For class use only
ACHARYA N.G. RANGA AGRICULTURAL UNIVERSITY
Course No. FDEN-321
Course Title:
INSTRUMENTATION & PROCESS CONTROL
Credits:
3 (2 + 1)
Prepared by
Er. B. SREENIVASULA REDDY
Assistant Professor (Food Engineering)
College of Food Science and Technology
Chinnarangapuram, Pulivendula – 516390
YSR (KADAPA) District, Andhra Pradesh
DEPARTMENT OF FOOD ENGINEERING
1
Course No
: FDEN - 321
2
Title
: INSTRUMENTATION & PROCESS CONTROL
3
Credit hours
: 3 (2+1)
4
General Objective
: To
impart
knowledge
to
the
students
on
instrumentation and process controls used in
food industry
5
Specific Objectives
:
a) Theory
: By the end of the course the students will be able
to
i) understand the different instruments used in
different operations of food industries
ii) know about working principles of different
instruments used in different operations
b) Practical
By the end of the practical exercises the student
will be able to
i) identify different instruments and controls used
in various operations
ii) identify and tackle the problems encountered
in use and operation of different instruments
A) Theory Lecture Outlines
1
Introduction – Instrumentation, Process Control -
measurements -
methods of measurements - Direct Methods-In-Direct Methods
2
Primary
measurements
-
secondary
measurements
-
tertiary
measurement -instruments and measurement systems - mechanical
instruments - electrical instruments - electronic instruments
3
Functional elements of measurement systems - basic functional elements
– auxiliary elements - transducer elements - examples of transducer
elements
4
Linear variable differential transformer (LVDT) - advantages of LVDT
- disadvantages of LVDT.
5
Classification of Instruments: Deflection and Null Types, Manually
2
Operated and Automatic Types, Analog and Digital Types, SelfGenerating and Power-Operated Types, Contacting and Non-Contacting
Types, Dumb and Intelligent Types
6
Indicating, recording and display elements: introduction-Digital voltmeters
(DVMs), cathode ray oscilloscope (CRO), galvanometric recorders,
magnetic tape recorders, digital recorder of memory type, data acquisition
systems, data display and storage
7
Errors in Performance Parameters: Types of Errors, Systematic or
Cumulative Errors, Accidental or Random Errors, Miscellaneous Type of
Gross Errors
8
Characteristics of transducer elements - signal conditioning elements –
amplification - Signal filtration
9
Standards of measurements - international standards - primary standards
– secondary standards - working standards - calibration - classification of
calibration
10
Performance
characteristics
-
static
and
dynamic
performance
characteristics – accuracy - precession - resolution - threshold - static
sensitivity - deflection factor
11
Performance characteristics- Linearity, Range and Span, Hysteresis,
Dead Band, Backlash, Drift
12
Primary sensing elements - mechanical devices as primary detectors springs, bimetallic strips - mechanical spring devices - cantilever - helical
spring - spiral spring - torsion bar - proving ring
13
Pressure sensitive primary devices: Some of the commonly used force
summing devices, Bourdon tubes, Diaphragms and Bellows
14
Temperature
Measurement
:
Introduction-
temperature
scales-
International Practical Temperature Scale (IPTS)
15
Measurement of Temperature: Classification of temperature measuring
devices - bimetallic thermometers - glass thermometers and pressure
gauge thermometers - thermocouples
16
Electrical resistance thermometers - Resistance- Temperature Detectors
(RTDs)- Thermocouple - Thermocouple Materials
3
17
Pressure - gauge pressure, absolute pressure, differential pressure,
vacuum - units of pressure - pressure scales - conversion of units- Types
of Pressure Measurement Devices
18
Measurement of pressure : Manometers - U tube manometer - inclined
tube manometer - well type manometer - Properties of Manometric Fluids
19
Elastic Pressure Elements - bourdon tube – bellows - diaphragms
20
Types of Fluid Flow : Steady flow and Unsteady flow- Uniform flow and
Non-uniform flow - One-dimensional flow, two dimensional flow and Three
dimensional flow- Rotational flow and Irrotational flow - Laminar flow and
Turbulent flow.
21
Flow measurement : introduction - primary or quantity meters - positive-
22
displacement meters - secondary or rate meters - variable head meters
The general expression for the rate of flow- Construction of Venturi Meter
23
Construction of Orifice Meter
24
Variable Area Meters- Rotameter; Pitot tube - its advantages - its
limitations
25
Variable Head and Variable Area Flow Meters (Weirs) - Hot Wire
Anemometers - Rotary Vane Meter
26
Measurement of Liquid Level - Direct Liquid Level Measurements - Dipstick Method- Sight Glass Method-
27
Hook Gauge- Float Gauge - Float-and-Shaft Liquid Level Gauge
28
Indirect Liquid Level Measurements - Hydrostatic Pressure Level
Measurement
Device
-
Bubbler
or
Purge
Technique
for
Level
Measurement
29
Capacitance Level Gauge - Ultrasonic Level Gauge - Nucleonic Gauge
30
Control Systems- Introduction- Basic components of the control systemClassification of Control Systems – Open Loop System - Closed Loop
System - Servo Mechanisms
31
Controllers and Control Action - Pneumatic Controller - Hydraulic
Controllers - Electric Controllers
32
Data Transmission Elements - Electrical Type Data Transmission
Elements - Pneumatic-Type Transmission Elements - Position-Type Data
4
Transmission Elements - Radio-Frequency (RF) Transmission System
B) Practical Class Outlines
1
Study of instrumentation symbols
2
Measurement of temperature by different thermometers
3
Measurement of pressure by U tube manometer (inclined tube manometer)
4
Measurement of liquid level in the tank with the help of Bob and tape
5
Determination of relative humidity by wet and dry bulb thermometer
6
Measurement of velocity of fluid by using venturi meter/orifice meter/pitot tube
7
Measurement of RPM of an electric motor by tachometer
8
Measurement of wind velocity by anemometer
9
Measurement of intensity of sunshine by sunshine recorder
10
Characteristic of valve PI performance, T, P flow and level close leep control
system
11
Measurement of viscosity
12
Calibration of common digital balance
13
Calibration and measurement of OD using spectrophotometer
14
Measurement of running fluid using rotameter
15
Measurement of vacuum - I
16
Measurement of vacuum - II
References
1
B.C. Nakra and K.K.Chaudhary, Instrumentation Measurement and Analysis. Tata
Mc Graw Hill, New Delhi.
2
Sahney and Sahney, A Course in Mechanical Measurement & Instrumentation.
Dhanpat Rai and Sons, New Delhi.
3
K. Krishnaswamy and S. Vijayachitra, Industrial Instrumentation. New Age
International (P) Limited, New Delhi.
5
LECTURE NO.1
INTRODUCTION – INSTRUMENTATION, PROCESS CONTROL MEASUREMENTS - METHODS OF MEASUREMENTS - DIRECT METHODSIN-DIRECT METHODS
Instrumentation
Instrumentation is defined as "the art and science of measurement and
control". Instrumentation can be used to refer to the field in which Instrument
technicians and engineers work in, or it can refer to the available methods and
use of instruments.
Instruments are devices which are used to measure attributes of
physical systems. The variable measured can include practically any
measurable variable related to the physical sciences. These variables
commonly include: pressure , flow , temperature , level , density , viscosity ,
radiation , current , voltage , inductance , capacitance , frequency ,chemical
composition , chemical properties , various physical properties, etc.
Instruments can often be viewed in terms of a simple input-output
device. For example, if we "input" some temperature into a thermocouple, it
"outputs" some sort of signal. (Which can later be translated into data.) In the
case of this thermocouple, it will "output" a signal in millivolts.
Process control
The purpose of process control is to reduce the variability in final
products so that legislative requirements and consumers’ expectations of
product quality and safety are met. It also aims to reduce wastage and
production costs by improving the efficiency of processing. Simple control
methods (for example, reading thermometers, noting liquid levels in tanks,
adjusting valves to control the rate of heating or filling), have always been in
place, but they have grown more sophisticated as the scale and complexity of
processing has increased. With increased mechanization, more valves need to
be opened and more motors started or stopped. The timing and sequencing of
these activities has become more critical and any errors by operators has led to
6
more serious quality loss and financial consequences. This has caused a move
away from controls based on the operators’ skill and judgment to technologybased control systems. Initially, manually operated valves were replaced by
electric or pneumatic operation and switches for motors were relocated onto
control panels. Measurements of process variables, such as levels of liquids in
tanks, pressures, pH, temperatures, etc., were no longer taken at the site of
equipment, but were sent by transmitters to control panels and gradually
processes became more automated.
Automatic control has been developed and applied in almost every
sector of the industry. The impetus for these changes has come from:
• increased competition that forces manufacturers to produce a wider
variety of products more quickly
• escalating labour costs and raw material costs
• increasingly stringent regulations that have resulted from increasing
consumer demands for standardized, safe foods and international
harmonization of legislation and standards.
For some products, new laws require monitoring, reporting and
traceability of all batches produced which has further increased the need for
more sophisticated process control.
All of these requirements have caused manufacturers to upgrade the
effectiveness of their process control and management systems. Advances in
microelectronics and developments in computer software technology, together
with the steady reduction in the cost of computing power, have led to the
development of very fast data processing. This has in turn led to efficient,
sophisticated, interlinked, more operator-friendly and affordable process control
systems being made available to manufacturers. These developments are now
used at all stages in a manufacturing process, including:
• ordering and supplying raw materials
• detailed production planning and supervision
• management of orders, recipes and batches
7
• controlling the flow of product through the process
• controlling process conditions
• evaluation of process and product data (for example, monitoring
temperature profiles during heat processing or chilling
• control of cleaning-in-place procedures
• packaging, warehouse storage and distribution.
MEASUREMENTS
Measurements provide us with a means of describing various
phenomena in quantitative terms. It has been quoted "whatever exists, exists in
some amount". The determination of the amount is measurement all about.
There are innumerable things in nature which have amounts.
The
determination of their amounts constitutes the subject of Mechanical
Measurements. The measurements are not necessarily carried out by purely
mechanical means. Quantities like pressure, temperature, displacement, fluid
flow and associated parameters, acoustics and related parameters, and
fundamental quantities like mass, length, and time are typical of those which
are within the scope of mechanical measurements. However, in many
situations, these quantities are not measured by purely mechanical means, but
more often are measured by electrical means by transducing them into an
analogous electrical quantity.
The Measurement of a given quantity is essentially an act or result of
comparison between a quantity whose magnitude (amount) is unknown, with a
similar quantity whose magnitude (amount) is known, the latter quantity being
called a Standard.
Since the two quantities, the amount of which is unknown and another
quantity whose amount is known are compared, the result is expressed in
terms of a numerical value. This is shown in the Fig. 1.1.
8
Fig. 1.1 Fundamental Measuring Process.
In order that the results of measurement are meaningful, the basic
requirements are:
(i) the standard used for comparison purposes must be accurately
defined and should be commonly acceptable,
(ii) the standard must be of the same character as the measurand (the
unknown quantity or the quantity under measurement).
(iii) the apparatus used and the method adopted for the purposes of
comparison must be provable.
METHODS OF MEASUREMENT
The methods of measurement may be broadly classified into two
categories:
Direct Methods.
In-Direct Methods.
Direct Methods.
In these methods, the unknown quantity (also called the measurand) is
directly compared against a standard. The result is expressed as a numerical
number and a unit. Direct methods are quite common for the measurement of
physical quantities like length, mass and time.
Indirect Methods
Measurements by direct methods are not always possible, feasible and,
practicable. These methods in most of the cases, are inaccurate because they
involve human factors. They are also less sensitive. Hence direct methods are
not preferred and are less commonly used.
In engineering applications Measurement Systems are used. These
measurement systems use indirect methods for measurement purposes.
A measurement system consists of a transducing element which
converts the quantity to be measured into an analogous signal. The analogous
9
signal is then processed by some intermediate means and is then fed to the
end devices which present the results of the measurement.
10
LECTURE NO.2
PRIMARY
MEASUREMENTS
TERTIARY
MEASUREMENT
-
SECONDARY
-INSTRUMENTS
MEASUREMENTS
AND
–
MEASUREMENT
SYSTEMS - MECHANICAL INSTRUMENTS - ELECTRICAL INSTRUMENTS ELECTRONIC INSTRUMENTS
PRIMARY, SECONDARY AND TERTIARY MEASUREMENTS
Measurements may be classified as primary, secondary and tertiary
based upon whether direct or indirect methods are used.
Primary Measurements:- A primary measurement is one that can be made by
direct observation without involving any conversion (translation) of the
measured quantity into length.
Example:(i)
the matching of two lengths, such as when determining the length of
an object with a metre rod,
(ii)
the matching of two colors, such as when judging the color of red hot
metals
Secondary Measurements:- A secondary measurement involves only one
translation (conversion) to be done on the quantity under measurement to
convert it into a change of length. The measured quantity may be pressure of a
gas, and therefore, may not be observable. Therefore, a secondary
measurement requires,
(i) an instrument which translates pressure changes into length changes,
and
(ii) a length scale or a standard which is calibrated in length units equivalent
to known changes in pressure.
Therefore, in a pressure gauge, the primary signal (pressure) is
transmitted to a translator and the secondary signal (length) is transmitted to
observer's eye.
Tertiary Measurements :-A tertiary measurement involves two translations. A
typical example of such a measurement is the measurement of temperature of
an object by thermocouple. The primary signal (temperature of object) is
transmitted to a translator which generates a voltage which is a function of the
11
temperature. Therefore, first translation is temperature to voltage. The voltage,
in turn, is applied to a voltmeter through a pair of wires. The second translation
is then voltage into length. The tertiary signal (length change) is transmitted to
the observer's brain. This tertiary measurement is depicted in, Fig. 2.1.
Fig. 2.1 A typical tertiary measurement.
INSTRUMENTS AND MEASUREMENT SYSTEMS
Measurements involve the use of instruments as a physical means of
determining quantities or variables. The instrument enables the man to
determine the value of unknown quantity or variable. A measuring instrument
exists to provide information about the physical value of some variable being
measured. In simple cases, an instrument consists of a single unit which gives
an output reading or signal according to the unknown variable (measurand)
applied to it. In more complex measurement situations, a measuring instrument
may consist of several separate elements. These elements may consist of
transducing elements which convert the measurand to an analogous form.
The analogous signal is then processed by some intermediate means and then
fed to the end devices to present the results of the measurement for the
purposes of display, record and control. Because of this modular nature of the
elements within it, it is common to refer the measuring instrument as a
measurement system.
MECHANICAL, ELECTRICAL AND ELECTRONIC INSTRUMENTS
The history of development of instruments encompasses three phases
of instruments, viz. : (i) mechanical instruments, (it) electrical instruments and
(iii) electronic instruments.
The three essential elements in modern instruments are :
(i) a detector,
12
(ii) an intermediate transfer device, and
(iii) an indicator, recorder or a storage device.
Mechanical Instruments. These instruments are very reliable for static and
stable conditions. Major disadvantage is unable to respond rapidly to
measurements of dynamic and transient conditions. This is due to the fact that
these instruments have moving parts that are rigid, heavy and bulky and
consequently have a large mass. Mass presents inertia problems and hence
these instruments cannot follow the rapid changes which are involved in
dynamic measurements. Thus it would be virtually impossible to measure a 50
Hz voltage by using a mechanical instrument but it is relatively easy to measure
a slowly varying pressure using these instruments. Another disadvantage of
mechanical instruments is that most of them are a potential source of noise and
cause noise pollution.
Electrical Instruments. Electrical methods of indicating the output of detectors
are more rapid than mechanical methods. Electrical system normally depends
upon a mechanical meter movement as indicating device. This mechanical
movement has some inertia and therefore these instruments have a limited
time (and hence, frequency) response. For example, some electrical recorders
can give full scale response in 0.2 s, the majority of industrial recorders have
responses of 0.5 to 24 s.
Electronic Instruments.: The necessity to step up response time and also the
detection of dynamic changes in certain parameters, which require the
monitoring time of the order of ms and many a times, µ s , have led to the
design of today's electronic instruments and their associated circuitry. These
instruments require use of semiconductor devices. Since in electronic
devices, the only movement involved is that of electrons, the response
time is extremely small on account of very small inertia of electrons. For
example, a Cathode Ray Oscilloscope (CRO) is capable of following dynamic
and transient changes of the order of a few ns (10-9 s).
Another advantage of using electronic devices is that very weak signals
can be detected by using pre-amplifiers and amplifiers. The foremost
importance of the electronic instruments is the power amplification provided by
the electronic amplifiers, which results in higher sensitivity. This is particularly
important in the area of Bio-instrumentation since Bio-electric potentials are
13
very weak i.e., lower than 1 mV. Therefore, these signals are too small to
operate electro-mechanical devices like recorders and they must be amplified.
Additional power may be fed into the system to provide an increased power
output beyond that of the input. Another advantage of electronic instruments is
the ability to obtain indication at a remote location which helps in monitoring
inaccessible or hazardous locations. The most important use of electronic
instrument is their usage in measurement of non-electrical quantities,
where the non-electrical quantity is converted into electrical form through the
use of transducers.
Electronic instruments are light, compact, have a high degree of reliability and
their power consumption is very low.
Communications is a field which is entirely dependent upon the
electronic instruments and associated apparatus. Space communications,
especially, makes use of air borne transmitters and receivers and job of
interpreting the signals is left entirely to the electronic instruments.
In general electronic instruments have (i) a higher sensitivity (ii) a faster
response, (iii) a greater flexibility, (iv) lower weight, (v) lower power
consumption and (vi) a higher degree of reliability
14
LECTURE NO.3
FUNCTIONAL
ELEMENTS
OF
MEASUREMENT
SYSTEMS
-
BASIC
FUNCTIONAL ELEMENTS – AUXILIARY ELEMENTS - TRANSDUCER
ELEMENTS - EXAMPLES OF TRANSDUCER ELEMENTS
FUNCTIONAL ELEMENTS OF MEASUREMENT SYSTEMS
A generalized 'Measurement System' consists of the following:
1. Basic Functional Elements, and
2. Auxiliary Functional Elements.
Basic Functional Elements are those that form the integral parts of all
instruments. They are the following:
1. Transducer Element that senses and converts the desired input to a more
convenient and practicable form to be handled by the measurement system.
2. Signal Conditioning or Intermediate Modifying Element for manipulating /
processing the output of the transducer in a suitable form.
3. Data Presentation Element for giving the information about the measurand
or measured variable in the quantitative form.
Auxiliary Functional Elements are those which may be incorporated in a
particular system depending on the type of requirement, the nature of
measurement technique, etc. They are:
1. Calibration Element to provide a built-in calibration facility.
2. External Power Element to facilitate the working of one or more of the
elements like the transducer element, the signal conditioning element, the
data processing element or the feedback element.
3. Feedback Element to control the variation of the physical quantity that is
being measured. In addition, feedback element is provided in the nullseeking potentiometric or Wheatstone bridge devices to make them
automatic or self-balancing.
4. Microprocessor Element to facilitate the manipulation of data for the purpose
of simplifying or accelerating the data interpretation. It is always used in
15
conjunction with analog-to-digital converter which is incorporated in the
signal conditioning element.
Transducer Element
Normally, a transducer senses the desired input in one physical form
and converts it to an output in another physical form. For example, the input
variable to the transducer could be pressure, acceleration or temperature and
the output of the transducer may be displacement, voltage or resistance
change depending on the type of transducer element. Sometimes the
dimensional units of the input and output signals may be same. In such cases,
the functional element is termed a transformer. Some typical examples of
transducer elements commonly used in practice are mentioned in Table 2.1.
Table 3.1 Typical Examples of transducer elements
S.
No
(1)
1
Input
variable
to
transducer
(2)
Temperature
Output
variable of
transducer
(3)
Voltage
2
Temperature
Displacement
3
Temperature
Resistance
Change
4
5
Temperature
Displacement
Pressure
Inductance
Change
6
Displacement
Resistance
8
9
Motion
Flow Rate
Flow velocity
Type of device
(4)
An emf is generated across the
junctions of two dissimilar metals
or semiconductors when that
junction is heated
There is a thermal expansion in
volume when the temperature of
liquids or liquid metals is raised
and this expansion can be shown
as displacement of the liquid in
the capillary
Resistance of pure metal wire with
positive temperature coefficient
varies with temperature
The pressure of a gas or vapor
varies with the change in
temperature
The differential voltage of the two
secondary windings varies linearly
with the displacement of the
magnetic core
(5)
Thermocouple
or Thermopile
Resistance
Positioning of a slider varies the
resistance in a potentiometer or a
bridge circuit
Relative motion of a coil with
respect to a magnetic field
generates a voltage
Differential pressure is generated
between the main pipe-line and
throat of the Venturimeter /
Orificemeter
Resistance of a thin wire/film is
change
varied by convective cooling in
change
7
Principle of operation
Voltage
Pressure
16
Liquid in Glass
Thermometer
Resistance
Thermometer
Pressure
Thermometer
Linear
Variable
Differential
Transducer
(LVDT)
Potentiometric
Device
Electrodynamic
Generator
Venturimeter
/
Orificemeter
Hot
Wire
Anemometer
(gas flows). Hot
stream of gas/liquid flows
10
11
Pressure
Movement of
The
a
balanced
liquid
column
Displacement
Pressure
impressed
pressure
by
the
is
Film
Anemometer
(liquid flows)
Manometer
pressure
generated by a column of liquid
The application of pressure
Bourdon Gauge
causes displacement in elastic
12
13
Gas Pressure
Force
Resistance
elements
Resistance of a heating element
change
varies by convective cooling
Displacement
The application of force against a
spring
14
Force
/
Torque
changes
its
length
Pirani Gauge
Spring Balance
in
Resistance
proportion to the applied force
The resistance of metallic wire or
Resistance
change
semiconductor
Strain Gauge
changed
by
element
is
elongation
or
compression due to externally
15
Force
Voltage
applied stress
An emf is generated
when
external force is applied on certain
crystalline
16
17
18
materials
Capacitance
quartz
Variation of the capacitance due
thickness
change
to
Capacitance
dielectric constant
Sound pressure
music / noise
change
capacitance between a fixed plate
Light
Voltage
and a movable diaphragm
A voltage is generated in a
Speech
/
the
changes
radiant
Light
Current
radiations
energy
in
Device
as
Liquid level /
semiconductor
19
such
Piezo-electric
Dielectric gauge
effective
varies
junction
the
when
stimulates
Condenser
Microphone
Light
Meter/Solar Cell
the
photoelectric cell
Secondary electron emission due
Photomultiplier
to
tube
incident
radiations
on
the
photosensitive cathode causes an
20
Humidity
Resistance
electronic current
Resistance of a conductive strip
Resistance
21
Blood flow /
change
Frequency
changes with the moisture content
The difference in the frequency of
Hygrometer
Doppler
any other gas
shift
the incident and reflected beams
Frequency Shift
or
of ultrasound known as Doppler's
Ultrasonic Flow
phase
frequency shift is proportional to
Meter
or
two
flow
liquid
the flow velocity of the fluid
