248
4.27
4.29
150
160
170
180
916.6
907.4
897.7
886.5
181
169
158
149
0.1975
0.1862
0.1760
0.1681
4.32
4.35
4.38
4.42
190
200
875.6
864.3
141
134
0.1610
0.1550
4.46
4.51
Table 4.A1.2 Some properties of air at a relative humidity of 50% and at
a pressure of 1.012 bar (from Rogers and Mayhew(41))
θ
/ °C
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
0
5
10
1.29
1.27
1.24
17.15
17.39
17.63
1.006
1.009
1.011
15
20
25
1.22
1.20
1.18
17.88
18.12
18.36
1.014
1.018
1.022
30
35
40
1.16
1.14
1.11
18.55
18.78
19.01
1.030
1.039
1.050
Table 4.A1.3 Freezing temperature of ethylene-glycol–water mixture
(derived from data provided by Shell Chemicals, Rotterdam)
Freezing temperature (/ °C) for ethylene-glycol solution at
stated concentration (% by mass)
25
30
40
50
90
95
100
–10.5
–13.7
–22.5
–33.7
–29.6
–21.8
–12.8
Temp.
/ °C
60
40
20
0
Density, ρ (/ kg·m–3), for stated concentration (% by mass)
0
20
30
40
50
60
80
100
983.2
992.2
999.8
999.8
1007.3
1017.3
1025.6
1031.8
1019.4
1030.3
1040.4
1047.9
1031.7
1042.5
1053.5
1063.9
1042.3
1054.8
1066.4
1078.6
1052.6
1065.5
1078.1
1091.1
1071.4
1084.5
1098.6
1112.3
1086.7
1100.0
1114.8
1129.1
Density, ρ (/ kg·m–3) for stated concentration (% by volume)
–20
–40
0
20
30
40
50
60
80
100
S
S
S
1089
1103
S
S
S
S
1116
1121
1142
1147
S
S
Note: ‘% by mass’ values adapted from data provided by Shell. ‘% by
volume’ values derived from unreferenced data(44); values shown in
italics are best estimates from that source.
‘S’ denotes solid.
S
4-64
Reference data
Table 4.A1.5 Kinematic viscosity of monoethylene-glycol–water mixture
100
60
40
20
θ
/ °C
Kinematic viscosity, ν (/ 10–6·m2·s–1), for stated
concentration (/ % by mass)
Temp.
/ °C
Table 4.A1.9 Some properties of carbon dioxide gas at 1 atm. (Eckert
and Drake(42))
0
20
30
40
50
60
80
100
0.291
0.471
0.656
1.002
0.382
0.675
0.956
1.56
0.457
0.812
1.20
2.01
0.555
1.00
1.54
2.60
0.680
1.27
2.00
3.38
0.790
1.56
2.50
4.44
1.19
2.54
4.35
8.41
2.02
4.54
8.59
17.9
220
250
300
350
400
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
2.4733
2.1667
1.7973
1.5362
1.3424
11.10
12.59
14.96
17.20
19.32
0.783
0.804
0.871
0.900
0.942
Kinematic viscosity, ν (/ 10–6·m2·s–1), for stated
concentration (/ % by volume)
0
–20
0
20
30
40
1.75
6.0
8.6
S
S
S
12
16.8
50
—
24
60
80
100
—
38
—
S
Note: ‘% by mass’ values adapted from data provided by Shell. ‘% by
volume’ values derived from unreferenced data(44); values shown in
italics are best estimates from that source.
‘S’ denotes solid.
Table 4.A1.10 Some properties of carbon monoxide gas at 1 atm. (Eckert
and Drake(42))
θ
/ °C
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
220
220
250
2.4733
1.5536
1.3668
11.10
13.83
15.40
0.783
1.043
1.042
300
350
400
1.1387
0.9742
0.8536
17.84
20.09
22.19
1.042
1.043
1.048
Table 4.A1.6 Specific thermal capacity of monoethylene-glycol–water
mixture
Specific thermal capacity, cp (/ kJ·kg–1·K–1), for stated
concentration (/ % by mass)
Temp.
/ °C
0
20–60
4.19
20
30
40
50
60
80
100
3.89
3.76
3.59
3.39
3.21
2.79
2.40
Specific thermal capacity, cp (/ kJ·kg–1·K–1), for stated
concentration (/ % by volume)
0
0
4.21
20
30
40
50
60
80
100
3.91
3.72
3.53
3.32
3.11
2.72
2.33
Table 4.A1.11 Some properties of ammonia gas at 1 atm. (Eckert and
Drake(42))
θ
/ °C
220
273
323
373
423
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
0.3828
0.7929
0.6487
0.5590
0.4934
7.255
9.353
11.03
12.89
14.67
2.198
2.177
2.177
2.236
2.315
Note: ‘% by mass’ values adapted from data provided by Shell. ‘% by
volume’ values derived from unreferenced data(44); values shown in
italics are best estimates from that source.
4.A1.4
Fuel gases
See Table 4.A1.12.
4.A1.3
Table 4.A1.12 Some properties of fuel gases at 1 atm. (from Eckert and
Drake(42) and HMSO(43))
Gases
See Tables 4.A1.7 to 4.A1.11
Fuel gas
θ
/ °C
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
Table 4.A1.7 Some properties of oxygen gas at 1 atm. (Eckert and
Drake(42))
Butane
(C4H10)
273
288
2.66
2.52
6.8
—
—
1.671
10.44
10.80
11.13
2.207
—
2.237
8.03
—
—
1.625
—
1.703
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
Methane
(CH4)
273
288
298
0.717
0.680
0.657
150
200
250
2.619
1.956
1.562
11.49
14.85
17.87
0.9178
0.9131
0.9157
Propane
(C3H8)
273
288
298
2.02
1.91
1.85
300
350
400
1.301
1.113
0.975
20.63
23.16
25.54
0.9203
0.9291
0.9420
Note: values of η and cp do not vary much with pressure; all the
properties vary with temperature.
θ
/ °C
Table 4.A1.8 Some properties of nitrogen gas at 1 atm. (Eckert and
Drake(42))
θ
/ °C
100
200
300
400
ρ
/ kg·m–3
η
/ 10–6 kg·m–1·s–1
cp
/ kJ·kg–1·K–1
3.481
1.711
1.142
0.8538
6.862
12.95
17.84
21.98
1.0722
1.0429
1.0408
1.0459
4.A1.5
Fuel oils
See Table 4.A1.13. The viscosity of fuel oils varies
considerably with temperature. Even within a single grade
of oil, properties can vary within a specified band. Thus
the properties of a particular oil are best obtained from the
manufacturer. Some approximate values are given in Table
4.A1.13, taken from the graphs in chapter 5 of this Guide.
Flow of fluids in pipes and ducts
4-65
Table 4.A1.13 Density and kinematic viscosity of fuel oils
Fuel oil
Class
Kerosene
Density, ρ
/ kg·m–3 at 15 °C
C2
Kinematic viscosity, ν (/ 10–6·m2·s–1),
at stated temperature (/ °C)
803
–10
0
0.34
2.75
Gas oil
D
850
Light fuel oil
E
940
11
—
Medium fuel oil
F
970
—
Heavy fuel oil
G
980
—
7.8
20
40
60
80
1.0–2.0
—
—
—
—
—
160
58
25
13.5
—
850
220
75
32
20.0 max
—
3400
705
205
75
40.0 max
600
1.5–5.5
—
100
8.2
Appendix 4.A2 : Pipe and duct sizing
4.A2.1
General
For a required mass flow, the constraint should normally
be that the mean fluid velocity should not exceed a
particular value, cmax. Such advice is given in section 4.5.1
for water, and in section 4.8.1 for air.
Values of pipe roughness are given in Table 4.1 and some
typical values are shown in Table 4.A2.1. These do not
necessarily constitute a recommendation for those wishing
to compute new values. The values of k chosen for
polymers are mid-range values, but for these materials the
surface is so smooth that the value of k is not significant in
the calculation.
Values of the fluid properties, i.e density ρ, and either
dynamic viscosity η or kinematic viscosity ν (ν = η / ρ),
are required and may be obtained from Appendix 4.A1.
The pipe to be selected can now be chosen, usually by
rounding up to the next available internal diameter, di ,
from which the nominal size will also be evident.
The linear steps in the calculation are now as follows.
Step 2
The actual fluid mean velocity is given by:
4 qm
c = ———
π ρ di 2
(4.A2.2)
Step 3
The Reynolds number is obtained from equation 4.2:
cd
Re = —–i
ν
Step 1
(4.A2.3)
The minimum internal pipe diameter is then given by:
(
4 qm
dmin = ———–
π ρ cmax
)
Step 4
0.5
(4.A2.1)
If the flow is laminar (Re < 2000), λ is obtained from
equation 4.3, i.e:
64
λ = —–
Re
Table 4.A2.1 Roughness coefficients (see also Table 4.1)
Material
Roughness coefficient,
k / mm
Pipework (metal):
— copper
— heavy grade steel
— cast iron
— galvanised steel
0.0015
0.046
1.0
0.15
Pipework (plastic):
— PB
— PE-X
— PVC-U
— ABS
0.007
0.007
0.007
0.007
Ductwork:
— galvanised steel
— spirally wound galvanised steel
0.075
0.090
(4.A2.4)
If the flow is turbulent (Re > 3000), λ is obtained from
equation 4.5, i.e:
[
( ) ]
1
6.9
k/d
—– = –1.8 log —– + ——–
√λ
Re
3.71
1.11
(4.A2.5)
Step 5
The pressure drop, or the pressure drop per unit length, is
obtained from equation 4.1:
Δp
1
—– = λ — 1/2 ρ c2
l
di
(4.A2.6)
4-66
Reference data
4.A2.1
Worked example: pipework
Problem
is required at a mean
A mass flow of water of 5.74
water temperature of 60 °C. Copper pipe is to be used.
The flow is turbulent, therefore equation (4.A2.5) applies:
[ ( )]
(
[
1
6.9
k /d
— = –1.8 log —– + ——–
–
√λ
Re
3.71
Solution
From Appendix 4.A1, for water:
ρ = 983.2 kg·m–3
—
ν = 0.4709 x 10–6 m2·s–1
]
m·s–1·m
–———
m2·s–1
= 2.16 × 105
kg·s–1
—
[
1.391 × 0.0731
Re = —–————–
0.4709 × 10–6
1.11
1
6.9
0.0015 ⫼ 73.1
—– = –1.8 log —–——––– + ——–––––—––
5
√λ
2.16 × 10
3.71
[
From Table 4.A2.1, for copper, k = 0.0015 mm
= –1.8 log 31.94 × 10–6 + 1.4605 × 10–6
From Table 4.6, an approximate value of cmax might be
1.5 m·s–1.
= 8.057
) ]
1.11
]
Therefore:
Using equation 4.A2.1:
(
(
λ = 0.01540
)
4 qm
dmin = ———–
π ρ cmax
0.5
From equation 4.A2.6:
)
0.5
4 × 5.74
= —————–—
π × 983.2 × 1.5
[
kg·s–1
——————–
(kg·m–3)(m·s–1)
]
Δp
1
—– = λ — 1/2 ρ c2
l
di
0.5
A possible choice of pipe is copper pipe R290 76.1 × 1.5,
having di = 73.1 mm.
Using equation 4.A2.2:
4 qm
c = ———
π ρ di 2
= 1.391
Pa
—–
m
= 200.5 Pa·m–1
In the event that a particularly long length of pipe were
involved, pumping requirements could be much reduced
by choosing the next larger pipe size. Equally, if only a
short length of pipe were involved, the next size smaller
could be chosen but the higher water velocity might lead
to greater noise generation.
The actual diameter and velocity may now be calculated.
4 × 5.74
= ————————–
π × 983.2 × 0.07312
[ ]
Δp
1
—– = 0.015405 —–––– 951.3
l
0.0731
= 0.0704 m = 70.4 mm
In summary:
[
kg·s–1
———––—
(kg·m–3) m2
]
—
c = 1.391 m·s–1
—
pv = 951.3 Pa
—
Δp / l = 200.5 Pa·m–1
m·s–1
The method may easily be programmed as a spreadsheet.
Table 4.A2.2 suggests a possible format for presenting the
results.
The velocity pressure is given by:
pv = 1/2 ρ c2
Hence:
Table 4.A2.2 Pipe sizing spreadsheet: possible format for displaying
results of calculation
pv = 1/2 × 983.2 × 1.391
[(kg·m–3)(m2·s–2)]
[= N·m–2 = Pa]
= 951.3 Pa
Using equation 4.A2.3:
cd
Re = —–i
ν
Input
Output
ρ c2
(Pa)
Temp
(°C)
Pipe size
(mm × mm)
c
(m·s–1)
Δp / l
(Pa·m–1)
5.74
60
66.7 × 1.2
1.80
372
1589
5.74
60
76.1 × 1.5
1.39
200
951
5.74
60
88.9 × 1.5
1.01
92
499
Mass flow
(kg·s–1)
1/
2
Fluid: water
Choose another pipe diameter?
Flow of fluids in pipes and ducts
4.A2.2
4-67
Worked example: ductwork
= 0.312 m2 = 312 000 mm2
With airflow, the requirement may be in terms of mass
flow (for heating or cooling requirements), or in terms of
volume flow (for ventilation requirements), illogical
though this may seem. In the following example, mass
flow is specified.
Problem
Consulting Table 4.17 for preferred dimensions of flat-oval
pipe, the following sizes would seem possible: 300 × 1115,
400 × 895, 450 × 865, 500 × 755.
For reasons of space, 450 mm × 865 mm is chosen. The
actual velocity must now be determined.
From Table 4.17:
kg·s–1
of air is required at a mean
A mass flow of 2.19
water temperature of 27 °C and 30% saturation. Flat-oval
galvanised ductwork is to be selected
A = 345 793 mm2 = 0.345793 m2
From Table 4.18:
Solution
de = 653 mm
The air conditions are assumed to be at a pressure of
101.3 kPa (unless otherwise specified). From the
psychrometric tables in chapter 1:
—
specific volume, v = 0.86 m3/kg dry air
—
moisture content, g = 0.0068 kg of steam/kg dry air.
Actual velocity, c, is given by:
= 5.408 m·s–1
Hence, the air density is:
[
]
kg·kg–1
–––––––
m3·kg–1
1.0068
ρ = ———
0.86
= 1.171
[ ]
m3·s–1
––––––
m2
1.870
qv
c = —– = ——–—
A
0.3458
kg·m–3
From Appendix 4.A1, Table 4.A1.2, by interpolation:
η = 18.44 × 10–6 kg·m–1·s–1
Everything can now be calculated as for the pipework
example.
Note that the velocity calculated above is the real velocity
of air in the flat-oval duct chosen. It is not the
hypothetical velocity in the equivalent circular duct.
However, for the purpose of calculating the equivalent
Reynolds number, Re, it will be sufficient.
From equation 4.A2.3, using the equivalent diameter:
But:
cd
Re = —–e
ν
η
ν=—
ρ
5.408 × 0.653
Re = ——————
15.49 × 10–6
Hence:
18.44 × 10–6
ν = —————
0.86
[
]
kg·m–1·s–1
———–—
kg·m–3
= 2.28 × 105
[ ( )]
(
[
1
6.9
k /d
—– = –1.8 log —– + ——–
√λ
Re
3.71
From Table 4.1, taking a mean value, for spirally wound
galvanised ductwork, k = 0.09 mm
From Table 4.11, an approximate value of cmax might be
6 m·s–1.
[
kg·s–1
——––
kg·m–3
]
= 1.870 m3·s–1
[
Hence:
From equation 4.20:
[
m3·s–1
——––
m·s–1
]
]
) ]
1.11
= –1.8 log 30.26 × 10–6 + 12.12 × 10–6 = 7.871
λ = 0.01614
Thus, to find the minimum area, Amin:
1.11
1
6.9
0.09 ⫼ 652
—– = –1.8 log —–——––– + ——–––––—–
5
√λ
2.28 × 10
3.71
It is worthwhile calculating the volume flow:
1.870
qv
Amin = —––
= ——–
cmax
6
]
The flow is turbulent, therefore equation 4.A2.5 applies:
= 15.49 × 10–6 m2 ·s–1
2.19
qm
qv = —–
= ——–
ρ
1.171
[
m·s–1·m
–––––––
m2 ·s–1
ρ 16 qv2
Δp
—– = λ –– –——
l
2 π2 de5
4-68
Reference data
1.171 16 × 1.870 2
= 0.01614 ––––– –——–––––
2
π2 0.652 5
[=
[
]
kg·m–3·m6·s–2
————–––
m5
N·m–3
=
Pa·m–1]
= 0.455 Pa·m–1
For use with ζ for ductwork components, the actual air
velocity is used. Thus:
pv = 1/2 ρ c2
= 1/2 × 1.171 × 5.4082
In summary, for the chosen size of flat-oval duct (450 mm
× 865 mm):
—
c = 5.408 m·s–1
—
pv = 17.12 Pa
—
Δp / l = 0.455 Pa·m–1
The method may easily be programmed as a spreadsheet.
Table 4.A2.3 suggests a possible format for presenting the
results.
Table 4.A2.3 Pipe sizing spreadsheet: possible format for displaying
results of calculation
[(kg·m–3)(m2·s–2) = Pa ]
= 17.12 Pa
In the event that a particularly long length of duct were
involved, fan power consumption could be much reduced
by choosing the next larger duct size. Equally, if only a
short length of duct were involved, the next smaller size
could be chosen, but the higher air velocity might lead to
greater noise generation.
Input
Mass flow
(kg·s–1)
Temp
(°C)
Output
Duct size
(mm × mm)
c
(m·s–1)
Δp / l
(Pa·m–1)
ρ c2
(Pa)
1/
2
Fluid: air
2.19
27
450 × 865
5.41
0.455
17.12
2.19
27
400 × 895
5.78
0.557
19.55
2.19
27
500 × 755
5.77
0.505
19.53
5.14
0.389
15.47
Choose another duct size?
2.19
27
500 × 835
Flow of fluids in pipes and ducts
4-69
Appendix 4.A3 : Capacity (K) and complex networks
Whilst it is most common practice for components and
fittings to have their pressure drop characteristic given in
terms of the pressure loss factor ζ , most manufacturers of
valves and dampers quote the performance in terms of the
‘capacity’ (K), defined in the following relationship:
—
qv = K √Δp
(4.A3.1)
This implies that K has units, usually of m3/(h·bar0.5) for
liquids, or m3/(s·Pa0.5) for gases. Some manufacturers may
quote values of K with different units, so care is needed.
There is a relation between K and ζ , but it is not really
necessary to convert one to the other. Pressure drops are
more simply calculated separately for those components
for which K is given.
K is also useful when dealing with the authority of a valve,
and in the prediction of flows in complex circuits.
Elements in series
K1
K2
For elements of the circuit in series, the overall capacity
Ko is given by:
1
1
1
—=—+—
K o K1 K2
(4.A3.3)
Thus for a complex circuit, the entire circuit can be
simplified until the circuit overall, ‘total’ capacity Ktot is
obtained. Equation 4.A3.1 then permits the calculation of
pressure drop for any value of total flow. Thus the
pipework or ductwork pressure drop characteristic is
obtained.
For every branch of a circuit, once the value of pressure
drop is known for a particular volume flow, the value of K
for that branch can be obtained from equation 4.A3.1.
1
4
2
Elements in parallel
3
5
K1
Figure 4.A3.1 Example of a complex circuit
K2
For elements of the circuit in parallel, the overall capacity
Ko is given by:
Ko = K 1 + K 2
(4.A3.2)
For example, in Figure 4.A3.1, sub-circuits 1, 2 and 3
having capacities K1, K2 and K3 respectively, can be
simplified to give Kx using equation 4.A3.2 for circuits in
parallel. Sub-circuits 4, 5 and x having capacities K4, K5
and Kx respectively, can be simplified to give Ktot using
equation 4.A3.3 for circuits in series.
Equation 4.A3.1 can then be used to determine the
characteristic for the system.
4-70
Reference data
Appendix 4.A4 : Steam flow in pipes
4.A4.1
General
Pre-calculated values of pressure drop are given in Table
4.A4.1 (pages 4.68 to 4.70). Values of the pressure factor Z
are given in Table 4.A4.2.
The calculation of pressure drops in flows of steam and
natural gas is much more complex than that of water and
of air. With water, the density remains constant irrespective of pressure in the system. With air, its use in
ventilation systems is always at a pressure of about around
1 bar so some general predictions can be made. With both
steam and natural gas, the density varies considerably
with pressure and a wide range of pressures are used.
Furthermore, large pressure drops along the pipework are
generally acceptable, and these affect the fluid density as it
flows along. The calculations are therefore best left to a
specialist.
4.A4.2
The values used for density ρ and kinematic viscosity ν
were obtained from the following relationships:
—
ρ = 7.83 × 10–3 p0.94
—
ν = 9.79 × 10–4 p–0.842
where the following units must be used: p (kPa (absolute)),
ρ (kg·m–3) and ν (m2·s–1).
4.A4.2
Steam flow in pipes
The pressure drop of the condensate flow may be obtained
in the same way as for hot water where:
The pressure drop due to friction in steel pipes may be
calculated from:
Z1 – Z2 30.32 qm1.889
——— = —————–
l
103 d 5.027
(a)
thermostatic traps, having small pressure differentials between inlet and outlet, are employed and
(b)
air and other gases are prevented from entering the
condensate drain by the use of automatic vents.
(4.A4.1)
where Z is given by:
Z = p1.929
Flow of condensate in pipes
(4.A4.2)
If air is required to traverse the condensate main and if
flash steam is produced by the pressure drops in the trap
and system then the resistance is greatly increased. The
pressure drop in two-phase flow is always greater than for
either phase individually, the calculation for which is
beyond the scope of this Guide. In the absence of definite
data it is recommended that where flash steam can occur
the condensate mains should be sized for three times the
normal hot water discharge.
where the following units must be used: qm (kg·s–1), d (m),
l (m), p (kPa (absolute)) and Z (kPa1.929).
These equations have been developed to cover initial
steam pressures of between 100 kPa and 1000 kPa and for
velocities ranging from 5 m·s–1 to 50 m·s–1. They may be
used with less accuracy for conditions outside these limits.
Table 4.A4.2 Pressure factors Z for compressible flow (from equation 4.A4.2)
Pressure,
p / kPa
Pressure factor, Z (/ kPa1.929) for stated pressure, p / kPa
0
10
20
30
40
50
60
70
80
90
0
100
200
300
400
0
7210
27 500
60 000
105 000
85
8670
30 200
63 900
110 000
323
10 300
33 000
68 000
115 000
707
12 000
36 000
72 100
120 000
1230
13 800
39 000
76 400
126 000
1890
15 800
42 230
80 800
131 000
2690
17 900
45 500
85 300
137 000
3620
20 100
49 000
90 000
143 000
4690
22 400
52 500
94 700
149 000
5880
24 900
56 200
99 600
155 000
500
600
700
800
900
1000
161 000
229 000
308 000
398 000
500 000
612 000
167 000
236 000
316 000
408 000
510 000
—
174 000
244 000
325 000
418 000
521 000
—
180 000
251 000
334 000
427 000
532 000
—
187 000
259 000
343 000
437 000
543 000
—
193 000
267 000
351 000
448 000
555 000
—
200 000
275 000
361 000
458 000
566 000
—
207 000
283 000
370 000
468 000
577 000
—
214 000
291 000
379 000
479 000
589 000
—
221 000
299 000
389 000
489 000
601 000
—
Flow of fluids in pipes and ducts
4-71
Table 4.A4.1 Flow of saturated steam in heavy steel pipes
HEAVY GRADE STEEL
⫽ mass flow rate (kg·s–1)
qm
p
⫽ pressure (absolute) (kPa)
ΔZ / l ⫽ pressure drop per unit length (Pa1.929·m–1)
ΔZ / l
SATURATED STEAM
Mass flow rate, qm, for stated nominal outside diameter
p
ΔZ / l
p
10 mm
15 mm
20 mm
25 mm
32 mm
40 mm
0.0001
0.0002
0.0003
0.0004
0.0004
0.0003
0.0004
0.0006
0.0008
0.0009
0.0007
0.001
0.001
0.001
0.002
0.001
0.002
0.003
0.003
0.004
0.003
0.004
0.006
0.007
0.008
0.004
0.006
0.009
0.011
0.013
0.0005
0.0005
0.0006
0.0006
0.0007
0.001
0.001
0.001
0.001
0.001
0.002
0.002
0.003
0.003
0.003
0.004
0.005
0.005
0.005
0.006
0.009
0.010
0.011
0.012
0.013
0.014
0.016
0.017
0.018
0.019
0.0007
0.0008
0.0009
0.0009
0.001
0.001
0.002
0.002
0.002
0.002
0.003
0.004
0.004
0.004
0.005
0.006
0.007
0.008
0.008
0.009
0.013
0.015
0.017
0.018
0.019
0.020
0.023
0.025
0.027
0.029
45
50
55
60
65
0.001
0.001
0.001
0.001
0.001
0.002
0.002
0.002
0.003
0.003
0.005
0.005
0.006
0.006
0.006
0.009
0.010
0.011
0.011
0.012
0.021
0.022
0.023
0.024
0.025
0.031
0.033
0.035
0.037
0.038
45
50
55
60
65
70
75
80
85
90
0.001
0.001
0.001
0.001
0.002
0.003
0.003
0.003
0.003
0.003
0.006
0.007
0.007
0.007
0.007
0.012
0.012
0.013
0.013
0.014
0.026
0.027
0.028
0.029
0.030
0.040
0.041
0.043
0.044
0.045
70
75
80
85
90
0.002
0.002
0.002
0.003
0.003
0.003
0.003
0.005
0.006
0.007
0.008
0.008
0.011
0.014
0.016
0.014
0.014
0.021
0.026
0.030
0.031
0.031
0.045
0.056
0.065
0.047
0.048
0.069
0.086
0.100
95
100
200
300
400
0.004
0.004
0.005
0.005
0.005
0.008
0.009
0.010
0.010
0.011
0.018
0.020
0.022
0.024
0.025
0.034
0.037
0.041
0.043
0.046
0.074
0.081
0.088
0.094
0.101
0.112
0.124
0.134
0.144
0.153
0.005
0.008
0.010
0.011
0.013
0.011
0.017
0.021
0.024
0.027
0.026
0.038
0.047
0.055
0.062
0.049
0.071
0.086
0.102
0.115
0.106
0.153
0.190
0.222
0.249
0.162
0.234
0.290
0.338
0.380
0.014
0.015
0.017
0.018
0.019
0.030
0.032
0.034
0.037
0.039
0.068
0.074
0.080
0.085
0.090
0.126
0.137
0.147
0.157
0.166
0.275
0.298
0.320
0.340
0.360
0.418
0.454
0.487
0.519
0.548
0.027
0.033
0.039
0.044
0.048
0.056
0.069
0.081
0.091
0.100
0.129
0.160
0.187
0.210
0.231
0.239
0.296
0.345
0.388
0.428
0.519
0.644
0.750
0.844
0.929
0.791
0.981
1.14
1.29
1.42
1
2
4
6
8
10
12
14
16
18
20
25
30
35
40
95
100
200
300
400
500
600
700
800
900
1000
2000
3000
4000
5000
6000
7000
8000
9000
10 000
20 000
30 000
40 000
50 000
60 000
10
30
50
100
300
500
1000
3000
30
50
1
2
4
6
8
10
12
14
16
18
100
300
500
20
25
30
35
40
500
600
700
800
900
1000
3000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10 000
20 000
30 000
40 000
50 000
60 000
Table continues
4-72
Reference data
Table 4.A4.1 Flow of saturated steam in heavy steel pipes — continued
HEAVY GRADE STEEL
⫽ mass flow rate (kg·s–1)
qm
p
⫽ pressure (absolute) (kPa)
ΔZ / l ⫽ pressure drop per unit length (Pa1.929·m–1)
ΔZ / l
SATURATED STEAM
Mass flow rate, qm, for stated nominal outside diameter
p
ΔZ / l
p
50 mm
65 mm
80 mm
90 mm
100 mm
125 mm
0.008
0.011
0.017
0.021
0.024
0.016
0.023
0.034
0.042
0.049
0.025
0.036
0.052
0.065
0.076
0.037
0.054
0.077
0.096
0.112
0.051
0.074
0.107
0.132
0.154
0.092
0.133
0.192
0.238
0.277
0.027
0.030
0.032
0.035
0.037
0.055
0.060
0.065
0.070
0.075
0.085
0.094
0.102
0.109
0.116
0.126
0.138
0.150
0.161
0.172
0.173
0.191
0.207
0.222
0.237
0.312
0.344
0.373
0.400
0.426
10
12
14
16
18
20
25
30
35
40
0.039
0.044
0.048
0.052
0.056
0.079
0.089
0.098
0.106
0.114
0.123
0.138
0.152
0.165
0.177
0.181
0.204
0.225
0.244
0.262
0.250
0.281
0.310
0.336
0.361
0.450
0.507
0.558
0.606
0.650
20
25
30
35
40
45
50
55
60
65
0.060
0.063
0.066
0.069
0.072
0.121
0.128
0.135
0.141
0.147
0.189
0.200
0.210
0.220
0.229
0.279
0.295
0.310
0.324
0.339
0.384
0.406
0.427
0.447
0.467
0.692
0.732
0.769
0.806
0.841
45
50
55
60
65
70
75
80
85
90
0.075
0.078
0.081
0.084
0.086
0.153
0.159
0.165
0.170
0.175
0.239
0.247
0.256
0.264
0.273
0.352
0.365
0.378
0.390
0.402
0.485
0.504
0.521
0.538
0.555
0.874
0.907
0.938
0.969
0.999
70
75
80
85
90
0.089
0.091
0.131
0.163
0.190
0.180
0.185
0.267
0.331
0.386
0.280
0.288
0.416
0.516
0.600
0.414
0.425
0.614
0.761
0.886
0.571
0.586
0.846
1.05
1.22
1.03
1.06
1.52
1.89
2.20
0.213
0.235
0.255
0.274
0.291
0.434
0.478
0.519
0.557
0.593
0.676
0.744
0.807
0.866
0.922
0.997
1.10
1.12
1.28
1.36
1.37
1.51
1.64
1.76
1.88
2.48
2.73
2.96
3.17
3.38
500
600
700
800
900
0.308
0.445
0.551
0.642
0.722
0.627
0.905
1.12
1.31
1.47
0.975
1.41
1.74
2.03
2.29
1.44
2.08
2.57
3.00
3.34
1.98
2.86
3.55
4.13
4.65
3.57
5.16
6.39
7.44
8.38
1000
2000
3000
4000
5000
0.795
0.863
0.926
0.986
1.04
1.62
1.76
1.88
2.01
2.12
2.52
2.73
2.93
3.12
3.23
3.71
4.03
4.33
4.60
4.87
5.12
5.56
5.97
6.35
6.71
9.22
10.0
10.7
11.4
12.1
6000
7000
8000
9000
10 000
1.50
1.86
2.17
2.44
2.69
3.06
3.79
4.42
4.97
5.48
4.76
5.90
6.87
7.74
8.52
7.03
8.71
10.1
11.4
12.6
9.69
12.0
14.0
15.7
17.3
17.4
21.6
25.2
28.3
31.2
20 000
30 000
40 000
50 000
60 000
1
2
4
6
8
10
12
14
16
18
95
100
200
300
400
50
100
300
500
500
600
700
800
900
1000
2000
3000
4000
5000
6000
7000
8000
9000
10 000
20 000
30 000
40 000
50 000
60 000
1000
3000
50
100
300
500
1000
3000
1
2
4
6
8
95
100
200
300
400
Table continues
Flow of fluids in pipes and ducts
4-73
Table 4.A4.1 Flow of saturated steam in heavy steel pipes — continued
HEAVY GRADE STEEL
⫽ mass flow rate (kg·s–1)
qm
p
⫽ pressure (absolute) (kPa)
ΔZ / l ⫽ pressure drop per unit length (Pa1.929·m–1)
ΔZ / l
SATURATED STEAM
Mass flow rate, qm, for stated nominal outside diameter
p
150 mm
ΔZ / l
p
175 mm
200 mm
225 mm
250 mm
300 mm
0.149
0.215
0.310
0.385
0.448
0.235
0.339
0.489
0.606
0.705
0.327
0.472
0.681
0.844
0.983
0.445
0.642
0.926
1.15
1.34
0.600
0.866
1.25
1.55
1.80
0.965
1.39
2.01
2.49
2.90
10
12
14
16
18
0.504
0.555
0.602
0.647
0.688
0.794
0.874
0.949
1.02
1.08
1.11
1.22
1.32
1.42
1.51
1.50
1.66
1.80
1.93
2.05
2.03
2.24
2.43
2.60
2.77
3.26
3.59
3.90
4.19
4.46
20
25
30
35
40
0.728
0.819
0.902
0.979
1.05
1.15
1.29
1.42
1.54
1.65
1.60
1.80
1.98
2.15
2.30
2.17
2.44
2.69
2.92
3.13
2.93
3.30
3.63
3.94
4.23
4.71
5.30
5.84
6.34
6.80
45
50
55
60
65
1.12
1.18
1.24
1.30
1.36
1.76
1.86
1.96
2.05
2.14
2.45
2.59
2.73
2.86
2.98
3.34
3.53
3.71
3.88
4.05
4.50
4.76
5.00
5.24
5.47
7.24
7.65
8.05
8.43
8.79
45
50
55
60
65
70
75
80
85
90
1.41
1.46
1.52
1.57
1.61
2.22
2.31
2.39
2.46
2.54
3.10
3.21
3.33
3.43
3.54
4.22
4.37
4.52
4.67
4.81
5.69
5.90
6.10
6.30
6.49
9.14
9.48
9.81
10.1
10.4
70
75
80
85
90
1.66
1.71
2.46
3.05
3.55
2.61
2.69
3.88
4.81
5.60
3.64
3.74
5.40
6.70
7.80
4.95
5.09
7.35
9.11
10.6
6.68
6.87
9.91
12.3
14.3
10.7
11.0
15.9
19.8
23.0
500
600
700
800
900
4.00
4.40
4.78
5.13
5.46
6.30
6.94
7.52
8.08
8.60
8.77
9.66
10.5
11.3
12.0
11.9
13.1
14.3
15.3
16.3
16.1
17.7
19.2
20.6
22.0
25.9
28.5
30.9
33.2
35.3
1000
2000
3000
4000
5000
5.77
8.33
10.3
12.0
13.5
9.09
13.1
16.3
18.9
21.3
12.7
18.3
22.7
26.4
29.7
17.2
24.9
30.8
35.9
40.4
23.2
33.5
41.6
48.4
54.5
37.4
53.9
66.8
77.8
87.6
1000
2000
3000
4000
5000
6000
7000
8000
9000
10 000
14.9
16.2
17.4
18.5
19.5
23.5
25.5
27.3
29.1
30.8
32.7
35.5
38.1
40.5
42.9
44.5
48.3
51.8
55.1
58.3
60.0
65.1
69.9
74.4
78.6
96.5
105
112
120
126
6000
7000
8000
9000
10 000
20 000
30 000
40 000
50 000
60 000
28.2
34.9
40.7
45.8
50.4
44.4
55.0
64.1
72.1
79.4
61.9
76.7
89.3
101
111
84.1
104
121
137
151
182
226
263
296
326
20 000
30 000
40 000
50 000
60 000
1
2
4
6
8
95
100
200
300
400
100
300
500
1000
3000
113
141
164
184
203
100
300
500
1000
3000
1
2
4
6
8
10
12
14
16
18
20
25
30
35
40
95
100
200
300
400
500
600
700
800
900
4-74
Reference data
Appendix 4.A5 : Compressible flow
In the case of compressible fluids flowing under conditions where the pressure drop is considerable in
proportion to the initial pressure (greater than 10 per
cent), the change in density between the initial and final
condition should be taken into account.
For determining Reynolds number (Re = ρ c d / η) there is
no problem. For a particular mass flow and constant pipe
diameter, c is inversely proportional to density; thus
density change has no effect on Reynolds number.
Viscosity η varies little with pressure (though varying
considerably with temperature). Thus, despite large
changes in pressure, Re and λ will remain constant, and
the calculation of total pressure drop need take into
account only the variation of density and velocity between
the inlet and outlet:
In other cases the theoretical equations become complex
and use is made of approximate formula derived empirically.
In all of the following equations, x, y, K1, K2 and K3 are
experimentally determined.
The equations are generally of the form:
dp
dl
= K1
qmx
(4.A5.3)
d ( 2 x + y ) ρ ( x −1)
Variation of density is of the form:
ρ = K2 p n
(4.A5.4)
Substitution into the previous equation gives:
2
∫
1
dp =
λ
2d
2
∫ρc
2
dl
l
1
Still considering isothermal flow, where despite pressure
loss there is sufficient heat transfer to maintain the fluid at
the temperature of the surroundings, the pressure loss
may be represented by:
p12 − p22 =
p1m − p2m
(4.A5.1)
32
2
qm
RT
2 4
π d
⎛ λl
p ⎞
+ ln 1 ⎟
⎜
p2 ⎠
⎝ 2d
(4.A5.2)
= K3
qmx
d (2 x + y)
(4.A4.5)
Table 4.A5.1 gives some values of the constants for steam
and compressed air.
Table 4.A5.1 Values of constants for steam and compressed air
Fluid
x
y
m
K3
Steam
1.889
1.249
1.929
3.032 × 10–3
Compressed air
1.889
1.249
1.929
4.268 × 10–3
5-1
5
Fuels and combustion
5.1
Introduction
5.2
Classification of fuels
5.3
Primary fuels
5.4
Secondary fuels
5.5
Specification of fuels
5.6
Combustion data
5.7
Stack losses
5.1
Introduction
There have been no significant changes in the classification or properties of fossil fuels since the 2001 edition of
this chapter. In addition there have been no changes in air
pollution regulations relevant to Local Authority supervision and the Clean Air Act 1993(1). Following the
ratification of the Kyoto treaty by Russia, new impetus has
been given to global greenhouse gas abatement in line
with Treaty obligations. The UK’s target is to reduce
emissions by 12.5% below 1990 levels by 2008–2012. A
further goal is to cut the UK’s emission of carbon dioxide
by 20% below 1990 levels by 2010. Major economic and
other measures have been introduced by the UK
government to limit fossil fuel usage and hence carbon
emissions. These include the Climate Change Levy(2,3) on
non-domestic users, promotion of energy conservation
with renewed emphasis on combined heat and power,
emissions trading and financial incentives for renewable
energy utilisation*. Building Regulations Approved
Document L2A (2006)(4) introduced a target CO2 emission
rate for new buildings other than dwellings.
As noted in earlier editions of this chapter, the data
presented are limited to those required by a practising
building services engineer. They are not intended to
represent full property specifications for each class of fuel
and reference should be made to suppliers and standard
literature for further information. A bibliography is
included at the end of the chapter. In some places sources
of information are included in brackets at the end of a
sentence. If appropriate these are intended to be accessed
using internet search engine(s). The familiar structure of
the previous edition has been retained and data assembled
according to the previous format.
* Up-to-date information may be obtained from the Carbon Trust
(www.carbontrust.co.uk).
5.2
Classification of fuels
Fossil fuels may be classified into primary and secondary
groups. Primary fuels occur naturally and are formed
within a geological time scale from the decay of animal
and vegetable matter. In general secondary fuels are
prepared from primary fuels, with the intention of
modifying the properties to suit particular applications.
Electricity is sometimes classed as a secondary fuel.
The carbon to hydrogen ratio of the fuel can also be used
as a means of classification. This ratio varies on a mass
basis from about 3:1 for natural gas, 7.6:1 for heavy fuel
oil, up to 30:1 for anthracites. Properties such as gross
calorific value and stoichiometric air requirement are seen
to vary in a regular manner with carbon to hydrogen ratio.
The ratio can also affect flame parameters such as
luminosity.
5.3
Primary fuels
5.3.1
Coal
British coals are classified according to caking properties
(Gray King Assay) and percentage volatile matter content.
These and other properties are related to the rank or age of
the coal. The Coal Rank Code (CRC) classification divides
coals into groups numbered in hundreds from 100 to 900,
the groups being sub-divided into classes and sub-classes
for a closer definition of property ranges.
Caking propensity increases from zero at both ends of the
scale (groups 100 and 900) to a maximum in groups 300
and 400. Coals in group 100 are the anthracites; those in
group 200 comprise the low volatile steam coals (coals in
these two groups are natural smokeless fuels); coals in
groups 300 to 900 are generally known as bituminous coals
5-2
Reference data
of which those in the groups 300 to 600 are generally used
as coking coals, with the lower ranking groups (600–900)
being general purpose coals for domestic and commercial
burning.
5.3.2
Natural gas
Most natural gas distributed in the UK stems from underground deposits beneath the North Sea and Irish Sea. As
these gas fields decline in output increasing quantities will
become available from Norway and the Russian Federation.
Gas quality is controlled under the auspices of the Gas Act
1986(5). Calorific value must be declared as gas is costed on
the basis of number of units of energy supplied. Similar
restrictions apply to the uniformity of calorific value,
supply pressure, Wobbe number, hydrogen sulphide
content and smell. The unit of energy ‘therm’ is 105
British Thermal Units (BTU) and this is equivalent to
105.5 MJ.
5.4
Secondary fuels
5.4.1
Smokeless solid fuels
Manufactured smokeless fuels are cokes and bonded
briquettes. In the heating field these are usually burned in
hand-fired or gravity-fed appliances. The use of briquetted
fuels is restricted to domestic appliances.
5.4.2
Electricity
Electricity is distributed over a high voltage grid system
which is reduced at the user to standard conditions of
415 V, three phase, 50 Hz for normal purposes and small
demands, but at higher voltages for large power requirements.
5.5
Specification of fuels
5.5.1
Solid fuels
5.5.1.1
Coal
The average properties of coals for the UK are given in
Table 5.1 for typical ‘as fired’ fuel. This is the form in
which the data are normally used for calculation. Physical
data are given in Tables 5.2 to 5.7.
Coal size is identified according to metric screen sizes
appropriate to BS 1016: Part 109(6). Sizes for various
graded coals are given in Tables 5.2 to 5.5.