17
18
LECTURE NO.4
LINEAR
VARIABLE
DIFFERENTIAL
TRANSFORMER
(LVDT)
-
ADVANTAGES OF LVDT - DISADVANTAGES OF LVDT.
The most widely used inductive transducer to translate the linear motion
into electrical signals is the linear variable differential Transformer (LVDT). The
basic construction of LVDt is shown in Fig. 4.1. The transformer consists of a
single primary winding P and two secondary windings S1 and S2 wound on a
cylindrical former. The secondary windings have equal number of turns and are
identically placed on either side of the primary winding. The primary winding is
connected to an alternating current source. A movable soft iron core is placed
inside the former. The displacement to be measured is
Fig. 4.1 Linear variable differential Transformer (LVDT)
applied to the arm attached to the soft iron core. In practice the core is made of
high permeability, nickel iron which is hydrogen annealed. This gives low
harmonics, low null voltage and a high sensitivity. This is slotted longitudinally
to reduce eddy current losses. The assembly is placed in stainless steel
housing and the end lids provide electrostatic and electromagnetic shielding.
The frequency of a.c. applied to primary windings may be between 50 Hz to 20
kHz.
Since the primary winding is excited by an alternating current source, it
produces an alternating magnetic field which in turn induces alternating current
voltages in the two secondary windings.
19
The output voltage of secondary, S1, is Es1 and that of secondary, S2 , is
Es2. In order to convert the outputs from S 1 and S2 into a single voltage signal,
the two secondaries S1 and S2 are connected in series as shown in Fig.4.2 (b).
Thus the output voltage of the transducer is the difference of the two voltages.
Differential output voltage,
E0 =E s1 −E s2
Fig.4.2 Circuits of an LVDT
When the core is at its normal (NULL) position, the flux linking with both
the secondary windings is equal and hence equal emfs are induced in them.
Thus at null position: E s = E s . Since the output voltage of the transducer is
1
2
the difference of the two voltages, the output voltage E0 is zero at null position.
Now if the core is moved to the left of the NULL position, more flux links
with winding S1 and less with winding S2. Accordingly output voltage Es1 of the
secondary winding S1 is greater than Es2, the output voltage of secondary
winding S2. The magnitude of output voltage is, thus, E0 =E s1 −E s2 and the
output voltage is in phase with, say, the primary voltage. Similarly, if the core is
moved to the right of the null position, the flux linking with winding S2 becomes
larger than that linking with winding S1. This results in Es2 becoming larger than
Es1. The output voltage in this case is E0 = E s − E s1 and is 1800 out of phase
2
with the primary voltage. Therefore, the two differential voltages are 180o out of
phase with each other.
20
The amount of voltage change in either secondary winding is
proportional to the amount of movement of the core. Hence, we have an
indication of amount of linear motion.
Advantages of L VDT
1. High range for measurement of displacement. This can be used for
measurement of displacements ranging from 1.25 mm to 250 mm. With
a 0.25 % full scale linearity, it allows measurements down to 0.003 mm.
2. Friction and Electrical Isolation. There is no physical contact between the
movable core and coil structure which means that the LVDT is a
frictionless device.
3. Immunity from External Effects. The separation between LVDT core and
LVDT coils permits the isolation of media such as pressurized, corrosive, or
caustic fluids from the coil assembly by a non-magnetic barrier interposed
between the core and inside of the coil.
4. High input and high sensitivity. The LVDT gives a high output and many a
time there is no need for amplification. The transducer possesses a high
sensitivity which is typically about 40 V/mm.
5. Ruggedness.
6. Low Hysteresis and hence repeatability is excellent under all conditions.
7. Low Power Consumption (less than 1 W).
Disadvantages of LVDTs.
1. Relatively large displacements are required for appreciable differential
output.
2. They are sensitive, to stray magnetic fields but shielding is possible.
This is done by providing magnetic shields with longitudinal slots.
3. Many a time, the transducer performance is affected by vibrations.
4. The receiving instrument must be selected to operate on a.c. signals
or a demodulator network must used if a d.c. output is required.
21
5. The dynamic response is limited mechanically by the mass of the core
6. Temperature affects the performance of the transducer.
22
LECTURE NO.5
CLASSIFICATION OF INSTRUMENTS: DEFLECTION AND NULL TYPES,
MANUALLY OPERATED AND AUTOMATIC TYPES, ANALOG AND DIGITAL
TYPES,
SELF-GENERATING
AND
POWER-OPERATED
TYPES,
CONTACTING AND NON-CONTACTING TYPES, DUMB AND INTELLIGENT
TYPES
CLASSIFICATION OF INSTRUMENTS
Instruments may be classified according to their application, mode of
operation, manner of energy conversion, nature of output signal and so on. The
instruments commonly used in practice may be broadly categorized as follows:
Deflection and Null Types
A deflection type instrument is that in which the physical effect
generated by the measuring quantity produces an equivalent opposing effect in
some part of the instrument which in turn is closely related to some variable like
mechanical displacement or deflection in the instrument. For example, the
unknown weight of an object can be easily obtained by the deflection of a
spring caused by it on the spring balance as shown in Fig. 5.1. Similarly, in a
common Bourdon gauge, the pressure to be measured acts on the C-type
spring of the gauge, which deflects and produces an internal spring force to
counter balance the force generated by the applied pressure.
Deflection instruments are simple in construction and operation.
Fig. 5.1 A typical spring balance – A deflection type weight measuring
instrument
23
A null type instrument is the one that is provided with either a manually
operated or automatic balancing device that generates an equivalent opposing
effect to nullify the physical effect caused by the quantity to be measured. The
equivalent null-causing effect in turn provides the measure of the quantity.
Consider a simple situation of measuring the mass of an object by means of an
equal-arm beam balance. An unknown mass, when placed in the pan, causes
the beam and pointer to deflect. Masses of known values are placed on the
other pan till a balanced or null condition is obtained by means of the pointer.
The main advantage of the null-type devices is that they do not interfere with
the state of the measured quantity and thus measurements of such instruments
are extremely accurate.
Manually Operated and Automatic Types
Any instrument which requires the services of human operator is a
manual type of instrument. The instrument becomes automatic if the manual
operation is replaced by an auxiliary device incorporated in the instrument. An
automatic instrument is usually preferred because the dynamic response of
such an instrument is fast and also its operational cost is considerably lower
than that of the corresponding manually operated instrument.
Analog and Digital Types
Analog instruments are those that present the physical variables of
interest in the form of continuous or stepless variations with respect to time.
These instruments usually consist of simple functional elements. Therefore, the
majority of present-day instruments are of analog type as they generally cost
less and are easy to maintain and repair.
On the other hand, digital instruments are those in which the physical
variables are represented by digital quantities which are discrete and vary in
steps. Further, each digital number is a fixed sum of equal steps which is
defined by that number. The relationship of the digital outputs with respect to
time gives the information about the magnitude and the nature of the input
data.
Self-Generating and Power-Operated Types
24
In self-generating (or passive) instruments, the energy requirements of
the instruments are met entirely from the input signal.
On the other hand, power-operated (or active) instruments are those that
require some source of auxiliary power such as compressed air, electricity,
hydraulic supply, etc. for their operation.
Contacting and Non-Contacting Types
A contacting type of instrument is one that is kept in the measuring
medium itself. A clinical thermometer is an example of such instruments.
On the other hand, there are instruments that are of non-contacting or
proximity type. These instruments measure the desired input even though they
are not in close contact with the measuring medium. For example, an optical
pyrometer monitors the temperature of, say, a blast furnace, but is kept out of
contact with the blast furnace. Similarly, a variable reluctance tachometer,
which measures the rpm of a rotating body, is also a proximity type of
instrument.
Dumb and Intelligent Types
A dumb or conventional instrument is that in which the input variable is
measured and displayed, but the data is processed by the observer. For
example, a Bourdon pressure gauge is termed as a dumb instrument because
though it can measure and display a car tyre pressure but the observer has to
judge whether the car tyre air inflation pressure is sufficient or not.
Currently, the advent of microprocessors has provided the means of
incorporating Artificial Intelligence (AI) to a very large number of instruments.
Intelligent or smart instruments process the data in conjunction with
microprocessor ( µP ) or an on-line digital computer to provide assistance in
noise reduction, automatic calibration, drift correction, gain adjustments, etc. In
addition, they are quite often equipped with diagnostic subroutines with suitable
alarm generation in case of any type of malfunctioning.
An intelligent or smart instrument may include some or all of the
following:
25
1. The output of the transducer in electrical form.
2. The output of the transducer should be in digital form. Otherwise it has
to be converted to the digital form by means of analog-to-digital
converter (A-D converter).
3. Interface with the digital computer.
4. Software routines for noise reduction, error estimation, self-calibration,
gain adjustment, etc.
5. Software routines for the output driver for suitable digital display or to
provide serial ASCII coded output.
26
LECTURE NO.6
INDICATING, RECORDING AND DISPLAY ELEMENTS:
INTRODUCTION-
DIGITAL VOLTMETERS (DVMS), CATHODE RAY OSCILLOSCOPE (CRO),
GALVANOMETRIC RECORDERS, MAGNETIC TAPE RECORDERS, DIGITAL
RECORDER OF MEMORY TYPE, DATA ACQUISITION SYSTEMS, DATA
DISPLAY AND STORAGE
INDICATING, RECORDING AND DISPLAY ELEMENTS
Introduction
The final stage in a measurement system comprises an indicating and /
or a recording element, which gives an indication of the input being measured.
These elements may also be of analog or digital type, depending on whether
the indication or recording is in a continuous or discrete manner. Conventional
voltmeters and ammeters are the simplest examples of analog indicating
instruments, working on the principle of rotation of a coil through which a
current passes, the coil being in a magnetic field.
Digital voltmeters (DVMs) are commonly used as these are convenient
for indication and are briefly described here. Cathode ray oscilloscopes
(CROs) have also been widely used for indicating these signals.
Recording instruments may be galvanometric, potentiometric, servo
types or magnetic tape recorder types. In addition to analog recorders, digital
recorders including digital printers, punched cards or tape recording elements
are also available.
In large-scale systems, data loggers incorporating digital computers are
extensively used for data recording. The present day availability of memory
devices has made the problem of data storage simpler than was previously
possible.
DIGITAL VOLTMETERS (DVMS)
Digital voltmeters convert analog signals into digital presentations which
may be as an indicator or may give an electrical digital output signal. DVMs
measure dc voltage signals. However, other variables like ac voltages,
27
resistances, current, etc. may also be measured with appropriate elements
preceding the input of the DVM.
CATHODE RAY OSCILLOSCOPE (CRO)
As an indicating element, a CRO is widely used in practice. It is
essentially a high input impedance voltage measuring device, capable of
indicating voltage signals from the intermediate elements as a function of time.
Fig. 6.1Cathode-ray-tube (a) Schematic (b) details of deflection plates
Figure 6.1 shows the block diagram of a cathode ray oscilloscope.
Electrons are released from the cathode and accelerated towards the screen
by the positively charged anode. The position of the spot on the
phosphorescent screen is controlled by voltages applied to the vertical and
horizontal plates. The impingement of the electron beam on the screen results
in emission of light and thus the signal becomes visible.
As seen in Fig. 6.1, the following are the essential components in a
CRO:
1. display device, viz. the tube,
2. vertical amplifier,
3. horizontal amplifier,
4. time base,
28
5. trigger or synchronizing circuit, to start each sweep at a desired time,
for display of signal, and
6. power supplies and internal circuits.
GALVANOMETRIC RECORDERS
These are based on the simple principle of rotation of a coil through
which current due to the input signal to be recorded, flows while the coil is in a
magnetic field, as shown in Fig. 6.2.
Fig. 6.2 Galvanometric Oscillograph
An ink pen attachment to the coil can be used to trace the signal on a
paper wrapped around a rotating drum. The system acts like a second order
instrument and the frequency response is limited to 200 Hz or so, due to the
inertia effects of the pen and the coil. A pen recorder is shown in Fig. 6.2(a). In
Fig.6.2 (b), the pen attachment is replaced by a light beam from a highpressure mercury lamp source, with the light getting reflected from a small
mirror attached to the coil. Due to rotation of the coil, the light beam gets
deflected and a trace is made on the light sensitized paper. The high-frequency
response is good till several kHz.
SERVO-TYPE POTENTIOMETRIC RECORDERS
These types of recorders, also known as self-balancing types of
potentiometers, are commonly used in industrial situations, as they are quite
rugged and not as delicate as the galvanometric recorders. Further, there is no
limitation as far as the power required to move the pointer mechanism is
concerned.
29
MAGNETIC TAPE RECORDERS
Of late, a magnetic tape recorder has been used increasingly for
recording data. The magnetic tape is made of a thin plastic material, coated
with oxide particles, which become magnetized when the tape passes across a
magnetizing head which acts due to an input signal. The signal is recovered
from the tape by a reproduce head. There are several types of magnetic
recording systems, viz. direct recording, frequency modulated (FM), pulse
duration modulation (PDM) and digital recording systems. Figure 6.3(a) shows
the block diagram of a direct recording system and Fig. 6.3 (b) a typical
magnetic head.
Fig.6.3 Direct recording system
DIGITAL RECORDER OF MEMORY TYPE
Another development in digital recording is to replace the magnetic tape
with a large semiconductor memory, as shown in Fig.6.4.
30
Fig. 6.4 Digital waveform recorder with memory
The analog input signal is sampled and converted to digital form by an
A-D converter. The signal is stored in the memory and converted to analog or
digital outputs for presentation as desired.
DATA ACQUISITION SYSTEMS
For large-scale data recording, data acquisition systems or loggers are
employed, e.g. in a power plant, the input signals, like temperatures, pressures,
speeds, flow rates, etc. from a number of locations, may have to be recorded
periodically or continuously. In such cases, such systems are employed.
The data acquisition systems used are usually of digital type using a
digital computer and may have multiple channels for measurement of various
physical variables, the number of channels may be upto 100 or even more.
Figure 6.5 shows a large-scale data acquisition system with the sensor
being of analog types. After signal conditioning including amplification, a
multiplexer is used, which is essentially a switching device, enabling each input
to be sampled in turn. A sample and hold (S and H) device is used where an
analog-to-digital converter (A - D converter) is employed and where the analog
signal might change during conversion. The S and H device employs a
capacitor, which is charged up to the analog signal value which is held at its
value, till called by the A-D converter.
The computer controls the addressing and data input and processes the
signals as desired, for display, printing and storage.
31
Fig. 6.5 Data acquisition system
The computer monitor unit is used for display, a laser or inkjet or dot
matrix printer for permanent record as per the software used with computer and
the measurement data may be stored in the hard disk and / or floppy disk for
record or communication, where needed.
DATA DISPLAY AND STORAGE
The data may be in analog or digital form as discussed earlier and may
be displayed or stored as such. The display device may be any of the following
types:
1. Analog indicators, comprising motion of a needle on a metre scale.
2. Pen trace or light trace on chart paper recorders.
3. Screen display as in cathode ray oscilloscopes or on large TV screen
display, called visual display unit (VDU).
4. Digital counter of mechanical type, consisting of counter wheel, etc.
5. Digital printer, giving data in printed form.
6. Punches, giving data on punched cards or tapes.
7. Electronic displays, using light emitting diodes (LEDs) or liquid crystal
displays, (LCDs) etc. In LEDs, light is emitted due to the release of
energy as a result of the recombination of unbound free electrons and
holes in the region of the junction. The emission is in the visible region in
case of materials like Gallium Phosphide. LEDs get illuminated ON or
32
OFF, depending on the output being binary 1 or 0. In a microcomputer,
the status of data, address and control buses may be displayed.
Fig. 6.6 Seven-segment display
Using LEDs, a seven-segment dislay as in Fig.6.6, can be made,
which would display most of the desired characters. LCDs are made
from organic molecules, which flow like liquids and have crystal like
characteristics, appearing dark or bright, depending on the application of
a certain voltage range across the crystal. The seven segment displays
may also be made up of LCDs.
8. The storage of data may be on cards, magnetic tapes, disks core
memories, etc. Figure 6.7 shows a floppy disk storage system, which is of
magnetic type.
The digital data on the disk is recorded in concentric-circles, known as
tracks. The disk is divided into sectors which are numbered and can hold a
number of characters. The formatting of the disk is done to identify the tracks
and the sectors. A reference hole is shown for numbering the start of the
tracks.
33
Fig.6.7 Floppy disk storage system
A read/write head is used for each disk surface and heads and moved by
an actuator. The disk is rotated and data is read or written. In some disks, the
head is in contact with the disk surface which in others, there is a small gap.
The hard disks are sealed unit and have a large number of tracks and
sectors and store much more data
9. The permanent record of data from a computer may be made on a dot
matrix or inkjet or laser printer.
The dot matrix printer is of impact type where dots are formed by wires,
controlled by solenoids pressed on ink ribbons onto the paper. The inkjet
printer is of non-impact type, in which a stream of fine ink particles are
produced. The particles can get deflected by two sets of electrodes is the
horizontal and vertical planes. The image of the characters is thus formed.
The laser printer has high resolution and works according to the principle
as shown in Fig. 6.8. The drum is coated with an organic chemical coating
which is an insulator and gets charged as it passes the charging wire (1). The
laser light is reflected from the white regions of the image or the characters to
be produced, to the drum, making these portions conducting. The toner gets
attracted to the charged regions of the drum. The paper is given a charge by
the charging wire (2), which is higher than that on the drum, transferring the
toner to the paper, creating the impressions of the character or images.
Further, the impressions get permanent by heating.
Fig. 6.8 View of a laser printer
34
LECTURE NO.7
ERRORS IN PERFORMANCE PARAMETERS: TYPES OF ERRORS,
SYSTEMATIC OR CUMULATIVE ERRORS, ACCIDENTAL OR RANDOM
ERRORS, MISCELLANEOUS TYPE OF GROSS ERRORS
ERRORS IN PERFORMANCE PARAMETERS
The various static performance parameters of the instruments are
obtained by performing certain specified tests depending on the type of
instrument, the nature of the application, etc. Some salient static performance
parameters are periodically checked by means of a static calibration. This is
accomplished by imposing constant values of 'known' inputs and observing the
resulting outputs.
No measurement can be made with perfect accuracy and precision.
Therefore, it is instructive to know the various types of errors and uncertainties
that are in general, associated with measurement system. Further, it is also
important to know how these errors are propagated.
Types of Errors
Error is defined as the difference between the measured and the true value (as
per standard). The different types of errors can be broadly classified as follows.
Systematic or Cumulative Errors
Such errors are those that tend to have the same magnitude and sign for
a given set of conditions. Because the algebraic sign is the same, they tend to
accumulate and hence are known as cumulative errors. Since such errors alter
the instrument reading by a fixed magnitude and with same sign from one
reading to another, therefore, the error is also commonly termed as instrument
bias. These types of errors are caused due to the following:
Instrument errors:
Certain errors are inherent in the instrument systems. These may be
caused due to poor design / construction of the instrument. Errors in the
divisions of graduated scales, inequality of the balance arms, irregular springs
35
tension, etc., cause such errors. Instrument errors can be avoided by (i)
selecting a suitable instrument for a given application, (ii) applying suitable
correction after determining the amount of instrument error, and (iii) calibrating
the instrument against a suitable standard.
Environmental errors:
These types of errors are caused due to variation of conditions external
to the measuring device, including the conditions in the area surrounding the
instrument. Commonly occurring changes in environmental conditions that may
affect the instrument characteristics are the effects of changes in temperature,
barometric pressure, humidity, wind forces, magnetic or electrostatic fields, etc.
Loading errors
Such errors are caused by the act of measurement on the physical
system being tested. Common examples of this type are: (i) introduction of
additional resistance in the circuit by the measuring milliammeter which may
alter the circuit current by significant amount, (ii) an obstruction type flow meter
may partially block or disturb the flow conditions and consequently the flow rate
shown by the meter may not be same as before the meter installation, and (iii)
introduction of a thermometer alters the thermal capacity of the system and
thereby changes the original state of the system which gives rise to loading
error in the temperature measurement.
Accidental or Random Errors
These errors are caused due to random variations in the parameter or
the system of measurement. Such errors vary in magnitude and may be either
positive or negative on the basis of chance alone. Since these errors are in
either direction, they tend to compensate one another. Therefore, these errors
are also called chance or compensating type of errors. The following are some
of the main contributing factors to random error.
Inconsistencies
associated
with
accurate
quantities
36
measurement
of
small
The outputs of the instruments become inconsistent when very accurate
measurements are being made. This is because when the instruments are built
or adjusted to measure small quantities, the random errors (which are of the
order of the measured quantities) become noticeable.
Presence of certain system defects
System defects such as large dimensional tolerances in mating parts
and the presence of friction contribute to errors that are either positive or
negative depending on the direction of motion. The former causes backlash
error and the latter causes slackness in the meter bearings.
Effect of unrestrained and randomly varying parameters
Chance errors are also caused due to the effect of certain uncontrolled
disturbances which influence the instrument output. Line voltage fluctuations,
vibrations of the instrument supports, etc. are common examples of this type.
Miscellaneous Type of Gross Errors
There are certain other errors that cannot be strictly classified as either
systematic or random as they are partly systematic and partly random.
Therefore, such errors are termed miscellaneous type of gross errors. This
class of errors is mainly caused by the following.
Personal or human errors
These are caused due to the limitations in the human senses. For
example, one may sometimes consistently read the observed value either high
or low and thus introduce systematic errors in the results. While at another time
one may record the observed value slightly differently than the actual reading
and consequently introduce random error in the data.
Errors due to faulty components / adjustments
Sometimes there is a misalignment of moving parts, electrical leakage,
poor optics, etc. in the measuring system.
Improper application of the instrument
37
Errors of this type are caused due to the use of instrument in conditions
which do not conform to the desired design / operating conditions. For
example, extreme vibrations, mechanical shock or pick-up due to electrical
noise could introduce so much gross error as to mask the test information.
38
LECTURE NO.8
CHARACTERISTICS
OF
TRANSDUCER
ELEMENTS
SIGNAL
CONDITIONING ELEMENTS – AMPLIFICATION - SIGNAL FILTRATION