Graded coals are separated into five standard groups for
which the upper and lower limits have a permitted range
(Table 5.2). Smalls are specified in terms of an upper size
only; for stoker firing smalls have a top size of either
25 mm or 50 mm. Treated smalls are washed or dry
cleaned. A guide to coal storage and handling is given in
reference 7.
Petroleum fuel oils
All fuel oils are refinery products. Crude oils, which are
obtained from the oil wells as mixtures of hydrocarbons,
are processed in the refinery to produce many hundreds of
commercial products, including fuel oil. The numerous
hydrocarbon compounds have different boiling points
and, by controlled heating of the crude oil, the various
fractions are distilled and condensed, producing gasolines,
kerosenes and gas oils which are termed distillates.
Blending of the residual oils with a suitable distillate
enables the production of the various grades of residual
fuel oils, which are commercially available for application
to the larger heating plants. Nitrogen and asphaltene
contents of residual fuel oils are significant in determining
levels of nitrogen oxide and particulate emissions to the
atmosphere. Careful selection of the appropriate equipment, boilers, burners and flues will enable the most
effective grade of fuel oil to be applied to the particular
plant requirements.
5.4.3
5.4.4
Liquefied petroleum gases
Liquefied petroleum gases, commonly known as LPG, are
the C3 and C4 members of the hydrocarbon family. They
are readily liquefied by the application of moderate
pressure at ambient temperature. These are marketed in
the UK as two grades, known as ‘commercial propane’ and
‘commercial butane’ under various brand names given by
the distributing companies. They are transported and
stored in the liquid phase but are used and handled as a
gas.
Calorific values
The following definitions are adopted in this chapter for
gross and net calorific values:
—
Gross calorific value: the calorific value of the fuel
including the latent heat of condensation of all
water vapour in the products of combustion.
—
Net calorific value: the calorific value of the fuel
when no water vapour is condensed from the
products of combustion.
The calorific values of the fuels are tabulated for certain
moisture contents. When the fuel has a different moisture
content from that tabulated, the calorific value can be
found from:
(100 – m) hgt
hg = ————–––
(100 – mt)
(5.1)
(100 – m) hnt
hn = ————––– – 24.5 (mt – m)
(100 – mt)
(5.2)
where hg is the gross calorific value (mass basis) at
moisture content m (kJ·kg–1), hgt is the tabulated gross
calorific value (mass basis) (kJ·kg–1), m is the moisture
content of the fuel (%), mt is the tabulated moisture
content of the fuel (%), hnt is the tabulated net calorific
value (mass basis) (kJ·kg–1) and hn is the net calorific value
(mass basis) at moisture content m (kJ·kg–1).
Fuels and combustion
5-3
Table 5.1 Average ‘as fired’ properties of coal
Fuel
Coal
rank
code
Moisture content / %
Constituent parts by mass / %
Air
dried
96% RH
30 °C
Moisture
Ash
Carbon Hydrogen Nitrogen Sulphur
Oxygen
Calorific value
/ MJ·kg–1
Gross
Net
(a) Washed smalls
Anthracite
101
102
2
1
4
2
8
7
8
8
78.2
77.9
2.4
3.1
0.9
1.1
1.0
1.0
1.5
1.9
29.65
30.35
28.95
29.30
Dry steam coals
201
1
1
7
8
77.4
3.4
1.2
1.0
2.0
30.60
29.65
Coking steam coals
202
204
1
1
1
1
7
7
8
8
77.1
76.8
3.5
3.8
1.2
1.2
1.0
1.0
2.2
2.2
30.70
30.80
29.75
29.80
Medium volatile
coking coals
301a
301b
1
1
1
1
7
7
8
8
75.8
74.8
4.1
4.2
1.3
1.3
1.2
1.2
2.6
3.5
30.80
30.45
29.75
29.40
Heat altered coals
302H
303H
1
2
2
3
7
8
8
8
74.4
72.7
4.2
4.2
1.7
1.4
1.2
1.2
3.5
4.5
30.35
29.75
29.25
28.60
2
2
3
4
4
2
3
4
6
5
9
9
10
11
11
8
8
8
8
8
71.6
71.0
68.8
67.8
67.0
4.3
4.3
4.4
4.3
4.4
1.6
1.5
1.5
1.4
1.4
1.7
1.7
1.7
1.7
1.7
3.8
4.6
5.5
5.9
6.1
29.55
29.20
28.60
27.80
27.80
28.40
28.05
27.40
26.60
26.55
5
5
8
10
6
7
11
13
13
13
16
18
8
8
8
8
65.7
65.0
61.3
59.0
4.0
4.2
4.0
3.7
1.4
1.3
1.3
1.2
1.7
1.7
1.7
1.7
6.2
6.8
7.7
8.4
26.75
26.75
25.25
23.85
25.50
25.50
23.95
22.60
—
—
7
82.0
0.4
1.7
—
—
27.90
26.30
—
—
15
6
71.0
2.4
2.4
—
3.2
27.45
25.40
High volatile coking coals:
— very strongly caking 401
— strongly caking
501
502
— medium caking
601
602
General purpose coals:
— weakly caking
— very weakly caking
— non-caking
701
702
802
902
Manufactured fuels:
— domestic and
—
industrial coke
— low temperature coke —
8–12
(b) Washed singles
Anthracite
101
102
2
1
4
2
4
3
5
5
84.7
84.3
2.6
3.4
1.0
1.2
1.1
1.1
1.6
2.0
32.10
32.85
31.45
31.80
Dry steam coals
201
1
1
3
5
83.7
3.7
1.3
1.1
2.2
33.10
32.20
Coking steam coals
202
204
1
1
1
1
3
3
5
5
83.4
83.1
3.8
4.1
1.3
1.3
1.1
1.1
2.4
2.4
33.20
33.30
32.30
32.35
Medium volatile
coking coals
301a
301b
1
1
1
1
3
3
5
5
82.1
81.0
4.4
4.5
1.4
1.4
1.3
1.3
2.8
2.8
33.30
32.95
32.30
31.90
Heat altered coals
302H
303H
1
2
2
3
3
4
5
5
80.6
78.7
4.5
4.6
1.8
1.5
1.3
1.3
3.8
4.9
32.85
32.20
31.75
31.10
2
2
3
4
4
2
3
4
6
5
4
5
5
6
7
5
5
5
5
5
78.5
77.0
75.5
74.5
73.2
4.7
4.7
4.8
4.6
4.8
1.7
1.5
1.6
1.5
1.5
1.9
1.8
1.9
1.9
1.9
4.2
5.0
6.2
6.5
6.6
32.40
31.65
31.40
30.60
30.15
31.25
30.50
30.20
29.35
28.95
5
5
8
10
6
7
11
13
9
9
11
16
5
5
5
5
71.5
70.8
67.8
63.0
4.4
4.6
4.4
3.9
1.5
1.4
1.4
1.3
1.8
1.8
1.9
1.8
6.8
7.4
8.5
9.0
29.15
29.15
27.90
24.45
27.80
27.90
26.60
24.10
High volatile coking coals:
— very strongly caking 401
— strongly caking
501
502
— medium caking
601
602
General purpose coals:
— weakly caking
— very weakly caking
— non-caking
701
702
802
902
Table 5.3 Size limits and bulk density of Welsh anthracite
Table 5.2 Standard size groups for graded coals
Name
Name of group
Cobbles
French nuts
Stove nuts
Stovesse
Beans
Peas
Grains
Washed duff
Round hole screen size / mm
Upper limit
Large cobbles
Cobbles
Trebles/large nuts
Doubles/nuts
Singles
>150
100–150
63–100
38–63
25–38
Lower limit
75
50–100
38–63
25–38
13–18
Size limits / mm
80–125
63–80
36–63
20/16–36
10–20
10–16
5–10
0–5
Bulk density / kg·m–3
770–800
770–800
770–800
750–785
750–785
750–785
750–785
785–820
5-4
Reference data
Table 5.4 Size limits and bulk density of Welsh dry steam coal
Name
Size limits / mm
Bulk density / kg·m–3
Cobbles
Large nuts
Small nuts
Beans
Peas
Washed duff
80–125
56–80
18–56
16–18
10–18
0–10
720–750
720–750
720–750
705–735
705–735
705–735
firing. The calorific value of d-RDF is about two-thirds that
of coal and ash yields on combustion significantly higher.
Appreciable fuel glass contents may provide low d-RDF ash
fusion temperatures and possible clinker formation under
adverse combustion conditions.
5.5.1.3
The sustainable use of wood fuels can provide environmental benefits in terms of reduced carbon dioxide,
nitrogen oxide and sulphur oxide emissions in comparison
to coal. Short rotation coppice (SRC) wood fuels, based on
fast growing poplar and willow species, are becoming
more available in the form of dried chips.
Table 5.5 Size limits and bulk density of hard coke
Name
Size limits / mm
Bulk density / kg·m–3
Large
Cobbles
Trebles
Doubles
Singles
Beans
Over 90
64–90
40–64
25–40
16–25
10–16
433
448
464
464
481
497
Wood chips are divided into grades of super, fine and
coarse covering size ranges of 2 mm to 25 mm. A
European classification system for wood sizes is given in
CEN/TS 1496(9). For small boiler plant operation it is
recommended that fuel moisture content does not exceed
35% (British Biogen).
Table 5.6 Natural angle of repose of solid fuels
Approximate size
of fuel / mm
Angle of repose (measured
from the horizontal)
20–30
12–20
6–12
0–6
408
428
528
588
Properties of wood fuels
Wood fuels contain high percentage volatile matter and
oxygen compositions with low ash. These properties
influence smoke emission and the stoichiometric air
requirement respectively. Table 5.9 gives an indicative
composition of a chipped wood fuel.
Table 5.7 Bulk density of loosely packed dry coal
Nature and size of coal
Bulk density / kg·m–3
Graded coal
640 ± 60
Small coal
770 ± 60
Coal dust (,3 mm)
530 ± 50
Pulverised fuel (50–90% passing
76 × 76 µm square mesh sieve)
450 ± 50
Liquid fuels
5.5.2.1
Petroleum oils
British Standard specifications are published for all grades
of petroleum oil fuels and are accepted as the basic
requirements for the UK (BS 2869(10)). The five classes
shown in Table 5.10 cover the fuels normally used in fixed
appliances. Class C1 is a paraffin type fuel for use in freestanding, flueless domestic burners, and is not detailed in
this section. Class C2 is a distillate fuel of the kerosene
type for vapourising and small atomising burners.
Note: The bulk density depends on a number of factors and is not
reproducible within 65% except under laboratory conditions.
Compaction may increase the density by up to 20%, whereas freshly
formed pulverised fuel has a wide variation in range and may be less than
50% of the quoted figure.
5.5.1.2
5.5.2
Class D is a distillate grade for larger atomising burners in
both domestic and industrial use, generally known as gas
oil. Under the Sulphur Content of Liquid Fuels
Regulations 2000(11) the maximum sulphur content of
Class D oils should not exceed 0.1% from January 2008.
Pelletised refuse derived fuel (d-RDF)
Pelletised refuse derived fuel remains a suitable energy
source for small boilers despite some problems in
manufacture and market viability. Table 5.8(8) compares
the properties of d-RDF with a typical coal used for stoker
Classes E, F and G are residual or blended fuel oils for
atomising burners and generally need pre-heating before
combustion. These will normally require storage and
Table 5.8 Properties of a commercial coal and d-RDF(8)
Fuel
Moisture / %
Volatile
matter / %
Ash / %
Calorific value,
as fired / MJ·kg–1
Bulk density
/ kg·m–3
Coal
8.4
25.9
10.2
27.2
900
d-RDF
7.3
67.5
15.0
18.7
600
Table 5.9 Indicative composition of a chipped wood fuel
Moisture content
as fired by mass
/%
Ash as fired,
by mass / %
Volatile matter,
dry as fired,
by mass / %
O2 dry as fired,
by mass / %
Gross calorific
value, dry as fired
/ MJ·kg–1
15
0.6
80
48
19.7
Fuels and combustion
5-5
Table 5.10 Properties of petroleum burner fuels (BS 2869(10))
Property
Class C2
Kinematic viscosity
(m2·s–1)
at 40 °C
1.00–2.00 ×
(min–max)
Class D
10–6
1.5–5.5 ×
(min–max)
10–6
—
—
Carbon residue (% mass); Ramsbottom
on 10% residue
—
0.3 (max)
38
—
Maximum water content
—
Maximum sediment content by mass (%)
—
Maximum ash content by mass (%)
—
Maximum sulphur content by mass (%)
0.20
Class F
Class G
—
—
—
20.0 × 10–6 (max)
40.0 × 10–6 (max)
15.0 (max)
18.0 (max)
20.0 (max)
—
66
—
66
—
66
8.2 × 10–6 (max)
Kinematic viscosity (m2·s–1) at 100 °C
Minimum closed flash point (°C):
— Abel
— Pensky–Martens
Class E
—
56
200 mg·kg–1
0.5% v/v
0.75% v/v
1.0% v/v
0.01
0.10
0.15
0.15
0.01
0.10
0.10
0.15
0.20
3.50
3.50
3.50
Table 5.11 Properties of typical petroleum fuel oils
Property
Kerosene
Class 2
Relative density at 15 °C
0.803
Gas oil
Class D
Light fuel oil
Class E
0.850
0.940
Medium fuel oil
Class F
0.970
Heavy fuel oil
Class G
0.980
Minimum closed flash point (°C)
38
60
66
66
66
Kinematic viscosity (m2·s–1):
— at 40 °C
— at 100 °C
—
—
3.2 × 10–6
—
—
8 × 10–6
—
16 × 10–6
—
35 × 10–6
Freezing point (°C)
< –40
—
—
—
—
Maximum pour point (°C)
—
—
26
24
30
Maximum cloud point (°C)
—
–5 (Mar/Sep)
–16 (Oct/Feb)
—
—
—
Gross calorific value (MJ·kg–1)
46.4
45.5
42.5
41.8
42.7
43.6
42.7
Net calorific value
(MJ·kg–1)
40.1
39.5
40.3
Maximum sulphur content by mass (%)
0.2
0.2
3.2
3.5
3.5
Maximum water content by volume (%)
negligible
0.05
0.5
0.75
1.0
Maximum sediment content by mass (%)
—
0.01
0.10
0.15
0.15
Maximum ash content by volume (%)
—
0.01
0.05
0.07
0.10
Mean specific heat capacity, 0–100 °C
(kJ·kg–1·K–1)
2.1
2.06
1.93
1.89
1.89
handling plant with heating facilities. Under the Sulphur
Content of Liquid Fuels Regulations 2000(11) the
maximum sulphur content of Class G oils should not
exceed 1% by mass unless an exemption is granted.
Commercial specifications follow the pattern shown in
Table 5.11 but usually include additional information so
that all points governing fuel performance can be assessed.
More detailed property data and updated information may
be obtained from the fuel supplier.
BS 799: Part 5(12) provides specifications for oil storage
tank installations.
Viscosity
Kinematic viscosity is a measure of resistance of the liquid
to flow and may be defined as the force needed to shear a
unit cube at unit speed and was formerly expressed in
units of centistokes (cSt), where 1 cSt = 1 mm2·s–1. The SI
unit is m2·s–1. (Thus 1 cSt = 1 mm2·s–1 = 1 × 10–6 m2·s–1).
Figure 5.1 (page 5-6) shows the relationship between
kinematic viscosity and temperature for fuel oils of grades
E, F G and H.
Maximum viscosities of 500 × 10–6 m2·s–1 for pumping and
12 to 15 × 10–6 m2·s–1 for pressure atomisation are normally used. Rotary cup atomisers employ a viscosity range
of 50 to 80 × 10–6 m2·s–1.
Pour point
Pour point (Table 5.11) is a laboratory test by which the
lowest temperature at which an oil will flow under
carefully defined conditions is measured. In order to
ensure mobility of the fuel, minimum storage temperatures are required for class E, F and G oil fuels. The
distillate grades require no heating.
5-6
Reference data
3000
Figure 5.1 Viscosity–temperature
chart for class E, F, G and H fuel
oils (reproduced from BS 2869(10)
by permission of the British
Standards Institution)
2000
1500
1000
750
500
ss
C la
400
G
F
200
H
ss
C la
ss
C la
300
250
ss
C la
100
E
Kinematic viscosity / mm2·s–1
150
75
50
40
30
25
20
15
12.5
10
9
8
10
20
30
40
50
60
70
80
90
100 100 120 130 140 150 160
Temperature / °C
Heating requirements
Fuel of classes C2 and D may be stored, handled and
atomised at ambient temperatures, but exposure for a long
period to extreme cold should be avoided otherwise
restrictions in the flow of oil from the tank may result.
The appropriate temperatures for the storage and
handling of fuels of classes E, F and G are given in Table
5.12.
Normally oil burners require that residual fuel oils should
be presented to the burner at a viscosity between 12 and
15 × 10–6 m2·s–1. The burner manufacturer’s actual
requirements should be ascertained at the design stage.
5.5.3
Gaseous fuels
5.5.3.1
Liquefied petroleum gas (LPG)
Typical properties of commercial butane and commercial
propane are given in Table 5.13. Limiting requirements
for the properties of commercial butane and commercial
propane are given in BS 4250(13).
Latent heat of vapourisation
Table 5.12 Storage and handling temperatures of fuel oils (BS 799:
Part 5(12))
Class of fuel
Minimum storage
temperature / °C
Minimum handling or
outflow from storage
temperature / °C
E
F
G
10
25
40
10
30
50
Reference to Table 5.13 shows that on a mass basis the
latent heats of vapourisation for propane and butane are
similar and equivalent to 0.75% of the calorific value of the
fuel. Unless the latent heat is supplied artificially with a
vapouriser it can only be taken from the atmosphere
through the walls of the container; this places a limit on
the rate at which gas can be taken off under natural,
ambient temperature conditions.
Fuels and combustion
5-7
Table 5.13 Typical properties of commercial butane and commercial propane
Property
Butane (C4H10)
Density at 15 ⬚C (kg·m–3)
Propane (C3H8)
570
Relative density of liquid at 15 ⬚C
500
0.570–0.580
0.500–0.510
Relative density of gas compared with air at STP
1.90–2.10
1.40–1.55
Volume of gas per kg of liquid at STP (m3)
0.41–0.43
0.53–0.54
Ratio of gas volume to liquid volume at STP
233
–274
0
–45
—
—
200
580
690
140
320
560
1570
1810
Boiling point (⬚C)
Absolute vapour pressure at stated temperature (for products of the maximum
specified vapour pressure) (kPa):
— ⫺40.0 ⬚C
— ⫺17.8 ⬚C
—
0 ⬚C
—
37.8 ⬚C
—
45.0 ⬚C
Latent heat of vapourisation at 15 ⬚C (kJ·kg–1)
Specific heat of liquid
370
(kJ·kg–1·K–1)
Sulphur content
2.4
Negligible to 0.02% by mass
Limits of flammability (percentage by volume of gas in gas/air mixture)
Calorific values (dry volumetric basis) (MJ·m–3):
— gross
— net
357
2.52
Negligible to 0.02% by mass
9.0 (upper)
1.8 (lower)
122
113
10.0 (upper)
2.2 (lower)
93
86
Calorific values (mass basis) (MJ.kg–1):
— gross
— net
49.5
46
50
46.5
Air required for combustion (m3 per m3 of gas)
30
24
Note: values of density and specific volume are given at STP, being 15 °C and 101.3 kPa; similarly values of relative density are given relative to dry air at
STP; the density of dry air to normalise gas density to relative density is 1.16 m3·kg–1.
Relative density
Both propane and butane are heavier than air and the
vapour will therefore tend to collect at a low level in the
event of a leak. This point must be borne in mind when
designing storage and handling systems. Conversely the
liquid density is low and this is important when considering transportation and filling of containers of known
internal volume.
Sulphur content
has a low sulphur content controlled by specification
limits (BS 4250) to 200 mg·kg–1 (0.02% by mass).
LPG
5.5.3.2
Natural gas
Table 5.14 Typical volume analysis and properties of natural gas
Components and properties
Value
Components:
— methane
— ethane
— propane
— butane
— pentane and above
— hydrogen
— carbon monoxide
— carbon dioxide
— nitrogen
92.6%
3.6%
0.8%
0.2%
0.1%
—
—
0.1%
2.6%
Properties:
— gross calorific value (MJ·m–3)
— net calorific value (MJ·m–3)
— relative density
— Wobbe No. (dry)
— air required for combustion (m3·per m3 gas)
38.7
34.9
0.602
49.9
9.73
Typical analyses and properties of natural gas are given in
Tables 5.14 and 5.15.
Where gas volume data are given they are based on
conventional reference conditions of 15 °C and 101.3 kPa.
Calorific value
The legal requirement is for the public gas transporter to
calculate each day in accordance with the Gas (Calculation
of Thermal Energy) Regulations(14), a ‘flow weighted
average’ calorific value (FWAC) which is passed to all gas
shippers for all charging areas.
Table 5.15 Operating properties of natural gas
Property
Value
Declared calorific value
≈ 38.7 MJ·m–3
Relative density
0.59–0.61
Wobbe No.
45.7–55.0 (Gas Group H)
Distribution pressure
1750–2750 Pa*
*Legal requirement: must not fall below 1250 Pa
5-8
Reference data
Sulphur compounds
16
Relative density
There is no legal requirement for relative density and the
average value is given in Tables 5.14 and 5.15.
15
Air supplied per kg of fuel / m3
The contract specification for natural gas limits the total
sulphur content to 35 parts per million expressed as
hydrogen sulphide. As distributed the sulphur content of
natural gas is approximately 0.0011 per cent by volume.
Wobbe number
12
Coke
11
10
(5.3)
9
8
6
8
9
10 11
12
13 14 15 16
CO2 dry gas / %
50
40
30
CRC 102 100 90 80 70 60 50 40
100 90 80 70 60
30
20
CRC 702 100 90 80 70 60 50 40
Landfill gas
There is significant potential for landfill gas as a fuel for
direct boiler firing or in CHP applications. Gas may require
cleaning and dewatering before use. The composition is
approximately 60 per cent methane and 40 per cent carbon
dioxide and also includes many other gases in trace
concentrations. The calorific value is in the range
15–25 MJ·m–3 depending upon the inert gas content and
the extent of raw gas conditioning(8).
20
20
19 20
10
10
0
0
10
0
15
14
13
12
11
Bituminous
coal (rank 702)
10
Coke
9
8
Anthracite
(Rank 102)
7
6
8
9
10 11
12
13 14 15 16
CO2 dry gas / %
50
40
30
CRC 102 100 90 80 70 60 50 40
30
20
Coke
Combustion data
30
17 18
Excess air scales / %
Figure 5.2 Combustion air requirements for solid fuels
Volume of wet products of combustion
per kg of fuel / m3
Natural gases all have Wobbe numbers falling within a
narrow range and all appliances are designed to operate on
gas corresponding to the mean of that range.
5.6
Anthracite
(Rank 102)
Bituminous
coal (rank 702)
Coke
where W is the Wobbe number (MJ·m–3), hg is the gross
calorific value (volume basis) (MJ·m–3) and d is the
relative density.
5.5.3.3
13
7
The thermal input of an appliance (e.g. central heating
boiler) for a given pressure and burner orifice is a function
of the Wobbe number. This number is defined as:
hg
W = ——
d 0.5
14
100 90 80 70 60
CRC 702 100 90 80 70 60 50 40
30
20
17 18
20
19 20
10
10
10
0
0
0
Excess air scales / %
5.6.1
Combustion air and waste gas
volume
It is necessary to determine combustion air requirements
and waste gas volumes for boiler plant and chimney/flue
designs. In order to simplify this assessment, charts are
reproduced below for various fuels where the required
volume under various CO2 per cent (excess air) conditions
can be read off. Percentage CO2 values are expressed on a
dry gas basis.
Note that all volumes are standardised at 15 °C, 101.3 kPa.
For volumes at other temperatures the following formula
may be used:
V (θg + 273)
Vg = —————–
288
(5.4)
where Vg is the volume at temperature θg (m3), θg is the
actual air or flue gas temperature (°C) and V is the
standard volume read from charts (m3).
Figure 5.3 Volumes of products of combustion for solid fuels
5.6.1.1
Solid fuels
The average figures given in Table 5.16 may be taken for
CO2 per cent, excess air, total air and gas requirements per
kilogram of fuel for plant working under normal conditions of combustion efficiency.
Where the anticipated CO2 per cent (and excess air values)
varies considerably from the averaged conditions listed in
Table 5.16, refer to the appropriate curves on Figures 5.2
and 5.3, which are accurate for practical design purposes.
5.6.1.2
Fuel oils
The average figures in Table 5.16 may be taken for CO2
per cent, excess air, total air and flue gas volume requirements per kilogram of fuel with plant working under
normal conditions of combustion efficiency.
Fuels and combustion
5-9
5.6.1.3
Table 5.16 Combustion conditions
Fuel
CO2 / %
Excess
air / %
Total air
volume
/ m3·kg–1
Flue gas
volume
/ m3·kg–1
Solid fuels:
— coke
— anthracite
— bituminous coal
13.7
12.7
12.3
50
50
50
11.7
12.3
10.8
11.9
12.7
11.4
Fuel oils:
— classes C and D
— classes E, F and G
11.6
12.1
30
30
15.4
14.1
16.3
14.7
Where the anticipated CO2 per cent (excess air) varies
considerably from the above averaged figures, refer to the
appropriate curves on Figures 5.4 and 5.5, which are
sufficiently accurate for practical design purposes.
21
20
Total air per kg of fuel / m3
19
Gaseous fuels
With gas fired boilers the flue gas/air volumes depend on
the type of boiler/burner unit installed and the design of
the union between the boiler exhaust gas outlet flue and
chimney.
The average figures given in Table 5.17 for natural gas
have been obtained from site tests. Two types are given:
(a)
boilers fitted with a naturally inspirated burner
and a draught diverter
(b)
boilers fitted with a forced draught burner and a
direct flue connection.
Excess air data are given in Figure 5.6. It is important to
note that it is possible to have an air deficiency when
measuring CO2 percentage alone. Since natural gas does
not produce black smoke when combustion is incomplete
it is necessary to measure the CO content in addition to
CO2 to determine if there is sufficient combustion air. For
example, from Figure 5.6 it is seen that 10.3% CO2 could
mean either 14% excess air or 15% air deficiency; measuring the CO content will show which air value is correct.
18
The water dew point of natural gas exhaust gases, appropriate to typical operating conditions of forced draught
condensing boilers, is approximately 55 °C.
17
16
15
Distillate oils
Table 5.17 Percentage volumes of combustion products for boilers
burning natural gas
14
Residual oils
13
Type of burner
CO2 / %
CO / %
Flue gas
temp. / °C
Natural inspirated burner
and draught diverter
(values measured in
primary flue)
7.5–9
0.001–0.008
190–290
Forced draught burner
8–11
with direct flue connection
0.001–0.006
55–320
12
11
10
8
9
10 11 12 13 14
CO2 dry gas / %
Distillates
70 60 50 40 30 20
10
Residuals
80 70 60 50 40 30 20
15
16
0
10
0
Excess air scales / %
Figure 5.4 Combustion air requirements for petroleum fuel oils
30
21
200
28
26
24
17
16
Distillate oils
15
14
Residual oils
13
12
11
150
22
20
100
18
Natural
gas CO2
16
60
14
40
12
20
10
8
8
9
10 11 12 13 14
CO2 dry gas / %
Distillates
70 60 50 40 30 20
Residuals
80 70 60 50 40 30 20
10
10
15
16
0
20
Natural
gas CO
6
10
80
Natural gas
excess air scale
18
4
2
0
0
0
Excess air scales / %
Figure 5.5 Volumes of products of combustion for petroleum fuel oils
0
1
2
3
4 5 6 7 8 9
CO2 or CO dry gas / %
10 11 12
Figure 5.6 Combustion air requirements for natural gas
Deficiency Excess
19
Total air supplied per m3 of fuel / m3
Volume of wet products of combustion
per kg of fuel / m3
20
5-10
Reference data
5.7
Stack losses
The major heat loss from combustion appliances is the
heat carried away in the flue gases. Several formulae have
been proposed for assessing these losses based mainly
upon variations to the ‘Siegert’ expression. In order to
simplify the assessment for practical requirements, graphs
are included in this section which give the stack losses
based upon the gross calorific value of the fuel. They do
not include any unburned gas loss, i.e. it is assumed that
there is no CO in the flue gases.
5.7.1
variables such as rank, grade and moisture content will
affect the gross heat loss. CO2 per cent values are denoted
on the basis of dry flue products.
5.7.2
The curves given in Figures 5.10 and 5.11 show the total
flue gas loss at various flue gas temperatures for various
CO2 per cent values (excess air quantities) expressed as a
per cent of gross calorific value.
5.7.3
Solid fuels
The curves given in Figures 5.7, 5.8 and 5.9 show the total
flue gas heat loss for various CO2 per cent values (excess
air quantities) expressed as a per cent of gross calorific
value. They are provided for general guidance because
Gaseous fuels
The curves given in Figure 5.12 show the total flue gas
loss at various flue gas temperatures for various CO2 per
cent values (excess air quantities) expressed as a per cent
of gross calorific value.
60
8%
40
%
10
30
%
12
%
4
1
16%
20
18%
10
0
6%
2
50
CO
Total heat loss in flue gases / % of gross CV
50
2
6%
60
CO
Total heat loss in flue gases / % of gross CV
Liquid fuels
8%
40
%
10
30
%
12
%
4
1
16%
20
18%
10
0
50 100
200
300
400
500
600
Difference between flue gas and room temperatures / K
Figure 5.7 Flue gas losses: bituminous coal (CRC 702)
50 100
200
300
400
500
600
Difference between flue gas and room temperatures / K
Figure 5.9 Flue gas losses: anthracite (CRC 102)
%
10
30
%
12
%
4
1
16%
20
18%
10
0
40
2
CO
Total heat loss in flue gases / % of gross CV
2
8%
40
Gross CV = 42.96 MJ·kg–1
Relative density = 0.95
6%
50
6%
50
CO
Total heat loss in flue gases / % of gross CV
60
8%
%
10
%
12
14%
30
15%
20
10
0
50 100
200
300
400
500
600
Difference between flue gas and room temperatures / K
Figure 5.8 Flue gas losses: coke
50 100
200
300
400
500
600
Difference between flue gas and room temperatures / K
Figure 5.10 Flue gas losses: residual fuel oils
Fuels and combustion
5-11
8%
%
10
%
2
1
30
14%
20
15%
13%
10
40
3.
4% 5%
2.5
%
3%
2%
CO
2 1
40
6%
2
O
C
Total heat loss in flue gases / % of gross CV
Total heat loss in flue gases / % of gross CV
Gross CV = 46.5 MJ·kg–1
Relative density = 0.79
%
1.5%
50
50
5% 5% 6%
4.
7%
8%
10%
30
12%
20
10
Gross CV = 38.7 MJ·m–3
0
0
50 100
200
300
400
500
600
Difference between flue gas and room temperatures / K
0
100
200
300
400
500
600
Difference between flue gas and room temperatures / K
Figure 5.11 Flue gas losses: distillate fuel oils
Figure 5.12 Flue gas losses: natural gas
References
Bibliography
1
Clean Air Act 1993 (London: Her Majesty’s Stationery Office)
(1993)
2
Climate Change Agreements and the Climate Change Levy
(London: Department for Environment, Food and Rural Affairs)
(2005) (http://www.defra.gov.uk/environment/ccl/intro.htm)
Breag G R, Joseph P G and Tariq A S Biomass Combustion Systems —
Flue Gas Losses and Equipment Efficiency (Greenwich: University of
Greenwich Natural Resources Institute) (1992)
3
The practical guide to the Climate Change Levy — energy efficient
solutions for industry, commerce and the public sector (Association
for the Conservation of Energy/Journal of Water, Energy and
the Environment) (2001)
4
Conservation of fuel and power in existing buildings other than
dwellings The Building Regulations 2000 Approved Document
L2B (London: The Stationery Office) (2006)
5
Gas Act 1986 (London: Her Majesty’s Stationery Office) (1986)
6
BS 1016: Methods for analysis and testing of coal and coke: Part
109: 1995 (ISO 1953: 1994): Size analysis of coal (London:
British Standards Institution) (1995)
7
Vesma V (ed.) Industrial Coal Handbook 1st edn. (Energy
Publications) (1985)
8
Williams P T Waste treatment and disposal (London: Wiley)
(1998)
9
10
11
DD CEN/TS 14961: 2005: Solid biofuels. Fuel specifications and
classes (London: British Standards Institution) (2005)
BS 2869: 2006: Fuel oils for agricultural, domestic and industrial
engines and boilers. Specification (London: British Standards
Institution) (2006)
BS 799: Oil burning equipment: Part 3: 1981: Automatic and semi-automatic
atomizing burners up to 36 litres per hour; Part 4: 1991: Specification for
atomizing burners (other than monobloc type) together with associated equipment
for single burner and multi burner installations; Part 5: 1987: Specification for
oil storage tanks (London: British Standards Institution) (1981/1987/1991)
BS 845: Methods for assessing thermal performance of boilers for steam, hot
water and high temperature heat transfer fluids: Part 1: 1987: Concise
procedure; Part 2: 1987: Comprehensive procedure (London: British
Standards Institution) (1987)
BS 1016: Methods for the analysis and testing of coal and coke: Parts 1–21
(1970–1998 with earlier parts withdrawn); Parts 100–113 (1991–1998);
Part 100: 1994: General introduction and methods for reporting results
(London: British Standards Institution) (dates as indicated)
Digest of United Kingdom Energy Statistics (London: Government
Statistical Service (published annually) (www.dti.gov.uk/energy/statistics/
publications/dukes/page19311.html)
Dryden I G C (ed.) The efficient use of energy 2nd edn. (Oxford:
Butterworth Scientific) (1982)
Energy Institute Yearbook and Directory 2006 (London: Energy Institute)
(published annually)
Environmental Protection Act 1990 (London: Her Majesty’s Stationery
Office) (1990; reprinted with corrections 1998, 2004)
The Sulphur Content of Liquid Fuels (England and Wales)
Regulations 2000 Statutory Instruments 2000 No. 1460; The
Sulphur Content of Liquid Fuels Regulations (Northern
Ireland) 2002 Statutory Rules of Northern Ireland 2002 No. 28;
The Sulphur Content of Liquid Fuels (Scotland) Regulations
2000 Scottish Statutory Instruments 2000 No. 169 (London:
The Stationery Office) (dates as indicated)
Establishing guidelines for wood fuel standards DTI Project Summary 369
(1st. issue) (London: Department of Trade and Industry) (October 1994)
12
BS 799: Oil burning equipment: Part 5: 1987: Specification for oil
storage tanks (London: British Standards Institution) (1987)
IP Standard Methods for analysis and testing of petroleum and related products,
and British Standard 2000 Parts (2 vols.) (London: Energy Institute)
(2006)
13
BS 4250: 1997: Specification for commercial butane and commercial
propane (London: British Standards Institution) (1997)
14
The Gas (Calculation of Thermal Energy) Regulations 1996
Statutory Instruments 1996 No. 439 (London: Her Majesty’s
Stationery Office) (1996)
Fuel and energy abstracts (London: Energy Institute/Elsivier) (bi-monthly)
Gunn D and Horton R Industrial boilers 1st edn. (London: Longman
Scientific and Technical) (1989)
Pollution Handbook 2006 (Brighton: National Society for Clean Air and
Environmental Protection) (published annually)
Rose J W and Cooper J R (eds.) Technical data on fuel 7th edn.
(Edinburgh: Scottish Academic Press) (1977)
6-1
6
Units, standard and mathematical data
6.1
Introduction
6.2
The International System of Units (SI)
6.3
Quantities, units and numbers
6.4
Metrication in the European Union
6.5
Conversion factors
6.1
Introduction
This section contains information which, although
essential to engineers and designers does not on the whole
belong exclusively to any other chapter of the Guide.
Inevitably, therefore, a large part of the section is devoted
to SI units, which are used throughout the Guide but are
not explained elsewhere. The development of SI is traced
and the definitions of the base and supplementary units
are given. There is also an explanation of how the units
adopted by the European Union differ from SI.
Comprehensive tables then list the conversion factors for
changing from old units to their practical SI equivalents.
Although SI units have been the official standard units in
Europe (including the UK) since 1971, conversion from
other units is still regularly required for three reasons:
—
some countries, notably the USA, have not fully
adopted SI units
—
some UK engineers still think in imperial units
—
much of the UK heritage of plant and buildings
was built to imperial unit designs.
6.2
The International System
of Units (SI)
All international matters concerning the metric system
have been the responsibility of the Conférence Générale
des Poids et Mesures (CGPM) since the signing of the
Metre Convention in 1875. Under the authority of CGPM
are the Comité International des Poids et Mesures (CIPM)
and the Bureau International des Poids et Mesures
(BIPM). UK participation in CGPM work is through the
Department of Trade and Industry (DTI). The International
Standards Organisation (ISO) provides recommendations
and advice and, more recently, International Standards on
the use and selection of SI units in industry and technology.
UK participation in ISO work is through the British
Standards Institution (BSI). The relevant standards are BS
ISO 31/0 to 31/13 and BS ISO 1000.
At its 10th meeting in 1954, CGPM adopted a coherent
system of units based on the metre, kilogram, second,
ampere, kelvin and candela. At its 14th meeting in 1971,
the mole was added as the seventh base unit. The 11th
meeting in 1960 gave the system its formal title ‘Le
Système International d’Unités — commonly abbreviated
to SI. The SI comprises:
—
seven named base units (Table 6.1)
—
two named supplementary units.
These units are defined below. Each unit has been allocated an internationally agreed symbol. All other units
may be derived from these base and supplementary units.
The supplementary units have since 1981 been redefined
as ‘derived units’.
Certain derived units have been given internationally
agreed names and symbols. The allocation of a name to a
derived unit has:
(a)
the advantage of simplicity in written and verbal
communication
(b)
the disadvantage of masking the derivation of the
unit.
Table 6.1 SI base units
Quantity
Name
Symbol
Length
Mass
Time
Electric current
Thermodynamic temperature
Luminous intensity
Amount of substance
metre
kilogram
second
ampere
kelvin
candela
mole
m
kg
s
A
K
cd
mol
6-2
Reference data
6.2.1
Definitions of base units
6.2.1.6
6.2.1.1
Unit of length
Name: candela
Name: metre
Symbol: m
The metre is the length of the path travelled in a vacuum
by light during 1/299 792 458 seconds. (17th CGPM
(1983), Resolution 1.)
Symbol: cd
The candela is the luminous intensity in a given direction
of a source emitting monochromatic radiation at
50 × 1012 H3 with a radiant intensity in that direction of
1/683 watt per steradian. (16th CGPM (1979), Resolution 3.)
6.2.1.7
6.2.1.2
Unit of luminous intensity
Unit of amount of substance
Unit of mass
Name: mole
Name: kilogram
Symbol: kg
With the object of removing the ambiguity which still
occurred in the common use of the word ‘weight’, the 3rd
CGPM (1901) declared: ‘the kilogram is the unit of mass
(and not of weight or of force); it is equal to the mass of
the international prototype of the kilogram’. This
international prototype made of platinum–iridium is kept
at the BIPM under conditions specified by the 1st CGPM
in 1889.
6.2.1.3
Unit of time
Name: second
Unit of electric current
Name: ampere
Symbol: A
Note: when the mole is used, the elementary entities must
be specified and may be atoms, molecules, ions, electrons,
other particles, or specified groups of such particles.
6.2.2
Definitions of supplementary
units
6.2.2.1
Unit of plane angle
Unit of thermodynamic temperature
Name: kelvin
Symbol: K
The kelvin, the unit of thermodynamic temperature, is the
fraction 1/273.16 of the thermodynamic temperature of the
triple point of water. (3th CGPM (1967), Resolution 4.)
The 13th CGPM (1967), Resolution 3, also decided that
the unit kelvin and its symbol K should be used to express
an interval or a difference of temperature.
In addition to the thermodynamic temperature expressed
in kelvins, use is also made of Celsius temperature defined
by:
θ = T – To
Name: radian
Symbol: rad
The radian is the angle between two radii of a circle which
cuts off on the circumference an arc equal in length to the
radius.
6.2.2.2
The ampere is that constant current which, if maintained
in two straight parallel conductors of infinite length, of
negligible circular cross-section, and placed 1 metre apart
in a vacuum, would produce between these conductors a
force equal to 2 × 10–7 newton per metre of length. (CPIM
(1946), Resolution 2 approved by the 9th CGPM 1948.)
6.2.1.5
The mole is the amount of substance of a system which
contains as many elementary entities as there are atoms in
0.012 kilogram of carbon 12. (14th CGPM (1971),
Resolution 3.)
Symbol: s
The second is the duration of 9 192 631 770 periods of the
radiation corresponding to the transition between the two
hyperfine levels of the ground state of the caesium-133
atom. (13th CGPM (1967), Resolution 1.)
6.2.1.4
Symbol: mol
Unit of solid angle
Name: steradian
Symbol: sr
The steradian is the solid angle which, having its vertex in
the centre of a sphere, cuts off an area of the surface of the
sphere equal to the square of the radius of the sphere.
6.2.3
Derived units
Derived units are expressed algebraically in terms of base
and/or supplementary units, see Table 6.2. Certain of these
have been given special names, see Table 6.3.
Table 6.2 Examples of SI derived units expressed in terms of base units
Quantity
Name
Symbol
Area
Volume
Velocity
Specific volume
Thermal conductivity
Luminance
square metre
cubic metre
metre per second
cubic metre per kilogram
watt per metre kelvin
candela per square metre
m2
m3
m·s–1
m3·kg–1
W·m–1·K–1
cd·m–2
(6.1)
where θ is the Celsius temperature (°C), T is the thermodynamic temperature (K) and To = 273.15 K by definition.
The Celsius temperature is in general expressed in degree
Celsius (symbol °C). The unit ‘degree Celsius’ is thus equal
to the unit ‘kelvin’ and an interval or a difference of
Celsius temperature may also be expressed in degrees
Celsius.