Characteristics of transducer element
1. The transducer element should recognize and sense the desired
input signal and should be insensitive to other signals present
simultaneously in the measurand. For example, a velocity transducer
should sense the instantaneous velocity and should be insensitive to the
local pressure or temperature.
2. It should not alter the event to be measured.
3. The output should preferably be electrical to obtain the advantages
of modern computing and display devices.
4. It should have good accuracy.
5. It should have good reproducibility (i.e. precision).
6. It should have amplitude linearity.
7. It should have adequate frequency response (i.e., good dynamic
response).
8. It should not induce phase distortions (i.e. should not induce time lag
between the input and output transducer signals).
9. It should be able to withstand hostile environments without damage
and should maintain the accuracy within acceptable limits.
10. It should have high signal level and low impedance.
11. It should be easily available, reasonably priced and compact in
shape and size (preferably portable).
12. It should have good reliability and ruggedness. In other words, if a
transducer gets dropped by chance, it should still be operative.
13. Leads of the transducer should be sturdy and not be easily pulled
off.
14. The rating of the transducer should be sufficient and it should not
break down.
Signal Conditioning Element
The output of the transducer element is usually too small to operate an
indicator or a recorder. Therefore, it is suitably processed and modified in the
signal conditioning element so as to obtain the output in the desired form.
39
The transducer signal is fed to the signal conditioning element by
mechanical linkages (levers, gears, etc.), electrical cables, fluid transmission
through liquids or through pneumatic transmission using air. For remote
transmission purposes, special devices like radio links or telemetry systems
may be employed.
The signal conditioning operations that are carried out on the transduced
information may be one or more of the following:
Amplification
Amplification The term amplification means increasing the amplitude of
the signal without affecting its waveform. The reverse phenomenon is termed
attenuation, i.e. reduction of the signal amplitude while retaining its original
waveform. In general, the output of the transducer needs to be amplified in
order to operate an indicator or a recorder. Therefore, a suitable amplifying
element is incorporated in the signal conditioning element which may be one of
the following depending on the type of transducer signal.
1. Mechanical Amplifying
2. Hydraulic/Pneumatic Amplifying
3. Optical Amplifying
4. Electrical Amplifying
1. Mechanical Amplifying Elements such as levers, gears or a combination of
the two, designed to have a multiplying effect on the input transducer signal.
2. Hydraulic/Pneumatic Amplifying Elements employing various types of
valves or constrictions, such as venturimeter / orificemeter, to get significant
variation in pressure with small variation in the input parameters.
3. Optical Amplifying Elements in which lenses, mirrors and combinations of
lenses and mirrors or lamp and scale arrangement are employed to convert the
small input displacement into an output of sizeable magnitude for a convenient
display of the same.
4. Electrical Amplifying Elements employing transistor circuits, integrated
circuits, etc. for boosting the amplitude of the transducer signal. In such
amplifiers we have either of the following:
Voltage Amplicatio n =
40
output voltage Vo
=
Input Voltage
Vi
output current I o
=
Input current
Ii
output power Vo I o
gain =
=
Input power
Vi I i
Current Amplicatio n =
Signal filtration
The term signal filtration means the removal of unwanted noise signals
that tend to obscure the transducer signal.
The signal filtration element could be any of the following depending on
the type of situation, nature of signal, etc.
1. Mechanical Filters that consist of mechanical elements to protect the
transducer element from various interfering extraneous signals. For example,
the reference junction of a thermocouple is kept in a thermos flask containing
ice. This protects the system from the ambient temperature changes.
2. Pneumatic Filters consisting of a small orifice or venturi to filter out
fluctuations in a pressure signal.
3. Electrical Filters are employed to get rid of stray pick-ups due to electrical
and magnetic fields. They may be simple R-C circuits or any other suitable
electrical filters compatible with the transduced signal.
Other signal conditioning operators Other signal conditioning operators that
can be conveniently employed for electrical signals are
1. Signal Compensation / Signal Linearization.
2. Differentiation / Integration.
3. Analog-to-Digital Conversion.
4. Signal Averaging / Signal Sampling, etc.
41
LECTURE NO.9
STANDARDS OF MEASUREMENTS - INTERNATIONAL STANDARDS PRIMARY STANDARDS – SECONDARY STANDARDS - WORKING
STANDARDS - CALIBRATION - CLASSIFICATION OF CALIBRATION
Standards of Measurements
A standard of measurement is defined as the physical representation of
the unit of measurement. A unit of measurement is generally chosen with
reference to an arbitrary material standard or to a natural phenomenon that
includes physical and atomic constants.
For example, the S.I. unit of mass, namely kilogram, was originally
defined as the mass of a cubic decimeter of water at its temperature of
maximum density, i.e. at 4°C. The material representation of this unit is the
International Prototype kilogram which is preserved at the International Bureau
of Weights and Measures at Sevres, France. Further, prior to 1960, the unit of
length was the carefully preserved platinum-iridium bar at Sevres, France. In
1960, this unit was redefined in terms of optical standards, i.e. in terms of the
wavelength of the orange-red light of Kr86 lamp. The standard meter is now
equivalent to 1650763.73 wavelengths of Kr86 orange-red light. Similarly, the
original unit of time was the mean solar second which was defined as 1/86400
of a mean solar day.
Standards of measurements can be classified according to their function
and type of application as:
International standards:
International standards are devices designed and constructed to the
specifications of an international forum. They represent the units of
measurements of various physical quantities to the highest possible accuracy
that is attainable by the use of advanced techniques of production and
measurement technology. These standards are maintained by the International
Bureau of Weights and Measures at Sevres, France.
For example, the International Prototype kilogram, wavelength of Kr86
orange-red lamp and cesium clock are the international standards for mass,
length and time, respectively. However, these standards are not available to an
ordinary user for purposes of day-to-day comparisons and calibrations.
42
Primary standards
Primary standards are devices maintained by standards organizations
/ national laboratories in different parts of the world. These devices represent
the fundamental and derived quantities and are calibrated independently by
absolute measurements. One of the main functions of maintaining primary
standards is to calibrate / check and certify secondary reference standards.
Like international standards, these standards also are not easily available to an
ordinary user of instruments for verification / calibration of working standards.
Secondary standards
Secondary standards are basic reference standards employed by
industrial measurement laboratories. These are maintained by the concerned
laboratory. One of the important functions of an industrial laboratory is the
maintenance and periodic calibration of secondary standards against primary
standards of the national standards laboratory / organization. In addition,
secondary standards are freely available to the ordinary user of instruments for
checking and calibration of working standards.
Working standards
These are high-accuracy devices that are commercially available and
are duly checked and certified against either the primary or secondary
standards. For example, the most widely used industrial working standard of
length are the precision gauge blocks made of steel. These gauge blocks have
two plane parallel surfaces a specified distance apart, with accuracy tolerances
in the 0.25-0.5 micron range. Similarly, a standard cell and a standard resistor
are the working standards of voltage and resistance, respectively. Working
standards are very widely used for calibrating general laboratory instruments,
for carrying out comparison measurements or for checking the quality (range of
accuracy) of industrial products.
Calibration
Calibration is the act or result of quantitative comparison between a
known standard and the output of the measuring system. If the output-input
response of the system is linear, then a single-point calibration is sufficient.
However, if the system response is non-linear, then a set of known
standard inputs to the measuring system are employed for calibrating the
corresponding outputs of the system. The process of calibration involves the
43
estimation of uncertainty between the values indicated by the measuring
instrument and the true value of the input.
Calibration procedures can be classified as follows:
Primary calibration
Secondary calibration
Direct calibration with known input source
Indirect calibration
Routine calibration
Primary calibration
When a device/system is calibrated against primary standards, the
procedure is termed primary calibration. After primary calibration, the device
can be employed as a secondary calibration device. The standard resistor
or standard cell available commercially are examples of primary calibration.
Secondary calibration
When a secondary calibration device is used for further calibrating
another device of lesser accuracy, then the procedure is termed secondary
calibration. Secondary calibration devices are very widely used in general
laboratory practice as well as in the industry because they are practical
calibration sources.
Direct calibration with known input source
Direct calibration with a known input source is in general of the same
order of accuracy as primary calibration. Therefore, devices that are calibrated
directly are also used as secondary calibration devices. For example, a turbine
flow meter may be directly calibrated by using the primary measurements
such as weighing a certain amount of water in a tank and recording the time
taken for this quantity of water to flow through the meter. Subsequently, this
flow meter may be used for secondary calibration of other flow metering
devices such as an orificemeter or a venturimeter.
Indirect calibration
Indirect calibration is based on the equivalence of two different devices
that can be employed for measuring a certain physical quantity. This can be
illustrated by a suitable example, say a turbine flow meter. The requirement of
44
dynamic similarity between two geometrically similar flow meters is obtained
through the maintenance of equal Reynold's number, i.e.
D1ρ1V1
µ1
=
D2 ρ2V2
µ2
where the subscripts 1 and 2 refer to the 'standard' and the meter to be
calibrated, respectively.
Routine calibration
Routine calibration is the procedure of periodically checking the
accuracy and proper functioning of an instrument with standards that are
known to be accurately reproducible. The entire procedure is normally laid
down for making various adjustments, checking the scale reading, etc. which
conforms to the accepted norms/standards. The following are some of the
usual steps taken in the calibration procedure:
1. Visual inspection of the instrument for the obvious physical defects.
2. Checking the instrument for proper installation in accordance with the
manufacturer's specifications.
3. Zero setting of all the indicators.
4. Leveling of the devices which require this precaution.
5. Recommended operational tests to detect major defects.
6. The instrument should preferably be calibrated in the ascending as well as
descending order of the input values to ensure that errors due to friction are
accounted for.
45
LECTURE NO.10
PERFORMANCE CHARACTERISTICS - STATIC AND DYNAMIC
PERFORMANCE CHARACTERISTICS – ACCURACY - PRECESSION RESOLUTION - THRESHOLD - STATIC SENSITIVITY - DEFLECTION
FACTOR
PERFORMANCE CHARACTERISTICS
The measurement system characteristics can be divided into two
categories:
(i) Static characteristics and (ii) Dynamic characteristics.
Static characteristics of a measurement system are, in general, those
that must be considered when the system or instrument is used to measure a
condition not varying with time.
However many measurements are concerned with rapidly varying
quantities and, therefore, for such cases the dynamic relations which exist
between the output and the input are examined. This is normally done with the
help of differential equations. Performance criteria based upon dynamic
relations constitute the Dynamic Characteristics.
Static characteristics
Accuracy
Accuracy of a measuring system is defined as the closeness of the
instrument output to the true value of the measured quantity. It is also specified
as the percentage deviation or inaccuracy of the measurement from the true
value. For example, if a chemical balance reads 1 g with an error of 10-2g, the
accuracy of the measurement would be specified as 1%.
Accuracy of the instrument mainly depends on the inherent limitations of
the instrument as well as on the shortcomings in the measurement process. In
fact, these are the major parameters that are responsible for systematic or
cumulative errors. For example, the accuracy of a common laboratory
micrometer depends on instrument errors like zero error, errors in the pitch
of screw, anvil shape, etc. and in the measurement process errors are
caused due to temperature variation effect, applied torque, etc.
46
The accuracy of the instruments can be specified in either of the
following forms:
1. Percentage of true value =
measured value - true value
× 100
true value
2. Percentage of full - scale deflection =
measured value - true value
× 100
maximum scale value
Precision
Precision is defined as the ability of the instrument to reproduce a
certain set of readings within a given accuracy. For example, if a particular
transducer is subjected to an accurately known input and if the repeated read
outs of the instrument lie within say ± 1 %, then the precision or alternatively
the precision error of the instrument would be stated as ± 1%. Thus, a highly
precise instrument is one that gives the same output information, for a given
input information when the reading is repeated a large number of times.
Precision of an instrument is in fact, dependent on the repeatability. The
term repeatability can be defined as the ability of the instrument to reproduce a
group of measurements of the same measured quantity, made by the same
observer, using the same instrument, under the same conditions. The precision
of the instrument depends on the factors that cause random or accidental
errors. The extent of random errors of alternatively the precision of a given set
of measurements can be quantified by performing the statistical analysis.
Accuracy v/s Precision
The accuracy represents the degree of correctness of the measured
value with respect to the true value and the precision represents degree of
repeatability of several independent measurements of the desired input at the
same reference conditions.
Accuracy and precision are dependent on the systematic and random
errors, respectively. Therefore, in any experiment both the quantities have to be
evaluated. The former is determined by proper calibration of the
instrument and the latter by statistical analysis. However, it is instructive to
note that a precise measurement may not necessarily be accurate and vice
versa. To illustrate this statement we take the example of a person doing
47
shooting practice on a target. He can hit the target with the following
possibilities as shown in Fig. 10.1.
1. One possibility is that the person hits all the bullets on the target plate
on the outer circle and misses the bull's eye [Fig. 10.1(a)]. This is a
case of high precision but poor accuracy.
2. Second possibility is that the bullets are placed as shown in Fig. 10.1
(b). In this case, the bullet hits are placed symmetrically with respect
to the bull's eye but are not spaced closely. Therefore, this is case of
good average accuracy but poor precision.
3. A third possibility is that all the bullets hit the bull's eye and are also
spaced closely [Fig. 10.1 (c)]. As is clear from the diagram, this is a
case of high accuracy and high precision.
4. Lastly, if the bullets hit the target plate in a random manner as shown
in Fig. 10.1 (d), then this is a case of poor precision as well as poor
accuracy.
Fig.10.1 Illustration of degree of accuracy and precision in a typical target
shooting experiment
Based on the above discussion, it may be stated that in any experiment
the accuracy of the observations can be improved but not beyond the precision
of the apparatus.
Resolution (or Discrimination)
It is defined as the smallest increment in the measured value that can be
detected with certainty by the instrument. In other words, it is the degree of
fineness with which a measurement can be made. The least count of any
instrument is taken as the resolution of the instrument. For example, a ruler
with a least count of 1 mm may be used to measure to the nearest 0.5 mm by
48
interpolation. Therefore, its resolution is considered as 0.5 mm. A high
resolution instrument is one that can detect smallest possible variation in the
input.
Threshold
It is a particular case of resolution. It is defined as the minimum value of
input below which no output can be detected. It is instructive to note that
resolution refers to the smallest measurable input above the zero value. Both
threshold and resolution can either be specified as absolute quantities in terms
of input units or as percentage of full scale deflection.
Both threshold and resolution are not zero because of various factors
like friction between moving parts, play or looseness in joints (more correctly
termed as backlash), inertia of the moving parts, length of the scale, spacing of
graduations, size of the pointer, parallax effect, etc.
Static sensitivity
Static sensitivity (also termed as scale factor or gain) of the instrument is
determined from the results of static calibration. This static characteristic is
defined as the ratio of the magnitude of response (output signal) to the
magnitude of the quantity being measured (input signal), i.e.
Static sensitivit
y, K =
=
change of output signal
change in input signal
∆qo
∆qi
where qo and qi are the values of the output and input signals, respectively.
In other words, sensitivity is represented by the slope of the input-output
curve if the ordinates are represented in actual units. With a linear calibration
curve, the sensitivity is constant (Fig. 10.2(a)]. However, if the relationship
between the input and output is not linear, the sensitivity varies with the input
value and defined as [Fig. 10.2(b)]:
49
Fig. 10.2 Static sensitivity of linear and non-linear instruments
Static sensitivit
y=
∆qo
∆qi
qi
The sensitivity of a typical linear spring, whose extension is directly
proportional to the applied force can be defined as say, 450 N/mm. Similarly,
the sensitivity of a non-linear type of copper / constantan thermocouple is found
to be maximum at 350 °C and is 60 µV / oC .
It may be noted that in certain applications, the reciprocal of the
sensitivity is commonly used. This is termed inverse sensitivity or the deflection
factor.
50
LECTURE NO.11
PERFORMANCE CHARACTERISTICS- LINEARITY, RANGE AND SPAN,
HYSTERESIS, DEAD BAND, BACKLASH, DRIFT
Linearity
A linear indicating scale is one of the most desirable features of any
instrument. Therefore, manufacturers of instruments always attempt to design
their instruments so that the output is a linear function of the input. In
commercial instruments, the maximum departure from linearity is often
specified in one of the following ways.
Independent of the input (11.1 (a))
Proportional to input (11.1 (b))
Combined independent and proportional to the input (11.1 (c))
Fig. 11.1 Typical specifications of non-linearity
51
The non-linearity of a complex type of calibration curve is obtained as
say ± y % of full-scale deflection and also as ± x % of the input value. The nonlinearity of the instrument is then stated as ± y % of full scale or ± x % of the
input, whichever is greater.
Range and Span
The range of the instrument is specified by the lower and upper limits in
which it is designed to operate for measuring, indicating or recording the
measured variable. The algebraic difference between the upper and lower
range values is termed as the span of the instrument. The range of the
instrument can either be unidirectional (e.g., 0-100°C) or bidirectional (e.g., -10
to 100°C) or it can be expanded type (e.g., 80 -100°C) or zero suppressed
(e.g., 5 - 40°C).
The over-range (or overload capacity) of the instrument is the maximum
value of measurand that can be applied to the instrument without causing a
perceptible change in its operating characteristics. Further, the recovery time of
the instrument is the amount of time elapsed after the removal of the overload
conditions before it performs again within the specified tolerances.
Hysteresis
It is defined as the magnitude of error caused in the output for a given
value of input, when this value is approached from opposite directions, i.e. from
ascending order and then descending order. This is caused by backlash,
elastic deformations, magnetic characteristics, but is mainly caused due to
frictional effects.
52
Fig.11.2 Typical output-input curves showing hysteresis effects
Hysteresis effects are best eliminated by taking the observations both for
ascending and descending values of input and then taking the arithmetic mean.
For example, in Fig. 11.2(a) and (b), for a value of input q i, the output in
ascending order is (qo)1 and in descending order is (qo)2. Then the mean value
is:
( qo ) mean
=
(qo )1 + (qo ) 2
2
As is clear from Figs. 11.2 (a) and (b), this value is more or less the
value obtained from the idealised straight line.
Dead Band
It is defined as the largest change of the measurand to which the
instrument does not respond. For example, in the output-input curve with
hysteresis effect due to Coulomb's friction, the extent of the dead band is
shown in Fig. 11.2 (a). In such a case, it is approximately twice the threshold
value.
Backlash
It is defined as the maximum distance or angle through which any part of
the mechanical system may be moved in one direction without causing motion
of the next part. The output-input characteristics of an instrument system with
53
backlash error is similar to hysteresis loop due to Coulomb's friction shown in
Fig. 11.2 (a). Backlash error can be minimized if the components are made to
very close tolerances.
Drift
It is defined as the variation of output for a given input caused due to
change in the sensitivity of the instrument due to certain interfering inputs like
temperature changes, component instabilities, etc.
54
LECTURE NO.12
PRIMARY SENSING ELEMENTS - MECHANICAL DEVICES AS PRIMARY
DETECTORS - SPRINGS, BIMETALLIC STRIPS - MECHANICAL SPRING
DEVICES - CANTILEVER - HELICAL SPRING - SPIRAL SPRING - TORSION
BAR - PROVING RING
PRIMARY SENSING ELEMENTS
Introduction
The measurand in an instrumentation system makes its first contact with
a Primary Detection Element or an Input Device. There are variety of
measurands
to
be
measured.
These
include
process
variables
like
temperature, pressure and flow rate. The measurands also include electrical
quantities like current, voltage, resistance, inductance, capacitance, frequency,
phase angle, power and magnetic quantities like flux, flux density, reluctance
etc.
All these quantities require a primary detection element and / or a
transducer to be converted into another analogous format which is acceptable
by the later stages of the measurement system.
Mechanical Devices as Primary Detectors
There are a number of mechanical quantities which are to be measured.
Some of these quantities are listed in Table 12.1 along with their modes of
operation for the purposes of measurement.
The initial concept of converting an applied force into a displacement is
basic to many types of primary sensing elements. The mechanical elements
which are used to convert the applied force into displacement are usually
elastic members. There are many types of these elastic members. They can be
classified into three categories as:
i)
Direct tension or compression type
ii)
Bending type
iii)
Torsion type
Table 12.1 Mechanical Quantities and their modes of operation
55
Type
Operation
A
Contacting spindle, pin or finger
B
Elastic Member
C
D
1
Proving ring
Force to displacement
2
Bourdon tube
Pressure to displacement
3
Bellows
Pressure to displacement
4
Diaphragm
Pressure to displacement
5
Spring
Force to displacement
Mass
1
Seismic mass
Forcing function to displacement
2
Pendulum scale
Force to displacement
3
Manometer
Pressure to displacement
Thermal
1
Thermocouple
Temperature to electric current
2
Bimaterial
Temperature to displacement
3
Temp-stick
Temperature to phase
E
Hydropneumatic
1
Static
2
Displacement to displacement
(a)
Float
Fluid level to displacement
(b)
Hydrometer
Specific gravity to displacement
Dynamic
(a)
Orifice
Velocity to pressure
(b)
Venturi
Velocity to pressure
(c)
Pitot tube
Velocity to pressure
(d)
Vanes
Velocity to force
(e)
Turbines
Linear to angular velocity
MECHANICAL SPRING DEVICES
56
Most mechanical-input measuring systems employ mechanical springs
of one form or another. The displacements are usually small and
engineering approximations for small displacements or deflections are
valid. Various common types of springs are shown in Fig.12.1. These range
from cantilever, helical and spiral springs to torsion bars (proof) rings and
spring flexure pivots.
Fig. 12.1 Spring elements used for sensing force (F) or torque (T)
57
Fig. 12.2 Cantilever
Cantilever
A cantilever is shown in Fig.12.2 which is subjected to a force at its free
end.
Fl
3
Deflection at the free end ( x ) is = 3 EI
Where
F = applied force, N
l = length of cantilever, m
E = modulus of elasticity, N/m2,
1  3
4
bt , m
12
 