6.2.4
Prefixes for multiples and
submultiples
The magnitude of SI units may be increased or decreased
by the use of named prefixes. Each prefix is allocated an
internationally agreed symbol which may be added (in
front) of the unit symbol.
Units, standard and mathematical data
6-3
Table 6.3 SI derived units with special names
Quantity
Name of SI
derived unit
Symbol
Expressed in terms of SI base
or supplementary units or in
terms of other SI derived
units
Plane angle
radian
rad
—
Solid angle
steradian
sr
—
Frequency
hertz
Hz
1 Hz = 1 s–1
Force
newton
N
1 N = 1 kg·m·s–2
Pressure and stress
pascal
Pa
1 Pa = 1 N·m–2
Work, energy, quantity of heat
joule
J
1 J = 1 N·m
Power
watt
W
1 W = 1 J·s–1
Apparent power
volt ampere
V·A
1 V·A = 1 J·s–1
Quantity of electricity
coulomb
C
1 C = 1 A·s
Electrical potential, potential difference, electromotive force
volt
V
1 V = 1 W·A–1 = 1 J·C–1
Electrical capacitance
farad
F
1 F = 1 A·s·V–1 = 1 C·V–1
Electrical resistance
ohm
Ω
1 Ω = 1 V·A–1
Electrical conductance
siemens
S
1 S = 1 Ω–1
Magnetic flux, flux of magnetic induction
weber
Wb
1 Wb = 1 V·s
Magnetic flux density, magnetic induction
tesla
T
1 T = 1 Wb·m–2
Inductance
henry
H
1 H = 1 V·s·A–1 = 1 Wb·A–1
Luminous flux
lumen
lm
1 lm = 1 cd·sr
Illuminance
lux
lx
1 lx = 1 lm·m–2
Celsius temperature
degree Celsius
°C
1 °C = 1 K
Activity
becquerel
Bq
1 Bq = 1 s–1
Specific energy imparted
gray
Gy
1 Gy = 1 J·kg–1
Dose equivalent
sievert
Sv
1 Sv = 1 J·kg–1
Catalytic activity
katal
kat
1 kat = 1 mol·s–1
The prefixes given in Table 6.4 may be used to construct
decimal multiples of units.
6.2.5
Table 6.4 SI prefixes
The following notes are intended as a guide to some
quantities and units.
Explanatory notes
Multiplying factor
Prefix
Symbol
1024
1021
1018
1015
yotta
zetta
exa
peta
Y
Z
E
P
1012
109
106
103
tera
giga
mega
kilo
T
G
M
k
102
101 10
101 0.1
102
hecto
deca
deci
centi
h
da
d
c
Since the bar is a special authorised EU multiple of the
pascal it is anticipated that the bar (and mbar) will remain
in use indefinitely.
103
106
109
1012
milli
micro
nano
pico
m
l
n
p
1015
1018
1021
femto
atto
zepto
f
a
z
The Institution has adopted the pascal (and the
internationally agreed multiples and sub-multiples) for
expressing both pressure and stress in documents
published after 1973. Operating pressures are usually
expressed in kilopascals, and sometimes followed by the
quantity in bars in parentheses; e.g. 60 kPa (0.6 bar). It
should be noted that operating pressures should be in
6.2.5.1
Pressure and stress
In terms of the SI base units the quantity pressure may be
expressed in the units (kg·m–1·s–2). This derived unit has
been given the name pascal (Pa). Pressure can also be
expressed as N·m–2, J·m–3, W·s·m–3 etc.
A non-SI unit in common use is the bar (1 bar = 105 Pa).
6-4
Reference data
terms of ‘gauge pressure’ and should be unambiguously
stated, e.g. gauge pressure 600 kPa (6 bar).
6.2.5.2
Weight and mass
The term ‘weight’ has for many years been used in two
different senses. In common parlance and in the Weights
and Measures Act 1963 it is used to mean ‘mass’, whereas
in some technical work the word ‘weight’ is used in the
sense of ‘gravitational force’. There is no explicit SI unit of
weight. When ‘weight’ is used to mean ‘mass’, then the
correct SI unit is the kilogram. When ‘weight’ is used to
mean ‘force’, the correct SI unit is the newton.
6.2.5.3
Specific heat capacity
Due to the original definitions of British thermal unit and
calorie, the quantity ‘specific heat capacity’ of water
approximated to unity when expressed in imperial or
technical metric units.
In SI units the specific heat capacity of water is
4.185 5 kJ·kg–1·K–1 at a reference temperature of 15 °C.
6.2.5.4
The radiation dose absorbed by any material is defined as
the mean energy imparted by ionising radiation per unit
mass at the point of interest and is expressed in J·kg–1. The
special unit gray for the quantity absorbed dose is defined
as:
1 Gy = 1 J·kg–1
6.2.5.7
Sound
The decibel is a unit which compares power and its
derivatives. When used in the context of sound, it is
known as a measure of sound level defined, in the case of
power, as:
W1
Lw = 10 log10 —–
W2
Clothing insulation
The clo is a dimensionless factor expressing the insulation
of clothing and is defined as:
Rcl
Icl = ——
Rr
Celsius temperature is in general expressed in degrees
Celsius (°C). The unit ‘degree Celsius’ is equal to the unit
‘kelvin’ and an interval of, or a difference of, Celsius
temperature may also be expressed in degrees Celsius. In
the CIBSE Guide temperature differences, particularly in
compound units, are expressed in kelvins, e.g. W·m–1·K–1.
(6.3)
Doses to people are expressed as dose equivalent, which is
obtained by multiplying the absorbed dose at the point of
interest in tissue by various modifying factors, which
among other things take account of the energy and type of
the ionising radiation. Where the radiation dose is
measured in grays the dose equivalent is measured in
sieverts.
Temperature
When adopting the kelvin as the unit of thermodynamic
temperature or for expressing temperature difference, the
13th CGPM recognised that the term degree Celsius (°C)
would continue in everyday use for as long as could be
foreseen. The degree Celsius is defined by equation 6.1.
6.2.5.5
Concentrations in air are expressed in reciprocal seconds
per cubic metre.
(6.4)
where Icl is the insulation factor (clo), Rcl is the total
thermal resistance from skin to outer surface of the
clothed bodies (m2·K·W–1) and Rr is the reference thermal
resistance (= 0.155) (m2·K·W–1)
A clo value of 1 is the insulation given by a typical
business suit with waistcoat.
6.3
Quantities, units and
numbers
A physical quantity is an attribute which can be measured.
The measurement is described in terms of a number
multiplied by a unit. The algebraic relationship:
physical quantity = number × unit
must always be maintained.
(6.2)
Examples of physical quantities expressed as number of
units are:
where Lw is the sound power level (dB), W1 is sound
power 1 (W) and W2 is sound power 2 (usually a reference
value) (W).
—
height of Nelson’s Column = 43.211 75 metres
—
velocity of light in vacuo = 299 792 500 metres per
second.
Sound intensity level and sound pressure level are defined
by similar equations which take into account their
relationship with sound power. Table 6.12 gives standard
reference values which are used in sound measurement.
—
thermal conductivity of balsa wood = 0.040 watts
per metre kelvin.
6.3.1
6.2.5.6
Radioactivity
The activity of a radioactive source is the number of
nuclear transformations occurring in a small time interval
divided by that time interval. The unit of activity is the
Becquerel second.
Some rules for physical
quantities
(1)
The algebraic symbol should be a single letter of
the Latin or Greek alphabet.
(2)
When necessary, subcripts, superscripts, or other
modifying signs may be attached.
Units, standard and mathematical data
6-5
(3)
The symbol should, if possible, be printed in
sloping (italic) type.
(4)
The word ‘specific’ is restricted to mean divided
by mass.
(5)
The word ‘molar’ is restricted to mean divided by
amount of substance.
6.3.2
(5)
The multiplication sign between numbers should
be a cross (×) and not the mathematical (.) as may
be used with unit symbols, e.g:
2.3 × 3.4
(6)
Division of one number by another may be
indicated in a number of ways.
129
—– or 129/298 or 129 × (298)–1
298
Some rules for units
(1)
There is one and one only SI unit for each physical
quantity.
(2)
To find the units of physical quantities other than
the base physical quantities:
(a)
define the physical quantity in terms of the
base physical quantities
(b)
obtain the units of the physical quantity by
mutiplying and/or dividing the constituent
base units.
(7)
More than one solidus should never be used in the
same expression unless parentheses are used to
eliminate ambiguity, e.g:
(129/298)/2.62 or 129/(298 × 2.62)
but never 129/298/2.62.
6.3.4
Some rules for prefixes
A combination of prefix and symbol is regarded as a single
symbol:
(3)
Only agreed symbols must be used.
(4)
The symbol should be printed in upright (i.e. not
italic) type.
cm2 means (0.01 m)2 not 0.01 m2
(5)
The symbol for a unit derived from a proper name
begins with a capital letter.
Compound prefixes should not be used:
(6)
When written in full, all units are written in lower
case letters (e.g. newton, pascal) with the exception
of Celsius, which starts with a capital letter.
(7)
10–9 m = nm not mμm
Note: decimal multiples of the kilogram are formed by
attaching an SI prefix to gram and not kilogram:
A product of two units may be represented in a
number of ways:
ms
m.s
mg not μkg for 10–6 kg
m·s
Mg not kkg for 103 kg
but not ms without the space.
(8)
A quotient of two units may be represented in a
number of ways:
m s–1
m·s–1
m/s
m
—
s
but not ms–1, i.e. there must always be a space
between the unit symbols.
(9)
More than one solidus (/) should not appear in the
same expression unless parentheses are used to
eliminate ambiguity.
6.3.5
Some rules for labelling graphs
and tables
When labelling the co-ordinate axes of graphs or the
column headings of tables it is essential to distinguish
between the quantity itself and the numerical value of the
quantity expressed in a particular unit. In graphs or tables
it is sets of numbers that are plotted or tabulated. The
normal presentation is to enclose the unit in brackets.
However, since:
number = physical quantity/unit
6.3.3
Some rules for numbers
the label may comprise ‘quantity / unit’. For clarity the
unit may be enclosed in brackets.
(1)
Numbers should be printed in upright type.
(2)
The decimal sign can be a point (.) on the line, e.g.
2.6 (as has been adopted for CIBSE Guides and
current British Standards), or raised above the
line, e.g. 2·6; in other European countries a comma
is normally used, i.e. 2,6.
6.4
Metrication in the
European Union
Digits should be grouped in threes about the
decimal sign, separated by a space, e.g:
6.4.1
Legislative background
(3)
2 576.392 72
(4)
When the decimal sign is before the first digit a
zero should be placed before the decimal sign, e.g:
0.292 not .292
Use of metric and other units within the EU is governed
by Council Directive 80/181/EEC of 20th December 1979
as modified 3rd January 1985 and 7th December 1989.
This Directive approved the use of metric units as defined
in ISO standard 2955 of 1st March 1974, authorising
6-6
Reference data
continued use of certain other units in certain
circumstances, and repealed Directive 71/354/EEC of 18th
October 1971, the original directive on metric units.
6.4.2
Obligatory units
The obligatory units for use within the EU are the SI base,
supplementary and derived units, as given in Tables 6.1
and 6.2. Some special names, given in Table 6.5, are
authorised.
6.4.3
Special authorised units
Certain non-SI units are specially authorised for use
within member states either for general use or for specific
purposes. Each state is entitled to select any or all of these
for internal use. These units are given in Table 6.6.
6.4.4
Forbidden units
All other units are forbidden although they may be
retained for use for products already on the market at the
time of decision and for spares for these and obsolete
products. They may still be used as supplementary
indications but may be no larger than the approved
indications, which must predominate.
6.5
Conversion factors
The tables of conversion factors (Tables 6.7 and 6.8) are
arranged in five columns: physical quantity, previous unit,
factor, SI unit, SI symbol. To convert a quantity in
previous units to the equivalent quantity in SI units,
multiply by the factor. To convert a quantity in SI units to
the equivalent quantity in old units, divide by the factor.
Table 6.5 EU units with special names
Description
Quantity
Decimal multiples of SI units
Units for special fields
of application
Defined from SI units but not
decimal multiples
Defined independently of SI units
Volume
Unit
Name
Symbol
Value
litre*
1
1 l = 1 dm3
Mass
tonne*
t
1 t = 1 Mg
Pressures and stress
bar*
bar
1 bar = 105 Pa
Area of farmland and real estate
are*
a
1 a = 100 m2
Vergency of optical systems
dioptre
1 = 1 m–1
Mass of precious stones
metric carat
1 = 2 × 10–4 kg
Mass/unit length (textile yarns and threads)
tex
tex
1 tex = 10–6 kg·m–1
Plane angle
revolution
gon*
degree
minute of angle‡
second of angle‡
r†
gon
1 r 2p rad
1 gon p/200 rad
1 p/180 rad
1 p/10 800 rad
1 p/648 000 rad
Time
minute
hour
day
min
h
d
1 min 60 s
1 h 3600 s
1 d 86 400 s
Mass
atomic mass unit*
u
l u ⬇ 1.660 565 5 × 1027 kg §
Energy
electronvolt*
eV
l eV ⬇ 1.602 189 2 × 1019 J §
* SI prefixes apply to these units
† UK symbol
‡ BS ISO 31: 1992 recommends use of decimal division of the degree, e.g. 30 0.5
§ Values from CODATA bulletin No. 11, December 1973
Table 6.6 Special EU authorised units
Quantity
Use
Unit
Name
Symbol
Value
in
ft
yd
2.540 × 10–1 mm
3.048 × 10–1 m
9.144 × 10–1 m
1.609 km
1.829 m
Length
Road traffic signs, distance and speed measures
Road traffic signs, distance and speed measures
Road traffic signs, distance and speed measures
Road traffic signs, distance and speed measures
Marine navigation
inch
foot
yard
mile
fathom
Area
Land registration
acre
Volume
Drinks in returnable containers
Spirits
Draught beer and cider, milk; drinks in returnable containers
fluid ounce
gill
pint
pt
2.841 × 10–2 dm3
1.421 × 10–1 dm3
5.683 × 10–1 dm3
Mass
Loose bulk goods
Precious metals
Loose bulk goods
ounce
troy ounce
pound
oz
oz tr
lb
2.835 × 101 g
3.110 × 101 g
4.536 × 10–1 kg
Pressure
Blood pressure
mm mercury
mm hg
1.333 × 102 Pa
4.047 × 103 m2
fl oz
Units, standard and mathematical data
6-7
Table 6.7 Conversion factors
Physical quantity
Previous unit
×
Factor
=
SI unit
SI symbol
micrometre
micrometre
millimetre
metre
metre
kilometre
lm
lm
mm
m
m
km
square millimetre
square centimetre
square metre
square metre
square metre
square metre
square metre
square kilometre
mm2
cm2
m2
m2
m2
m2
m2
km2
cubic centimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic metre
cubic metre
cubic metre
cm3
dm3
dm3
dm3
dm3
dm3
dm3
m3
m3
m3
quartic centimetre
quartic metre
cm4
m4
second
second
second
s
s
s
microradian
milliradian
radian
radian
radian
radian
radian
lrad
mrad
rad
rad
rad
rad
rad
metre/second
metre/second
metre/second
metre/second
metre/second
m·s–1
m·s–1
m·s–1
m·s–1
m·s–1
radian/second
radian/second
rad·s–1
rad·s–1
SPACE AND TIME
Length
micron
thou’ (mil)
inch
foot
yard
mile
1
2.54 × 101
2.54 × 101
3.048 × 10–1
9.144 × 10–1
1.609
Area
square inch
6.452 × 102
6.452
9.290 × 10–2
8.361 × 10–1
1 × 102
4.047 × 103
1 × 104
2.590
square foot
square yard
are
acre
hectare
square mile
E
E
E
E
E
E
E
US barrel (petroleum)
cubic yard
1.639 × 101
4.732 × 10–1
5.683 × 10–1
1
3.785
4.546
2.832 × 101
2.832 × 10–2
1.590 × 10–1
7.646 × 10–1
Second moment of area
quartic inch
quartic foot
4.162 × 101
8.631 × 10–3
Time
minute
hour
day
6 × 101
3.6 × 103
8.64 × 104
Angle
second
minute
grade
gon
degree
right angle
revolution
4.848
2.909 × 10–1
1.571 × 10–2
1.571 × 10–2
1.745 × 10–2
1.571
6.283
Velocity
foot/minute
kilometre/hour
foot/second
mile/hour
knot
5.080 × 10–3
2.778 × 10–1
3.048 × 10–1
4.470 × 10–1
5.148 × 10–1
Angular velocity
revolution per minute
revolution per second
1.047 × 10–1
6.283
Acceleration
foot/square second
3.048 × 10–1
E
metre/square second
m·s–2
Frequency
cycle/second
1
E
hertz
Hz
grain
ounce
pound
slug
hundredweight
ton (short)
tonne
ton
6.480 × 101
2.835 × 101
4.536 × 10–1
1.459 × 101
5.080 × 101
9.072 × 10–1
1
1.016
milligram
gram
kilogram
kilogram
kilogram
megagram
megagram
megagram
mg
g
kg
kg
kg
Mg
Mg
Mg
Mass per unit length
pound/foot
pound/inch
1.488
1.786 × 101
kilogram/metre
kilogram/metre
kg·m–1
kg·m–1
Mass per unit area
pound/square foot
4.882
kilogram/square metre
kg·m–2
Concentration
grain/cubic foot
2.288
gram/cubic metre
g·m–3
Density
pound/cubic foot
pound/gallon
pound/cubic inch
1.602 ×
9.978 × 101
2.768 × 101
kilogram/cubic metre
kilogram/cubic metre
megagram/cubic metre
kg·m–3
kg·m–3
Mg·m–3
Specific volume
cubic foot/pound
6.243 × 10–2
cubic metre/kilogram
m3·kg–1
Volume
cubic inch
US pint
pint
litre
US gallon
gallon
cubic foot
E
E
E
E
E
E
MASS AND DENSITY
Mass
E — exact conversion factor
101
E
The word ‘litre’ may be employed as a special name for dm3
6-8
Reference data
Table 6.7 Conversion factors — continued
Physical quantity
FLOW RATE
Mass flow rate
Previous unit
×
Factor
=
SI unit
SI symbol
pound/hour
kilogram/hour
pound/minute
kilogram/minute
1.260 × 10–1
2.778 × 10–1
7.560 × 10–3
1.667 × 10–2
gram/second
gram/second
kilogram/second
kilogram/second
g·s–1
g·s–1
kg·s–1
kg·s–1
cubic inch/minute
litre/hour
US gallon/hour
gallon/hour
cubic foot/hour
cubic inch/second
litre/minute
US gallon/minute
gallon/minute
cubic metre/hour
cubic foot/minute
cubic metre/minute
cubic foot/second
2.732 × 10–4
2.778 × 10–4
1.052 × 10–3
1.263 × 10–3
7.886 × 10–3
1.639 × 10–2
1.667 × 10–2
6.309 × 10–2
7.577 × 10–2
2.778 × 10–1
4.719 × 10–1
1.667 × 101
2.832 × 10–2
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic metre/second
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
m3·s–1
pound foot/second
1.383 × 10–1
kilogram metre/second
kg·m·s–1
Moment of inertia
pound square foot
4.214 ×
kilogram square metre
kg·m2
Moment of momentum
pound square foot/second
4.214 × 10–2
kilogram square metre/second
kg·m2·s–1
Force
dyne
poundal
pound force
kilogram force
kilopond
1 × 101
1.383 × 10–1
4.448
9.807
9.807
micronewton
newton
newton
newton
newton
lN
N
N
N
N
Torque
pound force foot
1.356
newton metre
N·m
millimetre of water
pound force/square foot
millimetre of mercury
torr
inch of water
foot of water
inch of mercury
pound force/square inch
kilogram force/square centimetre
bar
9.807
4.788 × 101
1.333 × 102
1.333 × 102
2.491 × 102
2.989
3.386
6.895
9.807 × 101
1 × 102
1 × 10–1
1.013 × 102
1.013 × 10–1
pascal
pascal
pascal
pascal
pascal
kilopascal
kilopascal
kilopascal
kilopascal
kilopascal
megapascal
kilopascal
megapascal
Pa
Pa
Pa
Pa
Pa
kPa
kPa
kPa
kPa
kPa
MPa
kPa
MPa
Volume flow rate
MOMENTUM
Momentum
10–2
FORCE AND TORQUE
E
PRESSURE AND STRESS
Pressure
standard atmosphere
E
E
Pressure drop per unit length
inch of water/hundred feet
foot of water/hundred feet
8.176
9.810 × 101
pascal/metre
pascal/metre
Pa·m–1
Pa·m–1
Stress
pound force/square foot
pound force/square inch
ton force/square foot
ton force/square inch
4.788 × 101
6.895
1.073 × 102
1.544 × 101
pascal
kilopascal
kilopascal
megapascal
Pa
kPa
kPa
MPa
pound/hour foot
centipoise
poise
pound force second/square foot
pound force hour/square foot
4.134 × 10–1
1 × 10–3
1 × 10–1
4.788 × 101
1.724 × 102
millipascal second
pascal second
pascal second
pascal second
kilopascal second
mPa·s
Pa·s
Pa·s
Pa·s
kPa·s
stokes
square metre/hour
square inch/second
square foot/minute
Redwood No. 1 and No. 2 seconds
SAE grades
1
E
2.778
6.452
1.548 × 10–3
No direct conversion
No direct conversion
square centimetre/second
square centimetre/second
square centimetre/second
square metre/second
cm2·s–1
cm2·s–1
cm2·s–1
m2·s–1
VISCOSITY
Dynamic viscosity
Kinematic viscosity
E — exact conversion factor.
E
E
The word ‘litre’ may be employed as a special name for dm3
Units, standard and mathematical data
6-9
Table 6.7 Conversion factors — continued
Physical quantity
Previous unit
×
Factor
=
SI unit
SI symbol
microjoule
joule
joule
joule
kilojoule
kilojoule
kilojoule
megajoule
megajoule
megajoule
gigajoule
lJ
J
J
J
kJ
kJ
kJ
MJ
MJ
MJ
GJ
watt
watt
watt
watt
kilowatt
kilowatt
kilowatt
kilowatt
W
W
W
W
kW
kW
kW
kW
watt/square metre
watt/square metre
watt/square metre
W·m–2
W·m–2
W·m–2
ENERGY
erg
foot pound force
calorie*
metre kilogram force
British thermal unit
frigorie†
kilocalorie*
horsepower hour
kilowatt hour
thermie†
therm
1 × 10–1
1.356
4.187
9.807
1.055
4.186
4.187
2.685
3.6
4.186
1.055 × 10–1
British thermal unit/hour
kilocalorie/hour
foot pound force/second
calorie/second
metric horsepower (cheval vapeur)
horsepower
ton of refrigeration
Lloyd’s ton of refrigeration
2.931 × 10–1
1.163
1.356
4.187
7.355 × 10–1
7.457 × 10–1
3.517
3.884
Intensity of heat flow rate
kilocalorie/hour square metre
Btu/hour square foot
watt/square foot
1.163
3.155
1.076 × 101
Heat emission
Btu/hour cubic foot
1.035 × 101
watt/cubic metre
W·m–3
Thermal conductivity
Btu inch/hour square foot degree
Fahrenheit
kilocalorie/hour metre degree
Celsius
Btu/hour foot degree Fahrenheit
calorie/second centimetre degree
Celsius
1.442 × 10–1
watt/metre kelvin
W·m–1·K–1
watt/metre kelvin
watt/metre kelvin
W·m–1·K–1
W·m–1·K–1
watt/metre kelvin
W·m–1·K–1
watt/square metre kelvin
W·m–2·K–1
5.678
watt/square metre kelvin
W·m–2·K–1
4.187 × 101
kilowatt/square metre
kelvin
kW·m–2·K–1
2.388 × 10–3
5.778 × 10–1
8.598 × 10–1
metre kelvin/watt
metre kelvin/watt
metre kelvin/watt
m·K·W–1
m·K·W–1
m·K·W–1
6.933
metre kelvin/watt
m·K·W–1
square metre kelvin/watt
m2·K·W–1
Energy, work, quantity of
heat
E
E
POWER
Power, heat flow rate
Thermal conductance
Thermal resistivity
Thermal resistance
kilocalorie/hour square metre
degree Celsius
Btu/hour square foot degree
Fahrenheit
calorie/second square centimetre
degree Celsius
centimetre second degree
Celsius/calorie
foot hour degree Fahrenheit/Btu
metre hour degree Celsius/kilocalorie
square foot hour degree
Fahrenheit/Btu inch
1.163
1.731
E
E
E
4.187 × 102
1.163
E
square centimetre second degree
Celsius/calorie
square foot hour degree
Fahrenheit/Btu
square metre hour degree
Celsius/kilocalorie
1.761 × 10–1
square metre kelvin/watt
m2·K·W–1
8.598 × 10–1
square metre kelvin/watt
m2·K·W–1
square inch/hour
square foot/hour
square metre/hour
1.792 ×
2.581 × 10–5
2.778 × 10–4
square millimetre/second
square metre/second
square metre/second
mm2·s–1
m2·s–1
m2·s–1
Heat capacity
Btu/degree Fahrenheit
kilocalorie/degree Celsius
1.899
4.187
kilojoule/kelvin
kilojoule/kelvin
kJ·K–1
kJ·K–1
Specific enthalpy
Btu/pound
kilocalorie/kilogram
2.326
4.187
kilojoule/kilogram
kilojoule/kilogram
kJ·kg–1
kJ·kg–1
Specific heat capacity
Btu/pound degree Fahrenheit
kilocalorie/kilogram degree Celsius
4.187
4.187
kilojoule/kilogram kelvin
kilojoule/kilogram kelvin
kJ·kg–1·K–1
kJ·kg–1·K–1
Entropy
Btu/degree Rankine
kilocalorie/kelvin
1.899
4.187
kilojoule/kelvin
kilojoule/kelvin
kJ·K–1
kJ·K–1
Thermal diffusivity
2.388 × 10–5
10–1
ENERGY CONTENT
E — exact conversion factor
* Based on the international calorie defined as 4.1868 J
† Based on the 15 C calorie determined as 4.1855 J
E
The word ‘litre’ may be employed as a special name for dm3
6-10
Reference data
Table 6.7 Conversion factors — continued
×
Physical quantity
Previous unit
Specific entropy
Btu/pound degree Rankine
kilocalorie/kilogram kelvin
foot pound force/pound
Btu/pound
kilocalorie/kilogram
4.187
4.187
2.989
2.326
4.187
Volumetric calorific value
kilocalorie/cubic metre
Btu/cubic foot
Specific heat (volume basis)
Latent heat
Factor
=
SI unit
SI symbol
kilojoule/kilogram kelvin
kilojoule/kilogram kelvin
joule/kilogram
kilojoule/kilogram
kilojoule/kilogram
kJ·kg–1·K–1
kJ·kg–1·K–1
J·kg–1
kJ·kg–1
kJ·kg–1
4.187
3.726 × 101
kilojoule/cubic metre
kilojoule/cubic metre
kJ·m3
kJ·m3
kilocalorie/cubic metre degree
Celsius
Btu/cubic foot degree Farenheit
4.187
6.707 × 101
kilojoule/cubic metre kelvin
kilojoule/cubic metre kelvin
kJ·m–3·K–1
kJ·m–3·K–1
grain inch/hour square foot inch
of mercury (perminch)
1.45
nanogram metre/newton
second
nanogram/second pascal
metre
milligram metre/newton
second
milligram/second pascal
metre
E
MOISTURE CONTENT
Vapour permeability
1.45
pound foot/hour pound force
8.620
8.620
Vapour permeance
ng·m·N–1·s–1
ng·s–1·Pa–1·m–1
mg·m·N–1·s–1
mg·s–1·Pa–1·m–1
grain/square foot hour inch of
mercury (perm)
grain/ square foot hour millibar
pound square inch/square foot
hour pound force
pound/hour pound force
5.72 × 101
1.940
nanogram/newton second
microgram/newton second
ng·N–1·s–1
lg·N–1·s–1
1.965 × 10–1
2.834 × 101
milligram/newton second
milligram/newton second
mg·N–1·s–1
mg·N–1·s–1
Moisture content
grain/pound
pound/pound
1.428 × 10–1
1
gram/kilogram
kilogram/kilogram
g·kg–1
kg·kg–1
Moisture flow rate
pound/square foot hour
grain/square foot hour
1.357
1.94 × 10–1
gram/square metre second
milligram/square metre
second
g·m–2·s–1
mg·m–2·s–1
foot/hour
8.47 ×
millimetre/second
mm·s–1
Luminous intensity
candle
9.810 × 10–1
candela
cd
Illumination
foot candle
lumen/square foot
1.076 × 101
1.076 × 101
lux
lux
lx
lx
Luminance
foot lambert
candela/square inch
3.426
1.550 × 103
candela/square metre
candela/square metre
cd·m–2
cd·m–2
Mass transfer coefficient
E
10–2
LIGHT
ELECTRICITY AND
MAGNETISM
Conductance
mho
1
Magnetic field strength
oersted
7.958 × 101
E
siemens
S
ampere/metre
A·m–1
Magnetic flux
maxwell
1 × 10–2
E
microweber
lWb
Magnetic flux density
gauss
1 × 10–1
E
millitesla
mT
curie
3.7 × 101
nanosecond–1
ns–1
rad
Equivalent absorbed dose
Exposure to ionisation
RADIOACTIVITY
Activity of a radioactive
source
Absorbed dose
1×
10–2
E
joule/kilogram
J·kg–1
rem
1×
10–2
E
joule/kilogram
J·kg–1
roentgen
2.58 × 10–1
millicoulomb/kilogram
mC·kg–1
E — exact conversion factor
Example 1
Example 2
A boiler is rated at 150 000 Btu·h–1. In SI units this is
150 000 × (2.931 × 10–1) = 43 965 W = 43.965 kW.
A heating plant has an annual energy consumption of
500 GJ. In imperial units this is 500/(1.055 × 10–1) = 4740
therms. In technical metric units the factor quoted is for
converting between thermies and megajoules. Thus, 500
GJ must be transposed to MJ before being divided by the
conversion factor, i.e. (500 × 103)/4.186 = 119 446 thermies.
Units, standard and mathematical data
6-11
Table 6.8 Conversion factors in alphabetical subject order
×
Physical quantity
Previous unit
SI unit
SI symbol
Absorbed dose
rad
1 × 10–2
E
joule/kilogram
J·kg–1
Acceleration
foot/square second
3.048 ×
E
metre/square second
m·s–2
Angle
second
minute
grade
gon
degree
right angle
revolution
4.848
2.909 × 10–1
1.571 × 10–2
1.571 × 10–2
1.745 × 10–2
1.571
6.283
microradian
milliradian
radian
radian
radian
radian
radian
lrad
mrad
rad
rad
rad
rad
rad
Angular velocity
revolution per minute
revolution per second
1.047 × 10–1
6.283
radian/second
radian/second
rad·s–1
rad·s–1
Area
square inch
6.452 × 102
square millimetre
mm2
square foot
square yard
are
acre
hectare
square mile
6.452
9.290 × 10–2
8.361 × 10–1
1 × 102
4.047 × 103
1 × 104
2.590
square centimetre
square metre
square metre
square metre
square metre
square metre
square kilometre
cm2
m2
m2
m2
m2
m2
km2
Concentration
grain/cubic foot
2.288
gram/cubic metre
g·m–3
Conductance, electrical
mho
1
E
siemens
S
Conductance, thermal
kilocalorie/hour square metre
degree Celsius
Btu/hour square foot degree
Fahrenheit
calorie/second square centimetre
degree Celsius
1.163
E
watt/square metre kelvin
W·m–2·K–1
5.678
watt/square metre kelvin
W·m–2·K–1
4.187 × 101
kilowatt/square metre kelvin
kW·m–2·K–1
1.442 × 10–1
watt/metre kelvin
W·m–1·K–1
watt/metre kelvin
watt/metre kelvin
W·m–1·K–1
W·m–1·K–1
4.187 × 102
watt/metre kelvin
W·m–1·K–1
Conductivity, thermal
Btu inch/hour square foot degree
Fahrenheit
kilocalorie/hour metre degree
Celsius
Btu/hour foot degree Fahrenheit
calorie/second centimetre degree
Celsius
Factor
=
10–1
1.163
1.731
E
E
E
Density
pound/cubic foot
pound/gallon
pound/cubic inch
1.602 ×
9.978 × 101
2.768 × 101
kilogram/cubic metre
kilogram/cubic metre
megagram/cubic metre
kg·m–3
kg·m–3
Mg·m–3
Diffusivity, thermal
square inch/hour
square foot/hour
square metre/hour
1.792 × 10–1
2.581 × 10–1
2.778
square millimetre/second
square centimetre/second
square centimetre/second
mm2·s–1
cm2·s–1
cm2·s–1
erg
foot pound force
calorie*
metre kilogram force
British thermal unit
frigorie†
kilocalorie*
horsepower hour
kilowatt hour
thermie†
therm
1 × 10–1
1.356
4.187
9.807
1.055
4.186
4.187
2.685
3.6
4.186
1.055 × 10–1
E
microjoule
joule
joule
joule
kilojoule
kilojoule
kilojoule
megajoule
megajoule
megajoule
gigajoule
lJ
J
J
J
kJ
kJ
kJ
MJ
MJ
MJ
GJ
Enthalpy, specific
Btu/pound
kilocalorie/kilogram
2.326
4.187
E
kilojoule/kilogram
kilojoule/kilogram
kJ·kg–1
kJ·kg–1
Entropy
Btu/degree Rankine
kilocalorie/kelvin
1.899
4.187
kilojoule/kelvin
kilojoule/kelvin
kJ·K–1
kJ·K–1
Entropy, specific
Btu/pound degree Rankine
kilocalorie/kilogram kelvin
4.187
4.187
kilojoule/kilogram kelvin
kilojoule/kilogram kelvin
kJ·kg–1·K–1
kJ·kg–1·K–1
Equivalent absorbed dose
rem
1 × 10–2
joule/kilogram
J·kg–1
roentgen
2.58 ×
millicoulomb/kilogram
mC·kg–1
pound/hour
kilogram hour
pound/minute
kilogram/minute
1.260 ×
2.778 × 10–1
7.560 × 10–3
1.667 × 10–2
gram/second
gram/second
kilogram/second
kilogram/second
g·s–1
g·s–1
kg·s–1
kg·s–1
Energy, work, quantity
of heat
Exposure to ionisation
Flow rate, mass
E — exact conversion factor
* Based on the international calorie defined as 4.186 8 J
† Based on the 15C calorie determined as 4.185 5 J
101
E
E
10–1
10–1
6-12
Reference data
Table 6.8 Conversion factors in alphabetical subject order — continued
×
Physical quantity
Previous unit
SI unit
SI symbol
Flow rate, volume
cubic inch/minute
litre/hour
US gallon/hour
gallon/hour
cubic foot/hour
cubic inch/second
litre/minute
US gallon/minute
gallon/minute
cubic metre/hour
cubic foot/minute
cubic metre/minute
cubic foot/second
2.3732 × 10–4
2.778 × 10–4
1.052 × 10–3
1.263 × 10–3
7.866 × 10–3
1.639 × 10–2
1.667 × 10–2
6.309 × 10–2
7.577 × 10–2
2.778 × 10–1
4.719 × 10–1
1.667 × 101
2.832 × 10–2
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic decimetre/second
cubic metre/second
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
dm3·s–1
m3·s–1
Force
dyne
poundal
pound force
kilogram force
kilopond
1 × 101
1.383 × 10–1
4.448
9.807
9.807
E
micronewton
newton
newton
newton
newton
lN
N
N
N
N
Frequency
cycle/second
1
E
hertz
Hz
Heat capacity
Btu/degree Fahrenheit
kilocalorie/degree Celsius
1.899
4.187
kilojoule/kelvin
kilojoule/kelvin
kJ·K–1
kJ·K–1
Heat capacity, specific
Btu/pound degree Fahrenheit
kilocalorie/kilogram degree Celsius
4.187
4.187
kilojoule/kilogram kelvin
kilojoule/kilogram kelvin
kJ·kg–1·K–1
kJ·kg–1·K–1
Heat emission
Btu/hour cubic foot
1.035 × 101
watt/cubic metre
W·m–3
Illumination
foot candle
lumen/square foot
1.076 ×
1.076 × 101
lux
lux
lx
lx
Intensity of heat flow rate
kilocalorie/hour square metre
Btu/hour square foot
watt/square foot
1.163
3.155
1.076 × 101
watt/square metre
watt/square metre
watt/square metre
W·m–2
W·m–2
W·m–2
Latent heat
foot pound force/pound
Btu/pound
kilocalorie/kilogram
2.989
2.326
4.187
joule/kilogram
kilojoule/kilogram
kilojoule/kilogram
J·kg–1
kJ·kg–1
kJ·kg–1
Length
micron
thou’ (mil)
inch
foot
yard
mile
1
2.54 × 101
2.54 × 101
3.048 × 10–1
9.144 × 10–1
1.609
micrometre
micrometre
millimetre
metre
metre
kilometre
lm
lm
mm
m
m
km
Luminance
foot lambert
candela/square inch
3.426
1.550 × 103
candela/square metre
candela/square metre
cd·m–2
cd·m–2
Luminous intensity
candle
9.810 × 10–1
candela
cd
Magnetic field strength
oersted
7.958 × 101
ampere/metre
A·m–1
Magnetic flux
maxwell
1 × 10–2
E
microweber
lWb
Magnetic flux density
gauss
1 × 10–1
E
millitesla
mT
Mass
grain
ounce
pound
slug
hundredweight
ton (short)
tonne
ton
6.480 × 101
2.835 × 101
4.536 × 10–1
1.459 × 101
5.080 × 101
9.072 × 10–1
1
1.016
milligram
gram
kilogram
kilogram
kilogram
megagram
megagram
megagram
mg
g
kg
kg
kg
Mg
Mg
Mg
Mass per unit area
pound/square foot
4.882
kilogram/square metre
kg·m–2
Mass per unit length
pound/foot
pound/inch
1.488
1.786 × 101
kilogram/metre
kilogram/metre
kg·m–1
kg·m–1
Mass transfer coefficient
foot/hour
8.47 × 10–2
millimetre/second
mm·s–1
grain/pound
pound/pound
1.428 ×
1
gram/kilogram
kilogram/kilogram
g·kg–1
kg.kg–1
pound/square foot hour
grain/square foot hour
1.357
1.94 × 10–1
gram/square metre second
milligram/square metre
second
g·m–2·s–1
mg·m–2·s–1
kilogram square metre
kg·m2
Moisture content
Moisture flow rate
Moment of inertia
E — exact conversion factor
pound square foot
Factor
=
101
E
E
E
E
E
E
E
E
10–1
4.214 × 10–2
E
The word ‘litre’ may be employed as a special name for dm3
Units, standard and mathematical data
6-13
Table 6.8 Conversion factors in alphabetical subject order — continued
×
Physical quantity
Previous unit
Factor
=
Moment of momentum
pound square foot/second
4.214 × 10–2
Momentum
pound foot/second
1.383 ×
Permeability, vapour
grain inch/hour square foot inch of
mercury (perminch)
1.45
10–1
8.620
8.620
Permeance, vapour
Power, heat flow rate
Pressure
SI symbol
kilogram square metre/
second
kg·m2·s–1
kilogram metre/second
kg·m·s–1
nanogram metre/newton
second
nanogram/second pascal
metre
milligram metre/newton
second
milligram/second pascal
metre
1.45
pound foot/hour pound force
SI unit
ng·m·N–1·s–1
ng·s–1·Pa–1·m–1
mg·m·N–1·s–1
mg·s–1·Pa–1·m–1
grain/square foot hour inch of
mercury (perm)
grain/square foot hour millibar
pound square inch/square foot hour
pound force
pound/hour pound force
5.72 × 101
1.940
nanogram/newton second
microgram/newton second
ng·N–1·s–1
lg·N–1·s–1
1.965 × 10–1
2.834 × 101
milligram/newton second
milligram/newton second
mg·N–1·s–1
mg·N–1·s–1
British thermal unit/hour
kilocalorie/hour
foot pound force/second
calorie/second
metric horsepower (cheval vapeur)
horsepower
ton of refrigeration
Lloyd’s ton of refrigeration
2.931 × 10–1
1.163
1.356
4.187
7.355 × 10–1
7.457 × 10–1
3.517
3.884
watt
watt
watt
watt
kilowatt
kilowatt
kilowatt
kilowatt
W
W
W
W
kW
kW
kW
kW
millimetre of water
pound force/square foot
millimetre of mercury
torr
inch of water
foot of water
inch of mercury
pound force/square inch
kilogram force/square centimetre
bar
9.807
4.788 × 101
1.333 × 102
1.333 × 102
2.491 × 102
2.989
3.386
6.895
9.807 × 101
1 × 102
1 × 10–1
1.013 × 102
1.013 × 10–1
pascal
pascal
pascal
pascal
pascal
kilopascal
kilopascal
kilopascal
kilopascal
kilopascal
megapascal
kilopascal
megapascal
Pa
Pa
Pa
Pa
Pa
kPa
kPa
kPa
kPa
kPa
MPa
kPa
MPa
standard atmosphere
E
E
E
Pressure drop per unit
length
inch of water/hundred feet
foot of water/hundred feet
8.176
9.810 × 101
pascal/metre
pascal/metre
Pa·m–1
Pa·m–1
Radioactivity
curie
3.7 × 101
nanosecond–1
ns–1
Resistance, thermal
square centimetre second degree
Celsius/calorie
2.388 × 101
square decimetre kelvin/
watt
dm2·K·W–1
1.761 × 10–1
square metre kelvin/watt
m2·K·W–1
8.598 × 10–1
square metre kelvin/watt
m2·K·W–1
2.388 × 10–3
5.778 × 10–1
8.598 × 10–1
metre kelvin/watt
metre kelvin/watt
metre kelvin/watt
m·K·W–1
m·K·W–1
m·K·W–1
6.933
metre kelvin/watt
m·K·W–1
square foot hour degree
Fahrenheit/Btu
square metre hour degree Celsius/
kilocalorie
Resistivity, thermal
centimetre second degree
Celsius/calorie
foot hour degree Fahrenheit/Btu
metre hour degree Celsius/kilocalorie
square foot hour degree
Fahrenheit/Btu inch
Second moment of area
quartic inch
quartic foot
4.162 × 105
8.631 × 10–3
quartic decimetre
quartic metre
dm4
m4
Specific heat (volume basis)
kilocalorie/cubic metre degree
Celsius
Btu/cubic foot degree Fahrenheit
4.187
6.707 × 101
kilojoule/cubic metre kelvin
kilojoule/cubic metre kelvin
kJ·m–3·K–1
kJ·m–3·K–1
cubic foot/pound
6.243 × 10–2
cubic metre/kilogram
m3·kg–1
Stress
pound force/square foot
pound force/square inch
ton force/square foot
ton force/square inch
4.788 ×
6.895
1.073 × 102
1.544 × 101
pascal
kilopascal
kilopascal
megapascal
Pa
kPa
kPa
MPa
Time
minute
hour
6 × 101
3.6 × 103
E
E
second
second
s
s
day
8.64 × 104
E
second
s
Specific volume
E — exact conversion factor
101
6-14
Reference data
Table 6.8 Conversion factors in alphabetical subject order — continued
×
Physical quantity
Previous unit
Torque
pound force foot
1.356
foot/minute
kilometre/hour
foot/second
mile/hour
knot
5.080 ×
2.778 × 10–1
3.048 × 10–1