I = moment of inertia = 
b = width of cantilever, m
t = thickness of cantilever, m.
Stiffness of cantilever K =
F
EI
=3 3 N / m
x
l
Helical Spring
Fig. 3 shows a closed coiled helical spring subjected to a compressive
force F.
Displacement of spring: x =
8 FD 3 n
Gd 4
where,
F = applied force, N,
D = mean diameter of coiled spring, m
d = diameter of spring wire, m
n = number of wires
58
G = shear modulus, N/m2
Stiffness of spring
F
K=
x
Gd 4
=
N /m
8 D3 n
FD
Maximum shear stress, τ =8 π d 3 N/m2
Fig.12.3 Closed-coiled helical spring
Spiral Spring. Fig. 12.4 shows a flat spiral spring subjected to a torque T.
Fig. 12.4 Flat spiral spring
The deflection of the spring is :
59
E bt 3T
12 l
θ=
, rad
where
E = modulus of elasticity, N/m2
b = width of spring, m
t = thickness of spring, m
l = length, of spring, m
T = torque, N-m
E bt
T
3
Stiffness of spring K = θ = 12 l Nm / rad
The springs should be stressed well below their elastic limit at maximum
deflection in order that there is no permanent set or that no change in
deflection (or zero shift) will occur from inelastic field.
Spiral springs are used for production of controlling torque in analog
instruments.
Torsion Bars or Shafts
These are primary sensing elements for torque. The deflection or twist of
the bar is proportional to the applied torque and the deformation is used as a
measure of the torque.
Some torque meters are designed so that the angular displacement due
to twisting of the bar is measured with the help of displacement transducer. In
others, the strain in the surface of the bar, which is proportional to the torque, is
measured with the help of strain gauges. The shear strain is a measure of the
torque.
16 T
Angle of twist, θ =π G d 3 rad
where
T = applied torque, Nm,
G = shear modulus, N/m2,
d = diameter of bar, m
60
Proving (Proof) Rings
They are used for measurement of force, weight or load. The applied
force causes a deflection which is measured with the help of electrical
transducers. Proving rings are made up of steel and are used as force
standards. They are particularly useful for calibration of material testing
machines in situations where dead weight standards are impracticable to use
on account of their bulkiness. A proving ring is a circular ring or rectangular
cross-section as shown in Fig. 12.5 which is subjected to either tensile or
compressive forces across its diameter.
Fig. 12.5 proving ring
The deflection is given by: x =
(π / 2 −4 / π) d 3
16 EI
F
where
d = outside ring diameter; m.
The common practice for measurement of displacement is to attach a
displacement transducer between the top and bottom of the proving ring. When
the force is applied, the relative displacement can be measured. An LVDT is
normally used for measurement of deflection which is of the order-of 1 mm or
so. Another method is to use strain gauges for measurement of strain caused
by the applied force. The strain, then, can be used to compute the applied
force.
Load Cells. Load cells utilize an elastic member as the primary transducer and
strain gauges as secondary transducers as shown in Fig. 12.6.
61
Fig. 12.6 Load Cells
62
LECTURE NO.13
PRESSURE SENSITIVE PRIMARY DEVICES: SOME OF THE COMMONLY
USED FORCE SUMMING DEVICES, BOURDON TUBES, DIAPHRAGMS
AND BELLOWS
PRESSURE SENSITIVE PRIMARY DEVICES
Most pressure measuring devices use elastic members for sensing
pressure at the primary stage. These elastic members are of many types and
convert the pressure into mechanical displacement which is later converted
into an electrical form using a secondary transducer. These devices are many a
time known as force summing devices. Fig. 13.1 shows some of the commonly
pressure sensitive primary devices
Fig. 13.1 Pressure sensitive primary devices
The principle of working of these devices is: the fluid whose pressure is
to be measured is made to press the pressure sensitive element and since the
element is an elastic member, it deflects causing a mechanical displacement.
The displacement is proportional to the pressure applied. The displacement is
then measured with the help of electrical transducers. The output of the
electrical transducers is proportional to the displacement and hence to the
applied input pressure.
Some of the commonly used force summing devices are,
63
(i)
Bourdon tubes,
(ii)
Diaphragms and
(iii)
Bellows
Bourdon Tubes
These are designed in various forms like:
(i) C type (ii) spiral (iii) twisted tube and (iv) helical
The Bourdon tubes are made out of an elliptically sectioned flattened
tube bent in such a way as to produce the above mentioned shapes. One end
of the tube is sealed or closed and physically held. The other end is open for
the fluid to enter. When the fluid whose pressure is to be measured enters the
tube, the tube tends to straighten out on account of the pressure. This causes
the movement of the free end and the displacement of this end is amplified
through mechanical linkages. The amplified displacement of the free end is
used to move a pointer over a scale calibrated in units of pressure. Bourdon
tubes normally measure gauge pressure. The materials used for Bourdon tubes
are brass, phosphor bronze, beryllium copper, and steel.
Diaphragms
The movement of a diaphragm is a convenient way of sensing low
pressures. A diaphragm is a circular disc of thin, springy metal firmly fixed at
its rim. The unknown pressure is applied to one side of the diaphragm and
since the rim of the diaphragm is rigidly fixed there is a deflection of the
diaphragm. The displacement of the centre of the diaphragm is directly
proportional to the pressure and therefore can be used as a measure of
pressure.
The displacement of the diaphragm may be transmitted by an arm
fastened to its centre to a mechanical linkage, which magnifies the
displacement before applying it to a pointer of the indicating device.
The diaphragms are of two types:
(i) Flat, and (ii) Corrugated.
64
Corrugated diaphragms have an advantage over flat diaphragms
because of the increased effective area and consequent greater sensitivity.
In many applications two or more diaphragms are joined to form a
capsule. A flat diaphragm is shown in Fig. 13.2.
Fig. 13.2 Flat diaphragm
The pressure (P) is given by:
P=
256 Et 3 d m
N / m2
3 ( 1 −v 2 ) D 4
where
E = Young's modulus, N/m2
D, t = diameter and thickness of diaphragm respectively, m
v = Poisson's ratio
d m = deflection at the centre of the diaphragm, m
The above relationship, between pressure, P, and the deflection at the
centre dm, is linear. But linearity holds good as long as dm < 0.5 t.
Bellows
The bellows element consists of a cylindrical metal box with corrugated
walls of thin springy material like brass, phosphor bronze, or stainless steel.
The thickness of walls is typically 0.1 mm. Bellows are used in applications
where the pressures involved are low.
The pressure inside the bellows tends to extend its length. This
tendency is opposed by the springiness of the metals, which tends to restore
the bellows to its original size. Pressure on the outside of the bellows tends to
65
reduce its length and this tendency also, is opposed by the springiness of
metal. When the pressures are small the springiness of the metal sufficient.
However, when, the pressures are high, the springiness of the walls may not be
sufficient to restore the bellows to its original size. For such applications springs
are located inside the bellows to provide additional springiness to restore the
bellows to its original size.
The action of the bellows is as under:
The pressure to be measured is applied from the left end as shown in
Fig.13.1. The pressure inside the bellows extends its length. Since the left hand
end is fixed, there is a displacement of the right hand end to which a rod is
connected. The displacement of this rod is directly proportional to the pressure
inside the bellows. The displacement of the rod is small and may be amplified
by using mechanical linkage and then transferred to a pointer moving over a
calibrated scale.
66
LECTURE NO.14
TEMPERATURE MEASUREMENT: INTRODUCTION- TEMPERATURE
SCALES- INTERNATIONAL PRACTICAL TEMPERATURE SCALE (IPTS)
INTRODUCTION
Temperature is a very widely measured and frequently controlled
variable used in numerous industrial applications. In general, chemical
reactions in the industrial processes and products are temperature dependent
and the desired quality of a product is possible only if the temperature is
accurately measured and maintained. In the heat treatment of steel and
aluminum alloys, temperature measurement and control plays a crucial role in
incorporating the desired material properties in the finished heat-treated
products. The other areas where measurement and control of temperature is
essential are: plastic manufacturing, nuclear reactor components, milk and
dairy products, plant furnace and molten metals, heating and air-conditioning
systems, space shuttle components, blades of gas turbines, etc.
The temperature is defined as the degree of hotness or coldness of a
body or an environment measured on a definite scale. Definition of temperature
is also defined based on its equivalence to a driving force or potential that
caused the flow of energy as heat. Thus, we can define temperature as a
condition of a body by virtue of which heat is transferred to or from other
bodies.
It may be noted that there is a difference between the quantities
temperature and heat. Temperature may be defined as 'degree' of heat
whereas heat is taken to mean as 'quantity' of heat. For example, a bucket of
warm water would melt more ice than a small spoon of boiling water. The warm
water in the bucket obviously contains greater quantity of heat than that in the
spoon containing boiling water. But its temperature is lower than the boiling
water, a fact that is readily apparent if a finger is dipped in both the
vessels.
Temperature is a fundamental quantity, much the same way as mass,
length and time. The law that is used in temperature measurement is known as
the Zeroth law of thermodynamics.
67
Zeroth law of thermodynamics
Zeroth law of thermodynamics states that if two bodies are in thermal
equilibrium with a third body, then they are all in thermal equilibrium with each
other.
TEMPERATURE SCALES
Two temperature scales in common use are the Fahrenheit and
Celsius scales. These scales are based on a specification of the number of
increments between freezing point and boiling point of water at the
standard atmospheric temperature.
The Celsius scale has 100 units between these points, while the
Fahrenheit scale has 180 units. The Celsius scale is currently more in use
because of the adoption of metric units. However, the absolute temperature
scale based on the thermodynamic ideal Carnot cycle has been correlated with
the Celsius and Fahrenheit scales as follows:
K (Absolute temperature, Kelvin scale) = °C + 273.15
where
°C is temperature on Celsius scale.
R (Absolute temperature, Rankine scale) = °F + 459.69
where
°F is the temperature on the Fahrenheit scale.
The zero points on both the scales represent the same physical state
and the ratio of two values is the same, regardless of the absolute scale used
i.e.
T2 
T 
= 2 
 
 T1  Rankine  T1  Kelvin
The boiling and freezing points of water at a pressure of one atmosphere
(101.3 kN / m2) are taken as 100° and 0° on the Celsius scale and 212° and
68
32° on the Fahrenheit scale. The relationships between Fahrenheit and Celsius
and Rankine and Kelvin scales are as follows:
o
9
F =32 + oC
5
9
R= K
5
with SI units, the kelvin temperature scale (which is also termed as
absolute temperature scale or 'thermodynamic' temperature scale) is used in
which the unit of temperature is the kelvin (K).
INTERNATIONAL PRACTICAL TEMPERATURE SCALE (IPTS)
To enable the accurate calibration of a wide range of temperatures in
terms of the Kelvin scale, the International Practical Temperature Scale (IPTS68) has been devised. This lists 11 primary 'fixed' points which can be
reproduced accurately. Some typical values are:
Table 14.1 Typical Values of Primary ‘Fixed’ points
S.
Primary fixed point
Temperature
(K)
No.
Temperature (
o
C)
1
Triple point of equilibrium hydrogen 13.18
(equilibrium between solid, liquid, and
vapour phases of equilibrium hydrogen)
-259.34
2
Boiling point of equilibrium hydrogen
20.28
-252.87
3
Triple point of oxygen
54.361
-218.789
4
Boiling point of oxygen
90.188
-182.962
5
Triple point of water (equilibrium between
solid, liquid and vapor phases of water)
273.16
0.01
6
Boiling point of water
373.15
100
7
Freezing point of zinc
692.73
419.58
8
Freezing point of silver
1235.58
961.93
9
Freezing point of gold
1337.58
1064.43
69
Apart from the primary standard points, there are 31 secondary points
on the International Practical Temperature Scale which forms the convenient
working standard for the workshop calibration of the temperature measuring
devices. Some typical values of these points are given in Table 14.2.
Table 14.2 Typical Values of Secondary Points
S.
Secondary points
Temperature
(K)
Temperature
( oC )
1
Sublimation point of carbon dioxide
194.674
-74.476
2
Freezing point of mercury
234.288
-38.862
3
Equilibrium between ice and water (ice 273.15
point)
4
Melting point of bismuth
544.592
271.442
5
Melting point of lead
600.652
327.502
6
Boiling point of pure sulphur
717.824
444.674
7
Melting point of antimony
903.87
630.74
8
Melting point of aluminium
933.52
660.37
9
Melting point of copper
1357.6
1084.5
10
Melting point of platinum
2045
1772
11
Melting point of tungsten
3660
3387
No.
70
0
LECTURE NO.15
MEASUREMENT
OF
TEMPERATURE:
CLASSIFICATION
OF
TEMPERATURE MEASURING DEVICES - BIMETALLIC THERMOMETERS GLASS THERMOMETERS AND PRESSURE GAUGE THERMOMETERS THERMOCOUPLES
MEASUREMENT OF TEMPERATURE
Temperature is measured by observing the effect that temperature
variation causes on the measuring device. Temperature measurement methods
can be broadly classified as follows:
1. non-electrical methods,
2. electrical methods, and
3. radiation methods.
NON-ELECTRICAL METHODS
The non-electrical methods of temperature measurement can be based
on anyone of the following principles:
1. change in the physical state,
2. change in the chemical properties, and
3. change in the physical properties.
BIMETALLIC THERMOMETER
This type of thermometer also employs the principle of solid expansion
and consists of a 'bimetal' strip usually in the form of a cantilever beam
[Fig.15.1 (a)]. This comprises strips of two metals, having different coefficients
of thermal expansion, welded or riveted together so that relative motion
between them is prevented. An increase in temperature causes the deflection
of the free end of the strip as shown in Fig.15.1 (b), assuming that metal A has
the higher coefficient of expansion. The deflection with the temperature is
nearly linear, depending mainly on the coefficient of linear thermal expansion.
Invar is commonly employed as the low expansion metal. This is an ironnickel alloy containing 36% nickel. Its coefficient of thermal expansion is around
71
1/20th of the ordinary metals. Brass is used as high expansion material for
the measurement of low temperatures, whereas nickel alloys are used when
higher temperatures have to be measured. A plain bimetallic strip is somewhat
insensitive, but the sensitivity is improved by using a longer strip in a helical
form as shown in Fig.15.2.
Bimetallic thermometers are usually employed in the range of -30 to 550
°C. Inaccuracies of the order of ± 0.5 to ± 1.0% of full-scale deflection are
expected in bimetallic thermometers of high accuracies.
Fig.15.1 Bimetallic Thermometer
Fig.15.2 Bimetallic Helix Thermometer
The bimetallic strip has the advantage of being self-generating type
instrument with low cost practically no maintenance expenses and stable
operation over extended period of time. However, its main disadvantage is its
inability to measure rapidly changing temperatures due to its relatively higher
thermal inertia.
72
LIQUID-IN-GLASS THERMOMETER/MERCURY-IN-GLASS THERMOMETER
The liquid-in-glass thermometer is one of the most common temperature
measuring devices. Both liquid and glass expand on heating and their
differential expansion is used to indicate the temperature. The lower
temperature limit is -37.8 ºC for mercury, down to –130 °C for pentane. The
higher temperature range is 340 °C (boiling point of mercury is 357 °C ) but this
range may be extended to 560 °C C by filling the space above mercury with
CO2 or N2 at high pressure, thereby increasing its boiling point and range. The
precision of the thermometer depends on the care used in calibration. A typical
instrument is checked and marked from two to five reference temperatures.
Intermediate points are marked by interpolation. The calibration of the
thermometer should be occasionally checked against the ice point to take into
account the aging effects. Precision thermometers are sometimes marked for
partial or total immersion and also for horizontal or vertical orientation. The
accuracy of these thermometers does not exceed 0.1°C. However, when
increased accuracy is required, a Beckmann range thermometer can be
used. It contains a big bulb attached to a very fine capillary. The range of the
thermometer is limited to 5 – 6 °C with an accuracy of 0.005°C.
Liquid-in-glass thermometers have notable qualities like low cost,
simplicity in use, portability and convenient visual indication without the use of
any external power. However, their use is limited to certain laboratory
applications. It is not preferred in industrial applications because of its fragility
and its lack of adaptability to remote indication. Further, it introduces time
lag in the measurement of dynamic signals because of relatively high heat
capacity of the bulb.
PRESSURE THERMOMETERS / PRESSURE SPRING THERMOMETERS
Pressure thermometer is based on the principle of fluid expansion due to
an increase in the pressure in a given volume of the temperature measuring
system. It is one of the most economical, versatile and widely used devices in
industrial temperature measurements. It has a relatively large metal bulb (often
stainless steel) instead of glass. This results in a robust, easy-to-read
thermometer that may be read remotely by connecting the bulb to a Bourdon
73
gauge or any other pressure measuring device by means of a capillary tube as
illustrated in Fig.3.
Fig.15.3 A schematic diagram of pressure thermometer
The entire assembly of the bulb, capillary and gauge is calibrated
directly on the basis of pressure change corresponding to the temperature
change. The bulb of the thermometer may be filled with either a liquid (usually
mercury) or gas or a liquid-vapor mixture and depending upon the type of fluid,
the thermometer is termed as mercury-in-steel thermometer or constant
volume gas thermometer or vapour pressure thermometer respectively.
Fluid expansion thermometers are low in cost, self-operated type,
rugged in construction, with no maintenance expenses, stable in operation and
accurate to ±1°C. Further, the response of these instruments can be increased
by using a small bulb connected to an electrical type of pressure sensor
connected through a short length of capillary tube.
74
LECTURE NO.16
ELECTRICAL
TEMPERATURE
RESISTANCE
DETECTORS
THERMOMETERS
(RTDS)
-
-
RESISTANCE-
THERMOCOUPLE
-
THERMOCOUPLE MATERIALS
ELECTRICAL METHODS
Electrical methods are in general preferred for the measurement of
temperature as they furnish a signal which can be easily detected, amplified or
used for control purposes. There are two main electrical methods used for
measuring temperature. They are:
1. Thermo-resistive type i.e., variable resistance transducers and
2. Thermo-electric type i.e., emf generating transducers.
ELECTRICAL RESISTANCE THERMOMETERS
In resistance thermometers, the change in resistance of various
materials, which varies in a reproducible manner with temperature, forms the
basis of this important sensing technique. The materials in actual use fall in
two classes namely, conductors (metals) and semiconductors. In general,
the resistance of the highly conducting materials (metals) increases with
increase in temperature and the coils of such materials are called metallic
resistance thermometers. Whereas the resistance of semiconductor
materials generally (not always) decreases with increase in temperature.
Thermo-sensitive resistors having such negative temperature characteristics
are commonly known as NTC thermistors. Figure 16.1 illustrates the typical
variation of specific resistance of the metals (platinum for example) and the
NTC thermistor.
75
Fig. 16.1 Resistance- temperature characteristics of platinum and a
typical NTC thermistor
METALLIC
RESISTANCE
THERMOMETERS
OR
RESISTANCE-
TEMPERATURE DETECTORS (RTDS)
Metals such as platinum, copper, tungsten and nickel exhibit small
increases in resistance as the temperature rises because they have a positive
temperature coefficient of resistance. Platinum is a very widely used sensor
and its operating range is from 4K to 1064 °C. Because it provides extremely
reproducible output, it is used in establishing International Practical
Temperature Scale from 13.81 K to 961.93 °C. However for the measurement
of lower temperatures up to 600°C, RTD sensor is made of nickel.
Metallic resistance thermometers are constructed in many forms, but the
temperature sensitive element is usually in the form of a coil of fine wire
supported in a stress-free manner. A typical construction is shown in Fig. 16.2,
where the wire of metal is wound on the grooved hollow insulating ceramic
former and covered with protective cement.
76
Fig. 16.2 Construction of a platinum resistance thermometer (PRT)
THERMO-ELECTRIC SENSORS / THERMOCOUPLE
The most common electrical method of temperature measurement uses
the thermo-electric sensor, also known as the thermocouple (TC). The
thermocouple is a temperature transducer that develops an emf which is a
function of the temperature between hot junction and cold junction. The
construction of a thermocouple is quite simple. It consists of two wires of
different metals twisted and brazed or welded together with each wire covered
with insulation which may be either.
1. mineral (magnesium oxide) insulation for normal duty, or
2. ceramic insulation for heavy duty.
The basic principle of temperature measurement using a thermo-electric
sensor was discovered by Seebeck in 1821 and is illustrated in Fig. 16.3.
When two conductors of dissimilar metals, say A and B, are joined together to
form a loop (thermocouple) and two unequal temperatures T1 and T2 are
interposed at two junctions J1 and J2, respectively, Then an infinite resistance
voltmeter detects the electromotive force E, or if a low resistance ammeter is
connected, a current flow I is measured Experimentally, it has been found that
the magnitude of E depends upon the materials as well as the temperature T1
and T2. Now, the overall relation between emf E and the temperatures T1 and
T2 forms the basis for thermoelectric measurements and is called the Seebeck
effect. Thus, in practical applications, a suitable device is incorporated to
indicate the emf E or the flow of current I. For convenience of measurements
77
and standardization, one of the two junctions is usually maintained at some
known temperature. The measured emf E then indicates the temperature
difference relative to the reference temperature, such as ice point which is very
commonly used in practice.
Fig. 16.3 Basic thermo-electric circuit
It may be noted that temperatures T1 and T2 of junctions J1 and J2
respectively are slightly altered if the thermo-electric current is allowed to flow
in the circuit. Heat is generated at the cold junction and is absorbed from the
hot junction thereby heating the cold junction slightly and cooling the hot
junction slightly. This phenomenon is termed Peltier effect. If the thermocouple
voltage is measured by means of potentiometer, no current flows and Peltier
heating and cooling are not present. Further, these heating and cooling effects
are proportional to the current and are fortunately quite negligible in a
thermocouple circuit which is practically a millivolt range circuit. In addition, the
junction emf may be slightly altered if a temperature gradient exists along either
or both the materials. This is known as Thomson effect.
The actual application of thermocouples to the measurements requires
consideration of the laws of thermo-electricity.
LAW OF INTERMEDIATE TEMPERATURES
This states that the emf generated in a thermocouple with junctions at
temperatures T1 and T3 is equal to the sum of the e.m.f. 's generated by similar
thermocouples, one acting between temperatures T1 and T2 and the other
between T2 and T3 when T2 lies between T1 and T3 (Fig.16.4).
78
Fig. 16.4 Law of intermediate temperatures
Law of Intermediate Metals
The basic thermocouple loop consists of two dissimilar metals A and B
[Fig.16.5 (a)]. If a third wire is introduced, then three junctions are formed as
shown in Fig. 16.5(b). The emf generated remains unaltered if the two new
junctions B-C and C-A are at the same temperature.
Fig.16.5 Law of intermediate metal
It may be noted that extension wires are needed when the measuring
instrument is to be placed at a considerable distance from the reference
junction. Maximum accuracy is obtained when the leads are of the same
material as the thermocouple element [Fig.16.6 (a)]. However, this approach is
not economical while using expensive thermocouple materials. Therefore, it is
preferable to employ the system shown in Fig. 16.6 (b) to keep the copper-iron
and copper-constantan junctions in the thermos flask at 0°C and provide
binding posts of copper. This ensures maximum accuracy in the thermocouple
operation.
79
(a) A thermocouple without extension leads
(b) Conventional method of establishing reference function temperature with
copper extension leads
Fig.16.6 Schematics of Thermocouple circuits with and without extension leads
in a typical iron-constantan thermocouple circuit
(a) A thermocouple without extension leads
(b)
Conventional method of establishing
temperature with copper extension leads
reference
function
THERMOCOUPLE MATERIALS
The choice of materials for thermocouples in governed by the following
factors:
1. Ability to withstand the temperature, at which they are used,
80
2. Immunity from contamination / oxidation, etc. which ensures
maintenance of the precise thermo-electric properties with
continuous use, and
3. Linearity characteristics.
It may be noted that the relationship between thermo-electric emf and
the difference between hot and cold junction temperatures is approximately of
the parabolic form:
E =aT +bT
2
Thermocouple can be broadly classified in two categories:
1. base-metal thermocouples, and
2. rare-metal thermocouple.
Base-metal thermocouples use the combination of pure metals and
alloys of iron, copper and nickel and are used for temperature up to 1450 K.
These are most commonly used in practice as they are more sensitive,
cheaper and have nearly linear characteristics. Their chief limitation is the
lower operating range because of their low melting point and vulnerability to
oxidation.
On the other hand, rare-metal thermocouples use a combination of
pure metals and alloys of platinum for temperatures up to l600 °C and
tungsten, rhodium and molybdenum for temperatures up to 3000 °C.
81
LECTURE NO.17
PRESSURE
-
DIFFERENTIAL
GAUGE
PRESSURE,
PRESSURE,
VACUUM
-
ABSOLUTE
UNITS
OF
PRESSURE,
PRESSURE
-
PRESSURE SCALES - CONVERSION OF UNITS- TYPES OF PRESSURE
MEASUREMENT DEVICES
PRESSURE MEASUREMENT
INTRODUCTION
Pressure means force per unit area, exerted by a fluid on the surface of
the container.
Pressure measurements are one of the most important measurements
made in industry especially in continuous process industries such as chemical
processing, food and manufacturing. The principles used in measurement of
pressure are also applied in the measurement of temperature, flow and liquid
level.
Pressure is represented as force per unit area.
Fluid pressure is on account of exchange of momentum between the molecules
of the fluid and a container wall.
Static and Dynamic Pressures
When a fluid is in equilibrium, the pressure at a point is identical in all
directions and is independent of orientation. This is called static pressure.
However, when pressure gradients occur within a continuum (field) of
pressure, the attempt to restore equilibrium results in fluid flow from regions of
higher pressure to regions of lower pressure. In this case the pressures are no
longer independent of direction and are called dynamic pressures.
Velocity and Impact Pressures
Pressure components of different nature exist in a flowing fluid. For
example, in case a small tube or probe for sampling, it is found that the results
depend upon how the tube is oriented. In case, the tube or probe is so aligned
that there is a direct impact of flow on the opening of the tube or probe as
shown in Fig.17.1 (a) it senses a total or stagnation pressure. If the tube or
probe is oriented as shown in Fig.17.1 (b), the results are different and what we
82
obtain is called static pressure.
Fig.17.1 Impact and Static Pressure tubes
Static Pressure
Static pressure is considered as the pressure that is experienced if
moving along the stream and the total pressure may be defined as the pressure
if the stream is brought to rest is entropically. The difference of the two
pressures is the pressure due to fluid motion commonly referred as the velocity
pressure.
Velocity pressure = stagnation
Therefore,
in
order
to
(total) pressure - static pressure
properly
interpret
flow
measurements,
consideration must be given how the pressure is being measured.
Absolute pressure.
Absolute pressure means the fluid pressure above the reference value
of a perfect vacuum or the absolute zero pressure.
Gauge pressure.
It represents the difference between the absolute pressure and the local
atmospheric pressure.
Vacuum
Vacuum on the other hand, represents the amount by which
atmospheric pressure exceeds the absolute pressure.
83
Fig.17.2 Various Pressure Terms used in Pressure Measurement
From the above definitions, we have:
Pg =Pa −Ps
Pv =Ps −Pa
where
Pa , Pg , Ps and
Pv are
absolute, gauge, atmospheric and vacuum
pressures, respectively.
The absolute pressure represents a positive gauge pressure and vacuum
represents a negative gauge pressure.
Units of Pressure
Some of the commonly used units of pressure are:
1m
mof
m
ercury
1atm
1atm
1N
/m
1bar
=1torr
= 1.0l3X105 N/m2
2
760m
mof
H
gat °C
= 1.0132 bar
=1P
ascal
0.987atm
The atmospheric pressure at sea level is 1.0l3 X105 N/m2 or 760 mm of
mercury.
Pressures higher than 1000 atm are usually regarded as very high while
those of the order of 1 mm of Hg or below are regarded as very low.
TYPES OF PRESSURE MEASUREMENT DEVICES
A number of devices can be used for measurement of pressure. In
industrial applications pressure is normally measured by means of indicating
84
gauges and recorders. These instruments are
 mechanical,
 electromechanical
 electrical or electronic in operation
(i) Mechanical Pressure Measuring Instruments.
Pressure can be easily transduced to force by allowing it to act on a
known area. Therefore, basic methods of measuring force and pressure are
essentially the same except for the pressures in the high vacuum region.
Mechanical instruments used for pressure measurement are based on
comparison with known dead weights acting on known areas or on the
deflection of elastic elements subjected to unknown pressures.
Instruments using this principle include manometers. And the elastic
members used are Bourdon tubes, bellows and diaphragms.
(ii) Electromechanical Instruments. These instruments generally employ
mechanical means for detecting pressure and electrical means for indicating or
recording pressure. Electromechanical instruments are very well suitable for
dynamic measurements as they have an excellent frequency response
characteristics.
(iii) Electronic Instruments. These pressure measuring instruments normally
depend on some physical change that can be detected and indicated or
recorded through electronic means. These instruments are used for vacuum
measurements.
85
LECTURE NO.18
MEASUREMENT OF PRESSURE: MANOMETERS - U TUBE MANOMETER INCLINED TUBE MANOMETER - WELL TYPE MANOMETER - PROPERTIES
OF MANOMETRIC FLUIDS
MANOMETERS
Manometers measure the unknown pressures by balancing against the
gravitational force of liquid heads. Manometers are self-balancing deflection
type of instruments and have continuous rather than stepwise output. These
are used in plant systems, as differential pressure devices. They are used as
primary standards for pressure measurements from low vacuum range to about
0.1 MN/m2.
Construction of Manometers. Manometer bodies are usually made of brass,
steel, aluminum or stainless steel. Tubes are made of pyrex. Scales are
provided which read pressures in terms of mm of water or in mm of mercury.
They can be provided to read in terms of kN/m2 (kPa).
Types of Manometers
The various types of manometers are:
U tube manometer, Well type Manometer, Inclined tube Manometer.
U tube manometer
The U tube manometer is shown in Fig. 18.1. This is used for
measurement of liquid or gas pressures. The manometer is filled with a
manometric fluid whose specific gravity is known. The difference between the
pressures on two limbs of the manometer is a function of h (the difference
between the levels of the manometric fluid in the two limbs).
86
Fig. 18.1 U Tube Manometer
The pressure balance equation is,
P1 +gh ρf =P2 +gh ρm
Differential pressure, P =P1 −P2 =gh ( ρm −ρf )
where
g is the gravitational constant (9.81 m/s2) and
ρm and ρf are
respectively the specific gravities of
manometric fluid and the transmitting fluid in kg/m3.
Well type Manometer
Unlike in the case of a U tube manometer, the two legs do not have the
same area. In the well type manometer (Fig. 18.2), one of the legs of a U tube
is substituted by a large well or reservoir. The cross-sectional area of the well
(used on the high pressure side) is very large as compared to the area of the
other leg. This means that even for a small displacement of liquid level in the
well there will be a very large change of height of liquid column in the other
limb. This results in increase of sensitivity.
A well type manometer operates in the same manner as the U-tube
manometer except that the construction is as shown in Fig.18.2. Since, the well
area is large compared to that of the tube, only a single leg reading may be
noted and the change in level in the well may be ignored.
87
Fig. 18.2 Well type Manometer
If, P1 and P2 are absolute pressures applied as shown, force equilibrium
gives:
P1 A −P2 A =A hρ g
ρ being mass density of the liquid.
p1 − p 2
=h
ρg
If P2 is atmospheric, h is a measure of the guage pressure applied at the
well.
Inclined Tube Manometer
An inclined tube manometer is a modified version of a well-type
manometer wherein the vertical leg is placed in an almost horizontal position so
that a very small change in pressure in the well causes a very large change in
the measured level of liquid in the inclined leg.
88
Fig.18.3 Inclined tube manometer
Fig. 18.3 shows an inclined tube manometer. Suppose a tube is inclined
at a slope of 1: 20 to the horizontal, the 20 units being measured as shown. A
rise of h mm in the liquid would mean that the displacement of liquid along the
tube is 20 h mm. Thus, the movement for a small change in level is easily
detected in an inclined tube manometer than in a vertical limbed manometer.
Hence, the inclined tube manometers have a much higher sensitivity than that
of vertical limbed manometers.
In these type of manometers, the length l along the inclined tube is read
as a measure of the pressure difference ( p1 − p 2 ) and l is derived as follows:
When pressure in the two limbs are the same, the levels of the liquid are
at equilibrium position xx. On application of pressure p1 and p 2 , difference in
levels between the two limbs is
h1 +h2 =
p1 −p 2
ρg
If A1 and A2 are the respective areas of the two limbs,
89
A1h1 =A2 l
h2 =l sin θ
From the above equations,
 A2

p1 − p 2 = ρgl 
 A +sin θ 

 1

If A1 >> A2 or A2 / A1 is negligible,
p1 − p 2 =ρgl sin θ =ρgh 2
If θ = 30 0 , l = 2h2 and thus it would be more accurate to read l rather
> A2 , the reading on one side only, viz. l is
than h2 as the output. Since A1 >
required.
Properties of Manometric Fluids
The desirable properties of manometric fluids are:
i. Low viscosity: Fluids with low viscosity give quick response.
ii. Low co-efficient of thermal expansion: The value of measured pressure
is affected by changes in density of manometreric fluids which is
dependent upon temperature.
iii. Low vapor pressure, negligible surface tension, and low capillary effects,
and non-sticky effects.
iv. Non-corrosive, non-poisoness
v. Long term stability
Some of the manometric fluids are: water, Mercury, transformer oil
(suitable for ammonia gas flow meters and measurements of small pressure
differences), Aniline (suitable for low pressure air or gas flow meters with the
exception of ammonia and chlorine)
Advantages of Manometers.
i. The advantages of manometers are:
ii. They are simple in construction, high accuracy, and good repeatability.
iii. Wide range of manometric fluids can be used
90
iv. They can be used both as measuring instruments and also as primary
standards for pressure measurement on account of their inherent
accuracy.
v. The accuracy level of manometers is quite good.
Disadvantages of Manometers.
The disadvantages of manometers are:
i. They are fragile in construction and hence lack portability.
ii. When visual reading of height h is used, corrections must be applied for
effect of temperature on the engraved (fixed) scale.
iii. The value of gravitational constant g is dependent upon the altitude of
the place
iv. Accurate leveling is required in order to have good accuracy.
v. Poor dynamic response.
Several types of modified manometers are available which have the
advantages of ease in use and high sensitivity.
91
LECTURE NO.19
ELASTIC PRESSURE ELEMENTS - BOURDON TUBE – BELLOWS DIAPHRAGMS
ELASTIC PRESSURE ELEMENTS
Elastic elements when subjected to pressure get deformed. The
deformation, when measured, gives an indication of the pressure. These
elements are in the form of diaphragms, capsules, bellows, Bourdon or helical
tubes (Fig. 19.1). The deformation may be measured by mechanical or
electrical means. These devices are convenient to use and can cover a wide
range of pressures, depending on the design of the elastic elements.
Fig. 19.1 Elastic elements / Pressure Elements
Among the elastic pressure elements, the three main types are:
(i) Bourdon Tube,
(ii) Bellows, and
(iii) Diaphragm.
BOURDON TUBE
A bourdon gauge is commonly used for measuring pressure. The Bourdon
tubes find wide applications because of their simple design and low cost.
There are three types of Bourdon elements and they are,
92
(i) C- type, (ii) spiral type, and (iii) helical type.
(i) C- type Bourdon element:
The tube which is oval in section is formed into an arc of 2500 and hence
the name C for the configuration which is shown in Fig. 19.2. One end called
the tip of the tube is sealed and is called free end. This is attached by a light
link-work to a mechanism which operates the pointer. The other end of the
tube is fixed to a socket where the pressure to be measured is applied. The
internal pressure tends to change the section of the tube. The degree of
linearity depends upon the quality of gauge from oval to circular, and this
tends to straighten out the tube. The movement of the tip is ideally
proportional to the pressure applied. The tip is connected to a spring
loaded link-work and a geared sector and pinion arrangement which
amplifies the displacement of tip and converts into the deflection of the
pointer. The linkage is constructed so that the mechanism may be
constructed for optimum linearity and minimum hysteresis, as well as to
compensate for wear which may develop over the time.
Fig. 19.2 C type Bourdon tube
Fig. 19.3 Displacement at the free end of Bourdon Tube
93
The displacement of tip is,
0.2
∆a =0.05
a P r 
 
E t 
0.33
x 

y 

 
3
x 
. 
t 
Where
E is the Modulus of Elasticity and other terms are as shown in the
above fig.
The normal accuracy of C type Bourdon tube is about ± 1 %.
(ii) Spiral type Bourdon tube
Spiral tubes are made by winding several turns of the tube with its
flattened cross-section in the form of a spiral. When the pressure to be
measured is applied to the spiral, it tends to uncoil producing a relatively long
movement of the tip whose displacement can be used for indication or
transmission. The accuracy of spiral tube elements is higher than that of C type
elements on account of absence of magnifying elements and is typically about
± 0.5%.
Fig. 19.4 Helical type Bourdon tube
(iii) Helical Type. A helical type Bourdon tube is shown in Fig. 19.4. Helical
and Spiral bourdon tube elements are similar, except it is wound in the form of
a helix. The displacement of the tip of a helical clement is larger than that of
spiral element. Usually a central shaft is installed within a helical clement and
the pointer is driven from this shaft by connecting links. This system transmits
only the circular motion of the tip to the pointer which is directly proportional to
the changes in pressure.
94
The advantages of helix elements include its stability in fluctuating
pressure applications, and its adaptability for high pressure service. The
number of coils employed in helix elements depends upon the pressure to be
measured. Helix type of pressure elements use as few as three coils while
elements used for measurement for high pressures may have as many as 16
coils or even more. The accuracies obtainable from helical elements may vary
from ± 0.5 % to ± 1 %.
Materials used for constructing Bourdon Tubes
Bourdon tubes are made up of different materials which include brass,
alloy steel, stainless steel, bronze, phosphor bronze, beryllium, copper, and
monel.
Phosphor bronze is used in low pressure applications where the
atmosphere is non-corrosive while in applications where corrosion and / or high
pressure is a problem, stainless steel or Monel are used.
Pressure gauges using bourdon tube elements are made with ranges from
760 mm of mercury to 700 M Pa or higher for special applications with the
minimum span being about 70 kPa.
Bellows
A metallic bellows consists of a series of circular parts, resembling the
folds shown in Fig.19.5. These parts are formed or joined in such a manner
that they are expanded or contracted axially by changes in pressure.
The metals used in the construction of bellows must be
thin enough to be flexible,
ductile enough for reasonably easy fabrication, and
have a high resistance to fatigue failure.
Materials commonly used are brass, bronze, beryllium copper, alloys of
nickel and copper, steel and monel.
95
Fig.19.5 Bellows Pressure Element
The displacement of bellows element is given by.
d =
0.453 Pb n D 2
Et 3
1 −v 2
Where,
P = Pressure, N/m2
b = radius of each corrugation, m
n = number of semi-circular corrugations
t =thickness of wall, m
D = mean diameter, m
E = Modulus of elasticity, N/m2
v = Poisson's ratio
The advantages of bellows include their simple and rugged construction,
moderate price, their usefulness for measurement of low, medium and high
pressures, and their applicability for use in measurement of absolute, gauge
and differential pressures. Bellows are useful to measure vacuum and low
pressures.
The disadvantages of bellows are that they are not suited for dynamic
measurements on account of their greater mass and longer relative movement.
Also they need temperature compensating devices to avoid errors resulting
from changes in ambient temperature.
DIAPHRAGMS
The operating principle of diaphragm elements is similar to that of the
bellows. The pressure to be measured is applied to the diaphragm, causing it
96
to deflect, the deflection being proportional to the applied pressure. The
movement of the diaphragm depends on its thickness and diameter.
The diaphragm element is essentially a flexible disc which may be either
flat or corrugated as shown in Fig. 19.6.
Fig. 19.6 Single Diaphragm elements
For the arrangement of a flat diaphragm shown in Fig. 19.7 the maximum
deflection, dm and the deflection at any radius, dr , are given by following
expressions:
dm =
and
3P
R 4 (1 − v 2 )
3
16 Et
3P (1 − v 2 )
dr =
(R 2 − r 2 )2
3
16 Et
Fig.19.7 Deflection of flat diaphragm.
In some cases, a diaphragm element may consist of a single disc, while in
others, two diaphragms are bonded together at their circumference by
soldering or pressure welding to form a capsule. A diaphragm element may
consist of one capsule or two or more capsules connected together with each
capsule deflecting on the application of pressure. The total deflection is the
sum of the deflections of individual capsules. Fig. 19.8 shows a diaphragm
element consisting of three capsules. In this assembly, the individual capsule is
97
connected axially with the next one and is allowed to expand without any
restraints.
Fig.19.8 Diaphragm element using three capsules
98
LECTURE NO.20
TYPES OF FLUID FLOW: STEADY FLOW AND UNSTEADY FLOWUNIFORM FLOW AND NON-UNIFORM FLOW - ONE-DIMENSIONAL FLOW,
TWO
DIMENSIONAL
FLOW
AND
THREE
DIMENSIONAL
FLOW-
ROTATIONAL FLOW AND IRROTATIONAL FLOW - LAMINAR FLOW AND
TURBULENT FLOW.
TYPES OF FLUID FLOW
Fluid flows are classified in several ways as indicated below:
I. Steady flow and Unsteady flow.
II. Uniform flow and Non-uniform flow.
III. One-dimensional flow, two dimensional flow and three dimensional flow.
IV. Rotational flow and Irrotational flow
V. Laminar flow and Turbulent flow.
Steady Flow
Fluid flow is said to be steady if at any point in the flowing fluid various
characteristics such as velocity, pressure, density, temperature etc., which
describe the behavior of the fluid in motion, do not change with time. The
various characteristics of the fluid in motion are independent of time.
However, these characteristics may be different at different points in the
flowing fluid.
Thus the steady flow is expressed mathematically by the following
expression at any point in the flowing fluid.
 ∂u 