4.470 × 10–1
5.148 × 10–1
pound/hour foot
centipoise
poise
pound force second/square foot
pound force hour/square foot
4.134 × 10–1
1 × 10–3
1 × 10–1
4.788 × 101
1.724 × 102
Viscosity, kinematic
stokes
square metre/hour
square inch/second
square foot/minute
Redwood No. 1 and No. 2 seconds
SAE grades
Volume
cubic inch
US pint
pint
litre
US gallon
gallon
cubic foot
Velocity
Viscosity, dynamic
Volumetric calorific value
Factor
=
SI unit
SI symbol
newton metre
N·m
metre/second
metre/second
metre/second
metre/second
metre/second
m·s–1
m·s–1
m·s–1
m·s–1
m·s–1
millipascal second
pascal second
pascal second
pascal second
kilopascal second
mPa·s
Pa·s
Pa·s
Pa·s
kPa·s
1 × 10–2
E
2.778 × 10–2
6.452
1.548 × 10–3
No direct conversion
No direct conversion
square decimetre/second
square decimetre/second
square decimetre/second
square metre/second
dm2·s–1
dm2·s–1
dm2·s–1
m2·s–1
US barrel (petroleum)
cubic yard
1.639 × 10–2
4.732 × 10–1
5.683 × 10–1
1
3.785
4.546
2.832 × 101
2.832 × 10–2
1.590 × 10–1
7.646 × 10–1
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic decimetre
cubic metre
cubic metre
cubic metre
dm3
dm3
dm3
dm3
dm3
dm3
dm3
m3
m3
m3
kilocalorie/cubic metre
Btu/cubic foot
4.187
3.726 × 101
kilojoule/cubic metre
kilojoule/cubic metre
kJ·m–3
kJ·m–3
10–3
E
E
E
E
E
The word ‘litre’ may be employed as a special name for dm3
E — exact conversion factor
Table 6.9 The Beaufort scale
Beaufort
number
Description of wind
Observations
Limit of wind
speed / m·s–1
0
1
2
3
Calm
Light air
Light breeze
Gentle breeze
Smoke rises vertically
Direction of wind shown by smoke drift but not by wind vanes
Wind felt on face; leaves rustle; ordinary vane moved by wind
Leaves and small twigs in constant motion; wind extends light flag
Less than 0.5
0.5 to 1.5
1.5 to 3.0
3 to 6
4
5
6
7
Moderate breeze
Fresh breeze
Strong breeze
Moderate gale
Raises dust and loose paper; small branches are moved
Small trees in leaf begin to sway
Large branches in motion; umbrellas used with difficulty
Whole trees in motion; inconvenience felt when walking into wind
6 to 8
8 to 11
11 to 14
14 to 17
8
9
10
11
Fresh gale
Strong gale
Whole gale
Storm
Twigs broken off trees; generally impedes progress
Slight structural damage occurs (slates and chimney pots removed from roofs)
Seldom experienced inland; trees uprooted; considerable structural damage occurs
Very rarely experienced; accompanied by widespread damage
17 to 21
21 to 24
24 to 28
28 to 32
12
Hurricane
(Yacht crews take up golf)
32 to 36
With acknowledgement to P. Heaton
Units, standard and mathematical data
6-15
Table 6.10 SI units for catalogues
Quantity
Unit
Boilers:
— heat output
— heat input
— steam generation rate
— fuel firing rate (solid)
— fuel firing rate (gaseous)
— fuel firing rate (liquid)
— volume flow rate (combustion products)
— power to input (to drives)
— operating pressure
— hydraulic resistance
— draught conditions
kW
kW
kg·s–1
kg·s–1
dm3·s–1*
kg·s–1
m3·s–1
kW
kPa (bar)
Pa
Pa
Coil (cooling and heating):
— heat, exchange rate
— mass flow rate (primary medium)
— hydraulic resistance (primary medium)
— air volume flow rate
— air flow static pressure loss
kW
kg·s–1
Pa
m3·s–1
Pa
Controls and instruments:
— mass flow rate
— volume flow rate
— operating pressure
— hydraulic resistance
— rotational frequency
kg·s–1
m3·s–1
kPa (bar)
Pa
rev·s–1
Cooling towers:
— heat extraction rate
— volume flow rate (air)
— volume flow rate (water)
— power input (to drive)
kW
m3·s–1
dm3·s–1*
kW
Diffusers and grilles:
— air volume flow rate
— air flow pressure loss
— specific velocity
m3·s–1
Pa
m·s–1
Fans
— air volume flow rate
— power input (to drive)
— fan static pressure
— fan total pressure
— rotational frequency
— outlet velocity
m3·s–1
kW
Pa
Pa
rev·s–1
m·s–1
Filters:
— air volume flow rate
— liquid volume flow rate
— static pressure loss
m3·s–1
dm3·s–1*
Pa
* The word ‘litre’ may be employed as a special name for dm3
Quantity
Unit
Fuels:
— calorific value (solid)
— calorific value (gaseous)
— calorific value (liquid)
MJ·kg–1
MJ·m–3
MJ·kg–1
Heat exchangers:
— heat output
— mass flow rate
— hydraulic resistance
— operating pressure
— flow velocity
— heat exchange surface area
kW
kg·s–1
Pa
kPa (bar)
m·s–1
m2
Induction terminals:
— heating or cooling output
— volume flow rate (primary air)
— static pressure loss (primary air)
— mass flow rate (secondary water)
— hydraulic resistance (secondary water)
kW
m3·s–1
Pa
kg·s–1
Pa
Pumps:
— mass flow rate
— volume flow rate
— power input (to drive)
— developed pressure
— operating pressure
— rotational frequency
kg·s–1
dm3·s–1*
kW
Pa
kPa (bar)
rev·s–1
Space heating apparatus:
— heat output
— air flow volume flow rate
— power input (to drive)
— mass flow rate (primary medium)
— hydraulic resistance
— operating pressure
— air flow static pressure loss
kW
m3·s–1
kW
kg·s–1
Pa
kPa (bar)
Pa
Vessels:
— operating pressure
— volumetric capacity
kPa (bar)
dm3* or m3
Washers (air):
— volume flow rate (air)
— volume flow rate (water)
— mass flow rate (water)
— power input (to drive)
— air flow static pressure loss
— hydraulic resistance
m3·s–1
dm3·s–1*
kg·s–1
kW
Pa
Pa
Water chillers:
— cooling capacity
— mass flow rate (water)
— power input (to drive)
— refrigerant pressure
— hydraulic resistance
kW
kg·s–1
kW
kPa (bar)
Pa
6-16
Reference data
Table 6.11 Birmingham gauge and standard wire gauge thickness
BG
SWG
Thickness
/ mm
BG
SWG
Thickness
/ mm
52
—
50
48
—
50
—
—
0.024
0.025
0.030
0.039
20
—
18
16
—
18
—
—
0.996
1.219
1.257
1.588
—
46
44
42
48
—
46
—
0.041
0.049
0.061
0.078
—
14
—
12
16
—
14
—
1.626
1.994
2.032
2.517
—
40
—
38
44
—
42
40
0.081
0.098
0.102
0.122
—
10
—
8
12
—
10
—
2.642
3.175
3.251
3.988
—
36
—
34
38
—
36
—
0.152
0.155
0.193
0.196
—
—
6
—
8
6
—
4
4.064
4.877
5.032
5.893
—
32
—
30
34
—
32
—
0.234
0.249
0.274
0.312
4
—
2
—
—
2
—
0
6.350
7.010
7.993
8.230
—
—
28
—
30
28
—
26
0.315
0.376
0.397
0.457
—
—
0
—
2/0
3/0
—
4/0
8.839
9.449
10.07
10.16
26
—
24
—
—
24
—
22
0.498
0.559
0.629
0.711
—
2/0
—
3/0
5/0
—
6/0
7/0
22
—
—
20
0.794
0.914
4/0
5/0
—
—
Table 6.13 Standard values and reference values
Physical quantity
Value
Air (CIBSE reference conditions):
— density
— pressure
— relative humidity
— specific heat capacity
— temperature (dry bulb)
1.200
101.325
43
1.02
20
6.02217 1023
mol–1
Base of natural logarithms (e)
2.718 28
—
Gas constants:
— universal
— dry air
— steam
8.314
287
461
Gravitational acceleration
9.806 65
Gravitational constant
Light, speed of (in vacuo)
299.792
J·s
Permeability of free space
1.257
lH·m–1
Permittivity of free space
8.854
pF·m–1
Sound, reference level:
— intensity
— reference power
— reference pressure
1
1
20
10.97
11.31
11.79
12.70
Sound, speed of:
— in dry air at 20 C
— in water at 20 C
— in copper
— in mild steel
343.6
1497
4760
5960
13.76
14.94
Stefan–Boltzmann constant
Velocity
/ m·s–1
0.25
0.25
0.35
0.40
0.20
0.20
0.20
0.25
2.5
3.0
4.0
5.0
0.45
0.50
0.70
0.80
0.35
0.35
0.50
0.50
6.0
8.0
10
12
1.0
1.25
1.5
1.75
0.75
0.75
0.75; 1.0; 1.25
1.0; 1.25; 1.5
16
20
24
30
2.0
2.5
3.0
3.5
1.0; 1.5
1.0; 1.5; 2.0
1.0; 1.5; 2.0
1.0; 1.5; 2.0; 3.0
36
42
48
56
4.0
4.5
5.0
5.5
1.5; 2.0; 3.0
1.5; 2.0; 3.0; 4.0
1.5; 2.0; 3.0; 4.0
1.5; 2.0; 3.0; 4.0
64
6.0
1.5; 2.0; 3.0; 4.0
Note: hexagon head bolts and screws are classified as
‘M’ followed by the nominal diameter, e.g. M10 is a
10 mm diameter bolt.
Mm·s–1
6.626 10–34
Nominal
diam. / mm
1.0
1.2
1.6
2.0
m·s–2
Planck’s constant
Table 6.14 Velocity pressure of wind
Fine
J·mol–1·K–1
J·kg–1·K–1
J·kg–1·K–1
pN·m2·kg–2
66.7
Table 6.12 Preferred ISO metric screw thread sizes
Coarse
kg·m–3
kPa
%
kJ·kg–1·K–1
C
Avogadro’s number
Circle, ratio of circumference
to diameter (π)
Pitch / mm
Unit
0.5
1
2
3
Pressure
/ Pa
1.56 × 101
6.25 × 10– 1
2.5
5.6
pW.m–2
pW
lPa
m·s–1
m·s–1
m·s–1
m·s–1
56.696
3.141 59
nW·m–2·K–4
—
Velocity
/ m·s–1
Pressure
/ Pa
10
11
15
20
6.25 × 10
7.55 × 10
1.39 × 102
2.5 × 102
4
5
6
7
10
1.56 × 10
2.25 × 10
3.05 × 10
25
30
35
40
3.9 × 102
5.63 × 102
7.61 × 102
1.0 × 103
8
9
4.0 × 10
5.05 × 10
45
50
1.27 × 103
1.56 × 103
Units, standard and mathematical data
6-17
Table 6.15 Dimensionless constants
Field
Name
Symbol
Definition
Momentum transport
Reynolds number
Re
Re
qvl
vl
g m
Euler number
Eu
Eu
Dp
q v2
Froude number
Fr
Fr
v
—–
√lg
Grashof number
Gr
Gr
l 3 g Dh
m2
Weber number
We
We
q v2 l
r
Mach number
Ma
Ma Knudsen number
Kn
Kn
k*
l
Strouhal number
Sr
Sr
lf
v
Fourier number
Fo
Fo
kt
at
2
cp q l 2
l
Péclet number
Pe
Pe
q cp v l
vl
Re × Pr
k
e
Rayleigh number
Ra
Ra
l 3 q2 cp g Dh
l 3 g Dh
Gr × Pr
gk
ma
Nusselt number
Nu
Nu
hl
k
Stanton number
St
St
h
Nu/Pe
q v cp
Fourier number
for mass transfer
Fo*
Fo* Dt
Fo/Le
l2
Péclet number
for mass transfer
Pe*
Pe* vl
Pe × Le
D
Grashof number
for mass transfer
Gr*
Gr* l 3 g b Dx
m2
Nusselt number
for mass transfer
Nu*
Nu* kl
qD
Stanton number
for mass transfer
St*
St* k
Nu*
qv
Pe*
Prandtl number
Pr
Pr
g cp
m
k
α
Schmidt number
Sc
Sc
g
m
qD
D
Lewis number
Le
Le
k
α
Sc
q cp D
D
Pr
Transport of heat
Transport of matter in
binary mixture
Constants of matter
Symbols used in table:
D
diffusion coefficient
c
velocity of sound
cp
specific heat capacity at constant pressure
f
characteristic frequency
g
acceleration due to gravity
h
coefficient of heat transfer:
heat/(time × cross-sectional area × temperature difference)
k
mass transfer coefficient:
mass/(time × cross-sectional area × mole fraction difference)
l
characteristic length
t
characteristic time interval
v
characteristic velocity
Δp
pressure difference
Δx
characteristic difference of mole fraction
Δh
α
b
g
h
k
k*
m
q
r
v
c
characteristic temperature difference
thermal diffusivity: α = k /q cq
1 q
b–
q x ,p
1 q
cubic expansion coefficient: = –
q h
viscosity (dynamic viscosity)
temperature
thermal conductivity
mean free path
kinematic viscosity (= g /q)
density (mass density)
surface tension
( )
( )
p
6-18
Reference data
Table 6.16 Geometric formulae
Shape
Triangle
c
b
Plan area, A
Centre of gravity (G)
ah
2
h
up from base
3
About G, in x-plane:
k2 =
h
2 a1 + a2
a1
a
Radius of gyration, k (I = A k2)
a2
3
Square
h2
18
About G, in y-plane:
across
a 21 a1 a2 a 22
k2 =
18
About base:
a2
At centre
a2
3
k2 =
a
About G:
a2
12
k2 a
Rectangle
About base:
At centre
ab
b2
3
k2 =
b
About G, in x-plane:
a
k2 =
Hollow square tube
b2
12
About G:
A2
–
a2
At centre
k2 =
A
A4 – a4
12 (A2 – a2)
a
a
A
Hollow rectangular tube
About G, in x-plane:
AB–ab
At centre
k2 =
A B3 – a b3
12 (A B – a b)
B
b
About G, in y-plane:
a
k2 =
A
A3 B – a3 b
12 (A B – a b)
I-section
About G, in x-plane:
AB–2ab=at+2BT
T
At centre
k2 =
B3 (A – a) + a (B – 2 b)3
12 (A B – 2 a b)
b
B
t
About G, in y-plane:
a
k2 =
A
A3 B – 2 a3 b
12 (A B – 2 a b)
Circle
π d2
d
4
About G:
At centre
k2 =
d2
16
Units, standard and mathematical data
6-19
Table 6.16 Geometric formulae — continued
Shape
Volume, V
Sector of circle
Plan area, A
Centre of gravity (G)
Radius of gyration, k (I = A k2)
d2 h
8
2 d sin ( /2)
3h
About G, in x-plane:
θ
k2 =
d 2 h – sin h
4
4h
(
)
About G, in y-plane:
k2 =
θ in radians
Cone
π d2 h
12
dh
2
h
up from base
4
h
d2 h + sin h 16 sin2 (/2)
–
4
4h
9 h2
(
About G, in x-plane:
k2 =
3 (h2 + d 2)
80
About tip:
On axis
k2 =
3 d2
40
d
Cylinder
π h d2
4
h
π d2
(x-plane)
4
About G, in x-plane:
At centre
k2 d h (z-plane)
(4 h2 + 3 d 2)
48
About G, in z-plane:
k2 =
d2
8
d
Hollow cylinder
π h (D2 – d2)
4
π (D2 – d 2)
(x-plane)
4
About G, in x-plane:
At centre
k2 =
4 h2 + 3 (D2 + d2)
48
h (D – d) (z-plane)
h
About G, in z-plane:
k2 =
D2 + d2
8
d
D
Sphere
About G:
π d3
6
π d2
4
At centre
abc
b c (x-plane)
At centre
k2 =
d
d2
10
Rectangular block
About G, in x-plane
k2 =
c
b
a
a2 + c2
12
)
6-20
Bibliography
BS 350: 2004: Conversion factors for units (London: British Standards
Institution) (2004)
BS ISO 31: Specifications for quantities, units and symbols: Part 0: 1992:
General principles; Part 1: 1992: Space and time; Part 2: 1992: Periodic and
related phenomena; Part 3: 1992: Mechanics; Part 4: 1992: Heat; Part 5:
1992: Electricity and magnetism; Part 6: 1992: Light and related
electromagnetic radiations; Part 7: 1992: Acoustics; Part 8: 1992: Physical
chemistry and molecular physics; Part 9: 1992: Atomic and nuclear physics;
Part 10: 1992: Nuclear reactions and ionizing radiations; Part 11: 1992:
Mathematical signs and symbols for use in physical sciences and technology;
Part 12: 1992: Characteristic numbers; Part 13: 1992: Solid state physics
(London: British Standards Institution) (dates as indicated)
BS ISO 1000: 1992: SI units and recommendations for the use of their
multiples and of certain other units (London: British Standards Institution)
(1992)
Reference data
Council Directive 80/181/EEC of 20 December 1979 on the
approximation for the laws of the Member States relating to units of
measurement and on the repeal of Directive 71/354/EEC Official J. of the
European Communities L39 40–50 (15.2.1980) (Brussels: Commission for
the European Communities) (1980)
Council Directive 85/1/EEC of 18 December 1984 amending Directive
80/181/EEC on the approximation of the laws of the Member States
relating to units of measurement Official J. of the European Communities
L2 11–12 (3.1.1985) (Brussels: Commission for the European
Communities) (1985)
Council Directive 89/617/EEC of 27 November 1989 amending Directive
80/181/EEC on the approximation of the laws of the Member States
relating to units of measurement Official J. of the European Communities
L357 28–30 (7.12.1989) (Brussels: Commission for the European
Communities) (1989)
Index
Index
absorptivity data for various materials 3-11 to
3-12
adiabatic saturation temperature, humid air
1-2
data 1-7 to 1-67
air ducts see ducts and ductwork
air handling units, air velocities 4-10
air properties 4-11, 4-63
see also psychrometric data
air velocity
ductwork and air handling units 4-10
effect on heat transfer at surfaces 3-24,
3-26, 3-31
open water 3-36
air velocity pressures, ductwork 4-17
aluminium, equivalent roughness 4-4
ammonia gas, properties 4-64
angle factors see view factors
ash content
coal 5-3
pelletised refuse derived fuel (d-RDF) 5-4
petroleum fuel oils 5-5
wood fuels 5-4
atmospheric pressures and temperatures 1-4
Beaufort scale 6-14
bends
pressure loss factors
circular ductwork 4-27 to 4-30, 4-31
to 4-33
flat-oval ductwork 4-51
pipes and pipework 4-19
rectangular ductwork 4-52 to 4-54
Birmingham gauge thickness 6-16
boiler rating, conversion factors 6-10
branch tees
pressure loss factors
circular ductwork 4-33 to 4-49
flat-oval ductwork 4-51 to 4-52
pipework 4-22 to 4-25
rectangular ductwork 4-56 to 4-58
brass pipes, equivalent roughness 4-4
brick, equivalent roughness 4-4
building components, thermal performance
3-36
buoyancy 4-7, 4-8
circulating pressures 4-9
buried pipes, heat emission 3-28 to 3-30
butane 5-6 to 5-7
properties 4-64
calorific values
coal 5-2 to 5-3, 5-4
landfill gas 5-8
liquefied petroleum gas 5-7
natural gas 5-7
pelletised refuse derived fuel (d-RDF) 5-4
petroleum fuel oils 5-5
wood fuel 5-4
capacity (K) 4-8, 4-69
carbon dioxide, properties 4-64
carbon monoxide, properties 4-64
cavities, free convection inside 3-4, 3-6
ceilings
heat emission/absorption 3-15 to 3-17
view factors 3-20
circular ductwork
pressure loss factors 4-27 to 4-51
angled off-sets 4-49
bends and elbows 4-31 to 4-33
branch tees 4-33 to 4-49
changes of section 4-30 to 4-33
elbows and bends 4-27 to 4-30
I-1
circular ductwork (continued)
pressure loss factors
inlets and outlets 4-50 to 4-51
transitions with rectangular
ductwork 4-60
see also ducts and ductwork
coal
calorific values 5-2 to 5-3, 5-4
classification 5-1 to 5-2
combustion data 5-8, 5-9
flue gas losses 5-10
properties 5-2 to 5-4
smokeless solid fuels 5-2
Colebrook-White equation 4-3
combined convective and radiative heat
transfer
in enclosures 3-17
human body and surroundings 3-15
combustion air requirements
natural gas 5-9
petroleum fuel oils 5-9
solid fuels 5-8, 5-9
combustion data
coal 5-8, 5-9
natural gas 5-9
petroleum fuel oils 5-8 to 5-9
combustion products
natural gas 5-9
petroleum fuel oils 5-9
solid fuels 5-8
compressible flow 4-74
concrete pipes, equivalent roughness 4-4
condensation, mass transfer 3-14
condensation temperature see saturation
temperature
condensers 3-35
see also heat exchangers
conduction see heat conduction
contractions
pressure loss factors
circular ductwork 4-31 to 4-33, 4-47
pipework 4-20 to 4-21, 4-21 to 4-22,
4-31
convection see heat convection
convection coefficients 3-4