=0 ;
 ∂t 
 ∂p 

=0 ;
 ∂t 
 ∂ρ 
 ∂T 

=0 ; 
=0
 ∂t 
 ∂t 
Unsteady Flow
Fluid flow is said to be unsteady if at any point in the flowing fluid any
one or all the characteristics which describe the behaviour of the fluid in motion
change with time. Thus a flow of fluid is unsteady, if at any point in the flowing
fluid
99
 ∂V 

≠0 ;
 ∂t 
 ∂p 

 ≠ 0 etc.
 ∂t 
Steady flow is simpler to analyze than unsteady flow. Most of the
practical problems of engineering involve only steady flow conditions.
Uniform Flow
When the velocity of flow of fluid does not change, both in magnitude
and direction, from point to point in the flowing fluid, for any given instant of
time, the flow is said to be uniform. In the mathematical form a uniform flow
may therefore be expressed as
 ∂V 

 = 0 t= constant
 ∂s 
where time is held constant and s represents any direction of displacement of
the fluid elements. The above expression states that there is no change in the
velocity vector in any direction throughout the flowing fluid at any instant of
time. For example flow of liquids under pressure through long pipe lines of
constant diameter is uniform flow.
Non-uniform Flow
If the velocity of flow of fluid changes from point to point in the flowing
fluid at any instant, the flow is said to be non-uniform. In the mathematical form
a non-uniform flow may be expressed as
 ∂V 

≠0
 ∂s 
For example, flow of liquids under pressure through long pipelines of
varying diameters is non-uniform flow.
All these types of flows can exist independent of each other so that any
of the four types of combinations of flows is possible, viz., (a) steady-uniform
flow; (b) steady-non-uniform flow; (c) unsteady uniform flow; and (d) unsteadynon-uniform flow. Examples of these combinations of flows are:
100
flow of liquid through a long pipe of constant diameter at a constant rate
is steady uniform flow;
flow of liquid through a long pipe line of constant diameter, at either
increasing or decreasing rate is unsteady-uniform flow;
flow of liquid through a tapering pipe at a constant rate is steady-nonuniform flow and
flow through a tapering pipe at either increasing or decreasing rate is
unsteady-non-uniform flow.
One-dimensional, Two-dimensional and Three-dimensional Flows
The various characteristics of flowing fluid such as velocity, pressure,
density, temperature etc, are in general the functions of space and time i.e.,
these may vary with the coordinates of any point x, y and z and time t. Such a
flow is known as a three-dimensional flow. If any of these characteristics of
flowing fluid does not vary with respect to time, then it will be a steady threedimensional flow.
When the various characteristics of flowing fluid are the functions of only
any two of the three coordinate directions, and time t, i.e., these may not vary in
anyone of the directions, then the flow is known as two-dimensional flow. For
example, if the characteristics of flowing fluid do not vary in the coordinate
direction Z, then it will be a two-dimensional flow having flow conditions
identical in the various planes perpendicular to the Z-axis.
When the various characteristics of flowing fluid are the functions of only
one of the three coordinate directions and time t, i.e., these may vary only in
one direction, then the flow is known as one dimensional flow. Similarly, it will
be a steady one dimensional flow if the characteristics of flowing fluid do not
vary with respect to time. Considering one of the characteristics of flowing
mass of fluid, say velocity of flow V, the following expressions may be written
which clearly exhibit the difference between these three types of flows:
Types of Flow
Unsteady
Steady
Three dimensional
V = f ( x, y , z , t )
V = f ( x, y , z )
101
Two dimensional
V = f ( x, y , t )
V = f ( x, y )
One dimensional
V = f ( x, t )
V = f ( x)
Rotational Flow
A flow is said to be rotational if the fluid particles while moving in the
direction of flow rotate about their mass centres. The liquid in the rotating tanks
illustrates rotational flow where the velocity of each particle varies directly as
the distance from the centre of rotation.
Irrotational Flow
A flow is said to be irrotational if the fluid particles while moving in the
direction of flow do not rotate about their mass centres.
Laminar Flow
A flow is said to be laminar when the various fluid particles move in
layers (or laminae) with one layer of fluid sliding smoothly over an adjacent
layer. Thus in the development of a laminar flow, the viscosity of the flowing
fluid plays a significant role.
Fig. 20.1 One, Two and Three-dimensional flows
Turbulent Flow
102
A fluid motion is said to be turbulent when the fluid particles move in an
entirely haphazard or disorderly manner that results in a rapid and continuous
mixing of the fluid leading to momentum transfer as flow occurs. In such a flow
eddies or vortices of different sizes and shapes are present which move over
large distances. This eddies and their random movement give rise to
fluctuations in the velocity and pressure at any point in the flow field, which are
necessarily the functions of time.
103
LECTURE NO.21
FLOW MEASUREMENT: INTRODUCTION - PRIMARY OR QUANTITY
METERS - POSITIVE-DISPLACEMENT METERS - SECONDARY OR RATE
METERS - VARIABLE HEAD METERS
FLOW MEASUREMENT: Introduction
Flow measurements are essential in many applications such as
transportation of solids as slurries, compressed natural gas in pipelines, water
and gas supply systems to domestic consumers, irrigation systems and a
number of industrial process control systems. The types of flows encountered
in the measurements may be any one or combination of the following types:
•
clean or dirty/opaque,
•
wet or dry,
•
hazardous/corrosive or safe,
•
single-phase, two-phase or multiphase,
•
laminar or transitional or turbulent,
•
pressure may vary from vacuums to high pressures of many
atmospheres,
•
temperature may vary from cryogenic levels to hundreds of
centigrade,
•
flow rate may be of miniscule type, i.e., few drops per minute or
massive type involving thousands of litres per minute.
The selection of a particular flow-measuring equipment depends
primarily on the nature of the metered fluid and the demands of the associated
plant. Many industrial flow meters have to work with fluids which may be
corrosive in nature or may contain foreign matters, but the equipment may be
relatively large and of fixed type. Additionally, the other factors that govern the
choice of a particular flow metering device are the various performance
parameters like range, accuracy, repeatability, linearity, dynamic response,
type of output like analog / digital, etc. Further, another requirement may be to
indicate or record the rate of flow, total flow or may be both these quantities.
104
Flow measuring devices generally fall into one of the two categories,
namely, primary devices or quantity meters and secondary devices known as
rate meters. The distinction between the two is based on the character of the
sensing element that interacts with the fluid flow. Quantity measurements, by
mass or volume, are usually accomplished by counting successive isolated
portions, whereas rate measurements are inferred from effects of flow rates on
pressure, force, heat transfer, flow area, etc. The quantity meters are generally
used for the calibration of rate meters.
PRIMARY OR QUANTITY METERS
Quantity or total flow measurement signifies the amount of fluid in terms
of mass or volume that flows past a given point in a definite period of time. In
other words, in this technique, the time required to collect a particular amount
of fluid is determined accurately and then the average flow rate can be
evaluated.
The flow meter calibration procedures using the quantity measurements
fall into the following two categories.
1. Voumetric Method
2. Gravimetric Method
Volumetric Method
In this technique, the fluid flowing in the flow meter which is being
calibrated is diverted into a tank of known volume. When the tank is completely
filled, then this known volume is compared with the integrated, volumetric
quantity registered by the flow meter under test.
Gravimetric Method
In this technique also, the fluid flowing in the flow meter, which is being
calibrated, is diverted into a vessel which can be weighed either continuously or
in the vessel after a pre-determined time. The weight of the liquid collected is
compared with the gravimetric quantity registered by the flow meter under test.
105
POSITIVE-DISPLACEMENT METERS
The term positive displacement meter is applied to a flow measuring
device so designed that the metered fluid is repeatedly filled and emptied from
a space of known volume. The principle of this measurement is that the
liquid flows through a meter and moves the measuring element that seals
the measuring chamber into a series of measuring compartments each
holding a definite volume. Each element is successively filled from the flow at
the inlet and emptied at the outlet of the meter. In other words, it is said that
positive-displacement meters chop the flow into ‘pieces' of known size and then
count the number of ‘pieces’.
Positive-displacement meters are widely used in low flow rate metering
applications where high accuracy and repeatability under steady flow
conditions are required. Further, they are easy to install and maintain and have
moderate cost. These types of meters are generally used by the water and oil
undertakings for accounting purposes. However, since there are moving parts
in these devices, the wear of the components may alter the accuracy.
Therefore, these instruments need calibration/adjustment over an interval of
time. Another limitation of such meters is their suitability to clean fluids only.
Further, these devices are generally flow totalizers and do not give
instantaneous rate of flow.
SECONDARY OR RATE METERS
The secondary or rate meters are also termed as inferential type of flow
measuring devices. This is because of the fact that they do not measure the
flow directly but instead measure another physical quantity which is related to
the flow. These devices fall into two categories, namely, the flow rate meters
and the velocity meters.
The transduction principle of some typical flow rate meters is as follows:
(i) Variable head meters: These are also termed as obstruction type of meters
in which the obstruction to the flow consists of an engineered constriction in the
metered fluid which causes a reduction in the flow pressure.
106
(ii) Variable area meters: The change in area causes change in the drag force
of a body placed in the flowing fluid.
(iii) Variable head and variable area meters: In these devices, a specified
shaped restriction is placed in the path of the flow which causes a rise in the
upstream liquid level, which is a function of the rate of flow.
(iv) Constant head device: In this device a constant head is applied to cause
a laminar flow in the capillary tube. In this device, the applied head is lost in
fluid friction but it causes a flow rate which can be metered.
Variable Head Meters
These meters essentially introduce an engineered constriction in the
flow passage. The, devices in general can be termed as obstruction type of
flow meters. The term ‘obstruction meter' applies to the devices that act as
obstacles placed in the path of the flowing fluid, causing localized changes in
the velocity. Concurrently with the velocity change, there is a corresponding
pressure change in the flow. This variation in pressure change is correlated
with the rate of flow of the fluid. It is noted that these devices cause a loading
error in the metered value because obstruction introduces extra resistance in
the flow system consequently, the flow rate reduces somewhat. The main
forms of restriction used in the flow are
venturi tube,
orifice plate and
a nozzle.
107
Fig. (a) Venturi meter
Fig.(b) Orifice meter
Fig. 21.1 Different types of variable head meters
The variation of pressure in these differential pressure devices is
indicated in Fig.21.1 (a) and Fig.21.1 (b). The position of minimum pressure is
located slightly downstream from the restriction at a point where the stream is
the narrowest and is called the vena-contracta. Beyond this point, the
pressure again rises but does not return to the upstream value and thus there
is a permanent pressure loss. The magnitude of this loss depends on the
type of restriction and on the dimensions of device. The ratio of the diameter at
the constriction to the diameter D of the pipe is called the diameter ratio. If this
ratio is too small, the opening is narrow and the pressure loss becomes
considerable and also the efficiency of the measurement is low. If the ratio is
rather large, then the reduction in pressure is too small for accurate
measurements. In practice, ratios in the range 0.2-0.6 are usually employed.
108
LECTURE NO.22
THE GENERAL EXPRESSION FOR THE RATE OF FLOW- CONSTRUCTION
OF VENTURI METER
The general expression for the rate of flow in these devices can be
derived as follows:
Say, the pressure, velocity and area of fluid stream at point 1, upstream
of obstruction are
obstruction are
p1 , V1 and A1 and at point 2 just downstream of the
p2 , V2 and A2 . Further,
we assume the flow to be
incompressible, i.e., its density does not vary in the flow field.
Applying the continuity equation in the flow we get
Rate of discharge Q =A1V1 =A2V2
------
(22.1)
Applying Bernoulli's equation (assuming the flow to be ideal) we get,
P1 +
ρV12
2
= P2 +
ρV22
2
(22.2)
The differential pressure head ∆h is given by
p1 − p2
= ∆h
ρg
(22.3)
Eliminating V1 and V2 from Eqs. (22.1) and (22.2) and substituting the
value of ∆h from eq. (3) we get the ideal rate of discharge as
Qideal =
A1 A2
A12 − A22
. 2g
∆h
(22.4)
In actual practice, the actual rate of fluid flow is always less than Qideal as
given by eq.(22.4), because of the losses in the fluid flow due to friction and
109
eddying motions. To account for this discrepancy, we define the term
coefficient of discharge Cd as
Cd =
Qactual
Qideal
(22.5)
Thus, we can write the actual rate of fluid flow as
Qactual = Cd
A1 A2
A12 − A22
. 2g
∆h
(22.6)
Equation (22.6) can be rewritten in the simplified from as
Qactual =Cd K (∆h)1
2
(22.7)
Where K is the constant of low obstruction device and
K=
A1 A2
A12 − A22
. 2g
where C d is the coefficient of discharge which depends on the type of flow,
obstruction type configuration and also on the Reynolds number of the flow.
Reynolds number =
ρVD
µ
The venturimeter offers the best accuracy, least head loss as compared
to the orifice meter. Because of the smooth surface, it is not much affected by
the wear and abrasion from dirty fluids. Further, due to low value of losses, the
coefficient of discharge is high and approaches unity under favourable
conditions. However, it is expensive and occupies substantial space.
An orifice meter consists of thin orifice plate which may be clamped
between pipe flanges. Since its geometry is simple, it is low in cost, easy to
install or replace and takes almost no space. However, it suffers from a head
loss which is of the order of 30-40%. Also, it is susceptible to inaccuracies
resulting from erosion, corrosion, clogging, etc. due to flow of dirty fluids.
110
The variable head devices are widely used in practice, because they
have no moving parts and require practically no maintenance. Further, they can
be used without calibration if made to standard dimensions. However the major
disadvantage is the square-root relationship between the pressure loss and the
rate of fluid flow. Further, it is not practical to measure the flow below 20% of
the rated meter capacity because of the inaccuracies involved in a very low
pressure differential measurements.
CONSTRUCTION OF VENTURI METER
A venturi meter is a device which is used for measuring the rate of flow
of fluid through a pipe. The basic principle on which a venturi meter works is
that by reducing the cross-sectional area of the flow passage, a pressure
difference is created and the measurement of the pressure difference enables
the determination of the discharge through the pipe.
Fig.22.1 Venturi Meter
Fig.22.2 Typical dimensions of Venturi Meter
As shown in Fig. 22.1 a venturi meter consists of (1) an inlet section
followed by a convergent cone, (2) a cylindrical throat, and (3) a gradually
111
divergent cone. The inlet section of the venturi meter is of the same diameter
as that of the pipe which is followed by a convergent cone. The convergent
cone is a short pipe which tapers from the original size of the pipe to that of the
throat of the venturi meter. The throat of the venturi meter is a short parallelsided tube having its cross-sectional area smaller than that of the pipe. The
divergent cone of the venturi meter is a gradually diverging pipe with its crosssectional area increasing from that of the throat to the original size of the pipe.
At the inlet section and the throat, i.e., sections 1 and 2 of the venturi meter,
pressure taps are provided through pressure rings as shown in Fig.22.1.
The convergent cone of a venturi meter has a total included angle of
21°± 1° and its length parallel to the axis is approximately equal to 2.7 (D - d),
where D is the diameter of the inlet section and d is the diameter of the throat.
The length of the throat is equal to d. The divergent cone has a total
included angle lying between 5° to 15°, (preferably about 6°). This results in the
convergent cone of the venturi meter to be of smaller length than its divergent
cone.
Since the cross-sectional area of the throat is smaller than the crosssectional area of the inlet section, the velocity of flow at the throat will become
greater than that at the inlet section, according to the continuity equation (
A1 V1 =A2 V2 ). The increase in the velocity of flow at the throat results in the
decrease in the pressure at this section as explained earlier. As such a
pressure difference is developed between the inlet section and the throat of the
venturi meter. The pressure difference between these sections can be
determined either by connecting a differential manometer between the pressure
taps provided at these sections or by connecting a separate pressure gage at
each of the pressure taps. The measurement of the pressure difference
between these sections enables the rate of flow of fluid to be calculated as
indicated below. Liquids ordinarily contain some dissolved air which is released
as the pressure is reduced and it too may form air pockets in the liquid. The
formation of the vapour and air pockets in the liquid ultimately results in a
phenomenon called cavitation, which is not desirable. Therefore, in order to
avoid the phenomenon of cavitation to occur, the diameter of the throat can be
reduced only upto a certain limited value which is restricted on account of the
112
above noted factors. In general, the diameter of the throat may vary from
1
to
3
3
of the pipe diameter and more commonly the diameter of the throat is kept
4
equal to 1/2 of the pipe diameter.
113
LECTURE NO.23
CONSTRUCTION OF ORIFICE METER
An orifice meter is another simple device used for measuring the
discharge through pipes. Orifice meter also works on the same principle as that
of venturi meter i.e., by reducing the cross-sectional area of the flow passage a
pressure difference between the two sections is developed and the
measurement of the pressure difference enables the determination of the
discharge through the pipe. However, an orifice meter is a cheaper
arrangement for discharge measurement through pipes and its installation
requires a smaller length as compared with venturi meter. As such where the
space is limited, the orifice meter may be used for the measurement of
discharge through pipes.
An orifice meter consists of a flat circular plate with a circular hole called
orifice, which is concentric with the pipe axis. The thickness of the plate t is less
than or equal to 0.05 times the diameter of the pipe. From the upstream face of
the plate the edge of the orifice is made flat for a thickness t1 less then or equal
to 0.02 times the diameter of the pipe and for the remaining thickness of the
plate it is bevelled with the bevel angle lying between 30° to 45° (preferably
45°).
Fig. 23.1 Orifice meter
114
Fig.23.2 Concentric orifice plate with 45 ° bevelled edges
Fig.23.3 Eccentric orifice plate
Fig.23.4 Segmental orifice plate
115
Fig.23.5 Quadrant edge orifice plate
However, if the plate thickness t is equal to t1 , then no beveling is done
for the edge of the orifice. The plate is clamped between the two pipe flanges
with the bevelled surface facing downstream. The diameter of the orifice may
vary from 0.2 to 0.85 times the pipe diameter, but generally the orifice diameter
is kept as 0.5 times the pipe diameter. Two pressure taps are provided, one at
section 1 on the upstream side of the orifice plate and the other at section 2 on
the downstream side of the orifice plate. The upstream pressure tap is located
at a distance of 0.9 to 1.1 times the pipe diameter from the orifice plate. The
position of the downstream pressure tap, however, depends on the ratio of the
orifice diameter and the pipe diameter. Since the orifice diameter is less than
the pipe diameter as the fluid flows through the orifice the flowing stream
converges which results in the acceleration of the flowing fluid in accordance
with the considerations of continuity. The effect of the convergence of flowing
stream extends upto a certain distance upstream from the orifice plate and
therefore the pressure tap on the upstream side is provided away from the
orifice plate at a section where this effect is non-existent. However, on the
downstream side the pressure tap is provided quite close to the orifice plate at
the section where the converging jet of fluid has almost the smallest crosssectional area (which is known as venacontracta ) resulting in almost the
maximum velocity off low and consequently the minimum pressure at this
section. Therefore a maximum possible pressure difference exists between the
sections 1 and 2, which is measured by connecting a differential manometer
between the pressure taps at these sections, or by connecting a separate
pressure gauge at each of the pressure taps. The jet of fluid coming out of the
116
orifice gradually expands from the vena contracta to again fill the pipe. Since in
the case of an orifice meter an abrupt change in the cross-sectional area of the
flow passage is provided and there being no gradual change in the crosssectional area of the flow passage as in the case of a venturi meter, there is a
greater loss of energy in an orifice meter than in a venturi meter.
Fig.23.6 Location of Vena contracta point
117
LECTURE NO.24
VARIABLE
AREA
METERS-
ROTAMETER;
PITOT
TUBE
-
ITS
ADVANTAGES - ITS LIMITATIONS
VARIABLE AREA METERS
In the variable area meter, the area of the restriction can be altered to
maintain a steady pressure difference.
A commonly used variable area flow meter is the rotameter.
ROTAMETER
The rotameter also known as variable-area meter is shown in Fig.24.1. It
consists of a vertical transparent conical tube in which there is a rotor or float
having a sharp circular upper edge. The rotor has grooves on its head which
ensure that as liquid flows past, it causes the rotor to rotate about its axis. The
rotor is heavier than the liquid and hence it will sink to the bottom of the tube
when the liquid is at rest. But as the liquid begins to flow through the meter, it
lifts the rotor until it reaches a steady level corresponding to the discharge. This
rate of flow of liquid can then be read from graduations engraved on the tube
by prior calibration, the sharp edge of the float serving as a pointer. The
rotating motion of the float helps to keep it steady. In this condition of
equilibrium, the hydrostatic and dynamic thrusts of the liquid on the under side
of the rotor will be equal to the hydrostatic thrust on the upper side, plus the
apparent weight of the rotor.
118
Fig. 24.1 Rotameter
PITOT TUBE
A pitot tube is a simple device used for measuring the velocity of flow.
The basic principle used in this device is that if the velocity of flow at a
particular point is reduced to zero, which is known as stagnation point, the
pressure there is increased due to the conversion of the kinetic energy into
pressure energy, and by measuring the increase in the pressure energy at this
point the velocity of flow may be determined.
119
Fig.24.2 A schematic diagram of a pitot tube
Fig. 24.3 A pitot tube with inclined tube manometer
In its simplest form a pitot tube consists of a glass tube, large enough for
capillary effects to be negligible, and bent at right angles. A single tube of this
type may be used for measuring the velocity of flow in an open channel. The
tube is dipped vertically in the flowing stream of fluid with its open end A,
directed to face the flow, and the other open end projecting above the fluid
surface in the stream as shown in Fig.24.3. The fluid enters the tube and the
level of the fluid in the tube exceeds that of the fluid surface in the surrounding
stream. This is so because the end A of the tube is a stagnation point where
the fluid is at rest, and the fluid approaching the end A divides at this point and
passes around the tube. Since at the stagnation point the kinetic energy is
converted into the pressure energy, the fluid in the tube rises above the
surrounding fluid surface by a height which corresponds to the velocity of flow
of fluid approaching the end A of pitot tube. The pressure at the stagnation
point is known as stagnation pressure.
120
Consider a point 1 slightly upstream of end A and lying along the same
horizontal plane in the flowing stream where the velocity of flow is V. Now if the
points 1 and A are at a vertical depth of ho below the free surface of fluid in the
stream and h is the height of the fluid raised in the pitot tube above the free
surface, then applying Bernoulli's equation between the points 1 and A and
neglecting the loss of energy, we get
V2
h0 +
=ho +h
2g
In the above expression (ho + h), is the stagnation pressure head at
point A, which consists of two parts viz., the static pressure head ho and the
dynamic pressure head h. By simplifying the expression, we get
V2
=h;
2g
or
V = 2 gh
Above equation indicates that the dynamic pressure head h is
proportional to the square of the velocity of flow in the stream at the point close
to the end A of the Pitot tube. Thus the velocity of flow at any point in the
flowing stream may be determined by dipping the pitot tube to the required
point and measuring the height h of the fluid raised in the tube above the free
surface. However, the velocity of flow given by equation is somewhat more
than the actual velocity of flow, because in deriving the above equation no loss
of energy has been considered. Moreover, when the flow is highly turbulent the
pitot tube records a value of h which is higher than that corresponding to the
mean velocity of flow in the direction of the tube axis. As such in order to take
into account the errors which may creep in due to the above noted factors the
actual velocity of flow may be obtained by introducing a coefficient C (or Cv)
called pitot tube coefficient, so that the actual velocity of flow is given by
V =C
2 gh
A probable value for the coefficient of the pitot tube, C is 0.98. However,
the actual value of the coefficient C for a pitot tube may be determined by
calibration.
121
When a pitot tube is used for measuring the velocity of flow in a pipe or
any other closed conduit then the pitot tube may be inserted. Since a pitot tube
measures the stagnation pressure head (or the total head) at its dipped end,
the static pressure head is also required to be measured at the same section
where the tip of the pitot tube is held, in order to determine the dynamic
pressure head h. For measuring the static pressure head a pressure tap (or a
static orifice) is provided at this section to which a piezometer may be
connected. Alternatively the dynamic pressure head may also be determined
directly by connecting a suitable differential manometer between the pitot tube
and the pressure tap meant for measuring the static pressure.
The pitot tube has the following advantages:
1. It is a simple and low-cost device,
2. It produces no appreciable pressure loss in the flow system,
3. It can be easily inserted through a small hole into the pipe or duct, and
4. It is very useful for checking the mean velocities of the flows in
venturi, nozzle, orifice plate or any other complex flow field.
The limitations of this device are follows:
1. It is not suitable for measuring low velocities, i.e., below 5 m/s,
because of difficulties in the accurate measurement of pressure
differential.
2. It is sensitive to misalignment of the probe with respect to free stream
velocity. Usually an angle of yaw or misalignment up to 5° has little
effect on the velocity values but beyond 20° the error in the velocity
determination is of the order of 2%.
3. It is not suitable for the measurement of highly fluctuating velocities,
i.e., highly turbulent flows.
4. The use of pitot-tube is limited to exploratory studies. It is not
commonly used in industrial applications as numerous pitot tube
122
traverses are required for velocity distribution data which is quite
tedious and time-consuming.
123
LECTURE NO.25
VARIABLE HEAD AND VARIABLE AREA FLOW METERS (WEIRS) - HOT
WIRE ANEMOMETERS - ROTARY VANE METER
VARIABLE HEAD AND VARIABLE AREA FLOW METERS (WEIRS)
Weirs are variable head, variable area flow meters used for measuring
large volumes of liquids in open channels. These devices operate on the
principle that if a restriction of a specified shape and form is placed in the path
of the flow, a rise in the upstream liquid level occurs which is a function of the
rate of flow through the restricted section.
Weirs have a variety of forms and are classified according to the shape
of the notch or opening. The most commonly used weirs are the rectangular,
the triangular or V-notch and the trapezoidal or cipolleti weir. The rectangular
weirs are quite suitable for measuring large flows, whereas the V-notch is used
for smaller flows below 50 l/s.
HOT WIRE ANEMOMETERS
Hot wire anemometers are hot wire resistance transducers which are
used for measurement of flow rates of fluids. Flow rates of non-conducting
liquids in open channels and closed pipes and of gases in closed pipes can be
measured very conveniently by suitably locating this transducer which is in the
form of a wire filament. The hot wire filament is usually a fine wire of platinum
or tungsten, and is mounted in the flow channel, by means of supports. The
transducer is in the form of a probe as shown in Fig. 25.1.
124
Fig. 25.1 Hot wire anemometer Probe
The diameter and length of wire depends upon the size of the pipe and
the maximum flow rate which has to be measured. The diameter of wire varies
from 5 µ m to 300 µ m and length is approximately equal to half the diameter
of the pipe. The probe is located at the centre of the pipe with direction of wire
perpendicular to the direction of fluid flow.
The hot wire techniques of measuring flow velocities has assumed great
significance as the measurement can be done without disturbing the existing
conditions. The method can be used for measurement of low velocities. The hot
wire probe can be placed in small sized pipes without causing any pressure
drop in the fluid stream. However, it can measure only the average velocity of
flow. The method is unsuitable for velocity measurements if the fluid is
conducting liquid. The main applications of hot wire anemometers are for gas
flow and wind velocity measurements and in the laboratory for flow
measurements of non conducting liquids and gases.
Hot wire anemometers are commonly used in two different modes i.e.
(i)
constant current type and
(ii)
constant temperature type.
The two types of anemometers use the same basic principle but in
different ways.
In the constant current mode, the fine resistance wire carrying a fixed
current is exposed to the flow velocity. The flow of current through the wire
generates heat on account of i 2 R loss. This heat is dissipated from the surface
of the wire by convection to the surroundings. (The loss of heat due to
conduction and radiation is negligible). The wire attains equilibrium temperature
when the heat generated due to i 2 R loss is equal to the heat dissipated due to
convective loss. The circuit is so designed that i 2 R heat is essentially constant
and therefore the wire temperature must adjust itself to change the convective
loss until equilibrium is reached. The resistance of the wire depends upon the
temperature and the temperature depends the rate of flow. Therefore, the
resistance of wire becomes a measure of the flow rate.
125
In the constant temperature mode, the current through the wire is
adjusted to keep the wire temperature, as measured by its resistance, constant.
Therefore, the current required to maintain the resistance and hence
temperature constant, becomes a measure of flow velocity.
2
Heat generated = I Rw
where
I = current through the wire; A,
Rw = resistance of wire; Ω
Heat dissipated due to convection = hA (θw −θf )
where
h = co-efficient of heat transfer; W/m2-°C
A = heat transfer area; m2
θw = temperature of wire; °C and
θf = temperature of flowing fluid; °C
For equilibrium conditions, we can write the energy balance for the hot
wire as,
I 2 Rw = hA (θw −θf )
ROTARY VANE METER
Rotary pumps are capable of furnishing smooth, pulsation free flows at
pressures upto 10 kN/m2 range. Smooth flow is obtained by having more than
one vane in action, so that some flow is maintained on a continuous basis. The
flow in this type of pump is controlled by valves internally by passing some of
the fluid.
A typical vane meter is shown in Fig.25.2. It comprises a casing
containing a rotor assembly with four vanes in opposing pairs. Each pair is
mounted on rigid tubular rods. The inlet and outlet manifold is bolted above the
rotor casing. The direct reading mechanical counter and the calibrating
126
mechanism are bolted on the front cover. The only moving parts in the fluid
being the rotor and vanes which are constantly immersed in the fluid.
In operation, fluid enters the meter through inlet manifold and causes the
rotor to revolve in a clockwise direction by pressure on centre shaft, while one
vane cavity is filled under the line pressure, the backflow is sealed off by the
next succeeding vane. Under normal operating conditions one vane discharges
its volume in the outlet manifold and at the same time the inlet manifold fills the
cavity of the receiving vane. In this flow meter the line pressure keeps the
vanes in motion, and no electrical or pneumatic source of power is required.
The seal between the vanes and the measuring cavity is maintained by
capillary action. The fluid being measured acts as the sealant in the same
manner as in the mutating piston meter.
Fig.25.2 Rotary vane meter.
An extension shaft driving through a pressure tight gland in the meter
front cover transmits the rotor revolutions through calibrated gearing and
thence to a counter or a pulse generator for remote indication.
Materials used in the construction of these meters are different. The
standard meters use an aluminium alloy rotor, carbon vanes and stainless steel
fittings. High flow rate meters employ cast iron inner capsules and rotor with
127
plastic tipped metal vanes, the other parts are made of stainless steel and
brass.
128
LECTURE NO.26
MEASUREMENT
OF
LIQUID
LEVEL
-
DIRECT
LIQUID
LEVEL
MEASUREMENTS - DIP-STICK METHOD- SIGHT GLASS METHOD
MEASUREMENT OF LIQUID LEVEL
In industry, usually vast quantities of liquids such as water, solvents,
chemicals, etc. are used in a number of industrial processes. Liquid level
measurements are made to ascertain the quantity of liquid held in a container
or vessel. The liquid level affects both pressure and rate of flow in and out of
the container and therefore its measurement and / or control becomes quite
important in a variety of processes encountered in modern manufacturing
plants. Liquid level measurements can be broadly classified as:
1. direct methods and
2. indirect methods
Direct Liquid Level Measurements
In these methods, the actual liquid level is directly measured by means
of a simple mechanical type of device.
Dip-stick Method
This is a commonly used method for determining the liquid level is
dipping a graduated rod in a liquid. Boatmen usually dip the oars in the canal /
river to know the depth of water at a particular place. Similarly, a dip-stick is
used to measure the level of oil in a car engine or the height of fuel oil in a
uniformly shaped storage tank. This method, though quite economical, is not
very accurate specially for moving fluids. Further, it is not possible to get
continuous on-line observations in industrial processes.
Sight Glass Method
The sight glass or piezo-meter tube is graduated glass tube mounted on
the side of the liquid containing vessel for providing a visual indication of the
liquid level (Fig. 26.1). Since the liquids keep level, therefore the rise or fall of
129
the liquid level in a tank / vessel results in a corresponding change in the level
indicated by the sight tube.
Fig. 26.1 Sight glass level gate
Sight tubes are usually made of toughened glass and are provided with
metallic protecting covers around them. Further, the diameter of such tubes is
neither too large to change the tank / vessel level, nor too small to cause
capillary action in the tube.
The measurement of liquid level with this device is simple and direct for
clean and coloured liquids. However, it is rather unsuitable for dirty, viscous
and corrosive liquids. Further, an operator is required to record the liquid levels
with this device.
130
LECTURE NO.27
HOOK GAUGE- FLOAT GAUGE - FLOAT-AND-SHAFT LIQUID LEVEL
GAUGE
Hook Gauge
Sometimes it becomes necessary to accurately measure very small
changes in liquid level in open tanks / containers. In a large tank / reservoir, a
small change in level would mean large volumetric changes. For such
applications, a simple hook gage is quite suitable. The schematic arrangement
of this gauge is shown in Fig. 27.1. In this device, a vertical tubular rod is
provided with a vernier scale to be clamped at a suitable height at the upper
end and a V-shaped hook at the lower end. This rod moves in a guide bracket
fixed to a rigid body at the datum or reference level and has a main graduated
scale in it. The movable rod is brought downwards so that the hook is first
pushed below the surface of the liquid. It is then gradually raised until the top of
the hook breaks through the surface of the liquid. The movable rod is then
clamped and the level is read off the scale. The device is accurate up to ±0.1
mm, the least count of the instrument. Further, the device is manually operated
and does not lend itself to automatic reading.
Fig. 27.1 Hook type level indicator
Float Gauge
131
A floating body, because of its buoyancy, would always follow the
varying liquid level. Therefore, float-operated devices are capable of giving
continuous, direct liquid level measurements. The floats generally used are
hollow metal spheres, cylindrical ceramic floats or / disc shaped floats of
synthetic materials. The top of the float is usually made sloping so that any
solid suspensions in the liquid do not settle on the float and change its weight.
Float gauges are sufficiently accurate when properly calibrated after
installation. Further, a proper correction is required if there is a change in the
liquid density due to a change in temperature.
Fig.27.2 Float and chain liquid level gauge
Figure 27.2 illustrates a typical float-and-chain liquid level gauge
generally used for directly measuring the liquid level in open tanks. The
instrument consists of a float, a counter weight and a flexible connection that
may be a chain or a thin metallic perforated tape. The counter weight keeps the
chain / tape taut as the liquid rises or falls with any changes in the liquid level.
The chain / perforated tape link is wound on a gear or sprocket wheel to which
the pointer is attached. Any movement of this wheel would indicate on a
suitably calibrated scale the level of the liquid in the tank.
Float-and-Shaft Liquid Level Gauge
Another version of the float-actuated instrument is the float-and-shaft
liquid level gauge (Fig.27.3). In this unit, the motion of the float on the surface
of the liquid is transferred to the shaft and the level is indicated by the pointer
on the dial.
132
Fig. 27.3 Float-and-shaft liquid level gauge
Further, there are a number of float-operated schemes with electrical
read-outs. In these, the float acts as a primary transducer that converts liquid
level variation into a suitable displacement. This displacement is sensed by the
secondary transducer such as a resistive type of potentiometric device,
inductive type of LVDT, etc. Figure 27.4 shows the schematic of the floatactuated rheostatic (resistive) device. The float displacement actuates the arm
which causes the slider to move over the resistive element of a rheostat. The
circuit resistance changes and this resistance change is directly proportional to
the liquid level in the tank.
Fig.27.4 Typical float-operated rheostatic liquid level gauge
133
LECTURE NO.28
INDIRECT LIQUID LEVEL MEASUREMENTS - HYDROSTATIC PRESSURE
LEVEL