external and internal surfaces 3-15
human body 3-18
straight plane tubes 3-32 to 3-33
conversion factors 6-6 to 6-14
in alphabetical subject order 6-11 to 6-14
electricity and magnetism 6-10
energy 6-9
energy content 6-9 to 6-10
flow rate 6-8
force and torque 6-8
light 6-10
mass and density 6-7
moisture content 6-10
momentum 6-8
power 6-9
pressure and stress 6-8
radioactivity 6-10
space and time 6-7
viscosity 6-8
cooling ponds, heat transfer 3-35 to 3-36
copper pipes
equivalent roughness 4-4
internal diameters 4-2 to 4-3, 4-5
wall thickness 4-5
corrosion, water pipes, allowance for 4-8
cross conduction between pipes 3-30
cross flow, forced convection in 3-4, 3-6
cylinders
forced convection over, in cross flow 3-4,
3-6
cylinders (continued)
heat conduction through
3-9
dampers, ductwork, pressure loss factors 4-58
D’Arcy equation 4-2
delivery pressure 4-7
density
air 4-11, 4-63
water 2-4 to 2-6, 4-9, 4-63
see also specific volume
dew point temperature
data 1-7 to 1-67
formula 1-2
dimensionless constants 6-17
double glazing 3-4, 3-36
d-RDF 5-4
ducts and ductwork
air flow in ducts 4-10 to 4-17
air velocities 4-10
flat-oval ductwork 4-15 to 4-16, 4-51
to 4-52
flexible ductwork 4-13
friction coefficients 4-13
noise 4-11
non-circular ducts 4-13
pressure drop per unit length 4-11
to 4-16
pressure loss factors see pressure loss
factors
rectangular ductwork 4-13 to 4-15,
4-58 to 4-60
spirally wound ductwork 4-11
fluid flow theory 4-1 to 4-8
basic principles 4-2 to 4-3
buoyancy 4-7
equivalent roughness for various
materials 4-4
flexible steel-reinforced smooth
rubber hoses 4-7
head and head loss 4-7
laminar flow 4-3
non-circular ducts 4-7
notation 4-1 to 4-2
pressure measurements 4-7
turbulent flow 4-3 to 4-4
unpredictable flow 4-7
sizing of ducts 4-10, 4-65 to 4-68
surface heat emission/absorption
3-30 to 3-32
dynamic viscosity
air 4-11
water 2-4 to 2-6, 4-9
elbows
pressure loss factors
circular ductwork 4-28 to 4-30
pipes and pipework 4-19 to 4-21
rectangular ductwork 4-54 to 4-56
electricity 5-2
emissivity
data for various materials 3-11 to 3-12
definition 3-10
enclosed spaces
combined convective and radiative heat
transfer 3-17
human body heat transfer 3-17 to 3-21
radiation exchange between internal
surfaces 3-15 to 3-17
enclosures see cavities; cylinders; tubes
energy consumption, conversion factors 6-10
enthalpy see specific enthalpy
equivalent diameters
flat-oval spirally wound ducts 4-16
non-circular ducts 4-13, 4-14
I-2
Reference data
equivalent radiative heat transfer coefficient
3-11, 3-14
equivalent roughness, pipe and duct materials
4-2 to 4-4
ethylene-glycol–water mixture, properties
4-63
EU units 6-5 to 6-6
evaporation, mass transfer 3-14
evaporators 3-35
see also heat exchangers
exhaust vents, pressure loss factors 4-50, 4-59
expansion (thermal)
water and pipework 4-8, 4-9
expansions
pressure loss factors
circular ductwork 4-30 to 4-33, 4-46
pipework 4-21 to 4-22
external surfaces
heat exchange 3-14 to 3-15
heat transfer coefficient 3-25, 3-27, 3-31
proximity effects on pipe heat emission
3-24
thermal performance 3-36
extracts, ductwork, pressure loss factors 4-50,
4-59
film coefficients see convection coefficients
finned surfaces, pipes 3-24
flat plates, forced convection over 3-4
flat structures, heat conduction 3-9
flat-oval ductwork
areas and perimeters 4-15
equivalent diameters 4-15 to 4-16
pressure loss factors 4-51 to 4-52
flexible ductwork
correction factors 4-13
equivalent roughness 4-4
flexible steel-reinforced smooth rubber hoses
4-7
floors
convection coefficients 3-15
view factors 3-18 to 3-20
see also internal surfaces
flue gas losses
coal 5-10
natural gas 5-11
petroleum fuel oils 5-10 to 5-11
fluid capacity see capacity
fluid flow in pipes and ducts 4-1 to 4-8
basic principles 4-2 to 4-3
buoyancy 4-7
compressible flow 4-74
equivalent roughness for various materials
4-4
flexible steel-reinforced smooth rubber
hoses 4-7
head and head loss 4-7
laminar flow 4-3
non-circular ducts 4-7
notation 4-1 to 4-2
pressure measurements 4-7
turbulent flow 4-3 to 4-4
unpredictable flow 4-4
see also ducts and ductwork; pipes and
pipework
form factors see view factors
fouling resistances, various types of water
3-33
friction coefficient 4-2 to 4-3
flexible rubber hoses 4-7
fuel classification 5-1
fuel gases, properties 4-64
fuel oils see petroleum fuel oils
gas flow in pipes
4-10
gas flow in pipes (continued)
see also pipes and pipework
gases, properties 4-64
see also air properties
geometric formulae 6-18 to 6-19
glass, equivalent roughness 4-4
glazing see windows
graded coals 5-2, 5-3 to 5-4
graphs, labelling 6-5
ground ambient temperatures 3-30
Haaland equation 4-4
head and head loss 4-7
heat capacity see specific heat capacity
heat conduction 3-8 to 3-10
combined with convection 3-9 to 3-10
cylindrical structures 3-9
flat structures 3-9
heat convection 3-3 to 3-8
combined convective and radiative heat
transfer in enclosures 3-17,
3-21
combined with conduction 3-9 to 3-10
convection coefficients 3-3 to 3-4
convective exchange at external surfaces
3-15
effect of air velocity 3-24
effect of proximity of walls 3-24
forced convection over cylinders in cross
flow 3-7
free convection in enclosures 3-4
free convection over surfaces 3-5
heat emission from place surfaces 3-23
human body heat transfer 3-18
internal surface convection coefficients
3-15
laminar flow in tubes 3-8
from plane surfaces 3-24
heat emission/absorption see heat transfer
heat exchangers 3-32 to 3-35
heat radiation 3-10 to 3-14
between an enclosure and a contained
surface 3-11
combined convective and radiative heat
transfer in enclosures 3-17,
3-21
concentric curved surfaces 3-10
data for various materials 3-11 to 3-12
effect of proximity of walls 3-24
equivalent radiative heat transfer
coefficient 3-11
human body heat transfer 3-18 to 3-20
parallel flat surfaces 3-10
plane surfaces, data 3-24
radiation exchange between internal
surfaces 3-15 to 3-17
radiative exchange at external surfaces
3-14
radiative heat transfer coefficient 3-11,
3-14
small surfaces, well separated 3-10
heat transfer 3-1 to 3-38
absorptivity/emissivity data for various
materials 3-11, 3-12
equipment and component surfaces 3-21
to 3-36
air ducts 3-30 to 3-32
bare pipes 3-21, 3-24 to 3-25, 3-26
building components 3-36
buried pipes 3-28 to 3-30
heat exchangers 3-32 to 3-35
insulated pipes 3-25, 3-27 to 3-28,
3-30
open water surfaces 3-35 to 3-36
plain surfaces 3-21, 3-22 to 3-24
heat transfer (continued)
external environment 3-14 to 3-15
human body 3-17 to 3-21
internal environment 3-14 to 3-15
mass transfer 3-14
notation 3-1 to 3-3
see also heat conduction; heat convection;
heat radiation
human body heat transfer 3-17 to 3-21
by convection 3-18
by radiation 3-18 to 3-20
total heat exchange with surroundings
3-21
humid air see psychrometric data
humidification, mass transfer 3-14
hydraulic diameter 4-13
non-circular ducts 4-7
imperial units, conversion factors 6-6 to 6-14
indoor pools, heat transfer 3-35 to 3-36
inlets, pressure loss factors
circular ductwork 4-50 to 4-51
rectangular ductwork 4-59, 4-60
insulated air ducts, U-values 3-31
insulated pipes
heat emission/absorption 3-25, 3-27 to
3-28, 3-30
buried pipes 3-28 to 3-30
data 3-27
insulating materials, thermal conductivity
3-27, 3-29
internal diameters
copper pipes 4-2 to 4-3, 4-5
polymer pipes 4-3, 4-6
steel and iron pipes 4-5
internal surfaces
convection coefficients 3-15
proximity effects on pipe heat emission
3-24
radiation exchange between 3-15 to 3-17
see also view factors
International System of Units (SI) 6-1 to 6-4,
6-15
iron pipes, internal diameters 4-5
kinematic viscosity, water
4-9
laminar flow 3-4, 3-8, 4-3
landfill gas 5-8
latent heats of vapourisation, liquefied
petroleum gas 5-6, 5-7
lead pipes, equivalent roughness 4-4
liquefied petroleum gas (LPG) 5-2
properties 5-6 to 5-7
mesh screens, ductwork, pressure loss factors
4-50, 4-60
methane, properties 4-64
metrication 6-5 to 6-6
moisture content
humid air 1-2
data 1-7 to 1-67
monoethylene-glycol–water mixture,
properties 4-63
Moody chart 4-1, 4-3
multipass heat exchangers, correction factors
3-34
multiple banks of pipes
heat emission/absorption 3-24
correction factors 3-26
natural gas 5-2
combustion data 5-9
flow in pipework 4-10
flue gas losses 5-11
Index
natural gas (continued)
properties 5-7 to 5-8
nitrogen, properties 4-64
noise
ducts and ductwork 4-11
water pipes 4-8
non-circular ducts 4-7, 4-13 to 4-16
see also flat-oval ductwork; rectangular
ductwork
notation
fluid flow in pipes and ducts 4-1 to 4-2
heat transfer 3-1 to 3-3
water and steam properties 2-1
Nusselt number
forced convection over cylinders in cross
flow 3-7
free convection in enclosures 3-6
free convection over surfaces 3-5
laminar flow in tubes 3-8
open water surfaces, heat transfer 3-35 to 3-36
orifices, pipework, pressure loss factors 4-26
outdoor pools, heat transfer 3-35 to 3-36
oxygen, properties 4-64
pelletised refuse derived fuel (d-RDF) 5-4
percentage saturation
humid air 1-2
data 1-7 to 1-67
petroleum burner fuels 5-5
petroleum fuel oils 5-2
classification 5-4 to 5-5
combustion data 5-8 to 5-9
flue gas losses 5-10 to 5-11
heating requirements 5-6
properties 4-65, 5-5 to 5-6
storage and handling temperatures 5-6
physical quantities
conversion factors 6-6 to 6-14
EU units 6-5 to 6-6
SI units 6-1 to 6-4
standard and reference values 6-16
pipes and pipework
fluid flow theory 4-1 to 4-8
basic principles 4-2 to 4-3
buoyancy 4-7
equivalent roughness for various
materials 4-4
flexible steel-reinforced smooth
rubber hoses 4-7
head and head loss 4-7
laminar flow 4-3
notation 4-1 to 4-2
pressure measurements 4-7
turbulent flow 4-3 to 4-4
unpredictable flow 4-7
gas flow 4-10
internal diameters 4-2 to 4-3, 4-5 to 4-6
pressure loss factors 4-18 to 4-26
branch tees 4-22 to 4-25
changes of section 4-21 to 4-22
elbows and bends 4-19 to 4-21
orifices 4-26
pipe joints 4-26
sizing of pipes 4-8, 4-9, 4-65 to 4-68
steam flow 4-10, 4-70 to 4-73
surface heat emission/absorption
buried pipes 3-28 to 3-30
effect of air velocity 3-26, 3-27
effect of proximity of walls 3-24
finned surfaces 3-24
horizontal pipes 3-21, 3-24, 3-25,
3-26
insulated pipes 3-25, 3-27 to 3-28,
3-30
I-3
pipes and pipework (continued)
surface heat emission/absorption
multiple banks of pipes 3-24, 3-26
outside surface heat transfer
coefficient 3-25, 3-27
vertical pipes 3-21, 3-26
water flow 4-8 to 4-10
allowances for ageing 4-8
buoyancy, thermosyphon 4-8
noise 4-8
pipe sizing 4-8, 4-9
pipework fittings 4-9 to 4-10
water expansion 4-8
water hammer 4-8
water velocities 4-8
polymer pipes
equivalent roughness 4-4
internal diameters 4-3, 4-6
pressure loss factors 4-26
pour point, petroleum fuel oils 5-5
Prandtl number
saturated steam, data 2-2 to 2-3
water, data 2-4 to 2-6
pressure drop per unit length 4-2
circular ducts 4-11 to 4-13
non-circular ducts 4-7, 4-13 to 4-16
see also pressure loss factors
pressure head 4-7
pressure loss factors 4-7
circular ductwork 4-27 to 4-51
angled off-sets 4-49
bends and elbows 4-27 to 4-30, 4-31
to 4-33
branch tees 4-33 to 4-49
changes of section 4-30 to 4-33
inlets and outlets 4-50 to 4-51
flat-oval ductwork 4-51 to 4-52
pipework fittings 4-9, 4-18 to 4-26
branch tees 4-22 to 4-25
changes of section 4-20 to 4-22
elbows and bends 4-19 to 4-21
orifices 4-26
pipe joints 4-26
valves 4-25 to 4-26
rectangular ductwork 4-52 to 4-60
angled off-sets 4-58
bends and elbows 4-52 to 4-56
branch tees 4-56 to 4-58
exhaust vents 4-59
inlet vents 4-59
inlets and outlets 4-59 to 4-60
mesh screens 4-60
pressure measurements, straight
pipes and ducts 4-7
propane 5-6 to 5-7
properties 4-64
psychrometric data 1-1 to 1-67
basis of calculations 1-1 to 1-3
corrections for non-standard barometric
pressures 1-3 to 1-4
psychrometric charts 1-4 to 1-6
pump head 4-7
quantities and units
6-4 to 6-5
radiation see heat radiation
radiation view factors
human body heat transfer 3-18 to 3-20
various geometries 3-12 to 3-13
radiative heat transfer coefficient 3-11, 3-14
rectangular ductwork
equivalent diameters 4-13 to 4-15
pressure loss factors
angled off-sets 4-58
bends and elbows 4-52 to 4-56
rectangular ductwork (continued)
pressure loss factors
branch tees 4-56 to 4-58
exhaust vents 4-59
inlet vents 4-59
mesh screens 4-60
opposed blade dampers 4-58
transitions with circular ductwork
4-60
reference values 6-16
refuse derived fuel (d-RDF) 5-4
relative humidity 1-2
data 1-7 to 1-67
relative roughness 4-2 to 4-4
reservoirs, heat transfer 3-35 to 3-36
Reynolds equation 4-2
rooms
combined convective and radiative heat
transfer in enclosures 3-17, 3-21
human body heat transfer 3-17 to 3-21
radiation exchange between internal
surfaces 3-15 to 3-17
roughness, relative 4-2 to 4-4
rubber hoses, flexible steel-reinforced 4-7
saturated vapour pressures
humid air 1-1, 1-2
data 1-7 to 1-67
saturation temperature
humid air 1-2
data 1-7 to 1-67
scaling, water pipes, allowance for 4-8
screw thread sizes 6-16
SI units 6-1 to 6-4
conversion factors 6-6 to 6-14
equipment and components 6-15
smokeless solid fuels 5-2
soils, thermal conductivity 3-29, 3-30
specific enthalpy
humid air 1-3
data 1-7 to 1-67
non-standard barometric pressures
1-3 to 1-4
saturated steam 2-2 to 2-3
superheated steam 2-7
water 2-4 to 2-6
specific heat capacity
air 4-11, 4-63
saturated steam 2-2 to 2-3
water 2-4 to 2-6, 4-63
specific volume
humid air 1-2 to 1-3
data 1-7 to 1-67
saturated steam 2-2 to 2-3
see also density
spirally wound ductwork
additional pressure drop 4-11, 4-13
flat-oval ductwork 4-15
stack losses
coal 5-10
natural gas 5-11
petroleum fuel oils 5-10 to 5-11
standard values 6-16
standard wire gauge thickness 6-16
steam flow in pipes 4-10, 4-70 to 4-73
steam properties
notation 2-1
saturated, data 2-2 to 2-3
superheated 2-7
steel duct, equivalent roughness 4-4
steel pipes
equivalent roughness 4-4
internal diameters 4-5
Stefan–Boltzmann law 3-10
superheated steam, specific enthalpy 2-7
I-4
sulphur content
coal 5-3
liquefied petroleum gas (LPG) 5-7
natural gas 5-8
petroleum fuel oils 5-5
surface heat transfer 3-21 to 3-36
air ducts 3-30 to 3-32
bare pipes 3-21, 3-24 to 3-25, 3-26
building components 3-36
buried pipes 3-28 to 3-30
forced convection 3-4
free convection 3-4, 3-5
heat exchangers 3-32 to 3-35
insulated pipes 3-25, 3-27 to 3-28
open water surfaces 3-35 to 3-36
plain surfaces 3-21, 3-22 to 3-24
swimming pools, outdoor, heat transfer 3-35
to 3-36
symbols and units see notation
tables, labelling 6-5
tapers see contractions; expansions
tees see branch tees
thermal capacity see specific heat capacity
thermal conductivity
insulating materials 3-27, 3-29
soils 3-29, 3-30
thermal expansion, water and pipework 4-8,
4-9
thermosyphon 4-7, 4-8
circulating pressures 4-9
tubes
convective film coefficient 3-32 to 3-33
forced convection inside 3-4, 3-8
Electricity in buildings
turbulent flow
4-3 to 4-4
units and quantities 6-1 to 6-5
see also notation
valves, pipework, pressure loss factors 4-25 to
4-26
vapour pressures
humid air 1-1, 1-2
data 1-7 to 1-67
water 2-4 to 2-6
velocity pressures
air 4-17
water 4-9 to 4-10
wind 6-16
vertical pipes
heat emission/absorption 3-21
correction factors 3-26
view factors
human body heat transfer 3-18 to 3-20
various geometries 3-12 to 3-13
viscosity
air 4-11, 4-63
petroleum fuel oils 5-5, 5-6
water 4-9, 4-63
wall thickness, copper pipes 4-5
walls, external see external surfaces
walls, internal see internal surfaces
waste gas volume
natural gas 5-9
petroleum fuel oils 5-9
solid fuels 5-8
water flow in pipes and pipework 4-8 to 4-10
water flow in pipes and pipework (continued)
allowances for ageing 4-8
buoyancy, thermosyphon 4-8
noise 4-8
pipe sizing 4-8, 4-9, 4-65 to 4-68
pipework fittings 4-9
water expansion 4-8
water hammer 4-8
water velocities 4-8
see also pipes and pipework
water hammer 4-8
water properties 4-63
data 2-4 to 2-6, 4-9
expansion 4-9
notation 2-1
velocity pressures 4-9 to 4-10
water surfaces (open), heat transfer 3-35 to
3-36
water tanks, heat transfer 3-35 to 3-36
water velocities, pipework 4-8
water velocity pressure 4-9, 4-10
water-glycol mixtures, properties 4-63
wet bulb temperature 1-2
data 1-7 to 1-67
wind velocity
Beaufort scale 6-14
velocity pressure 6-16
windows
double glazing 3-4, 3-36
thermal performance 3-36
view factors 3-18, 3-20
wire gauges 6-16
Wobbe number 5-7, 5-8
wood fuels 5-4
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement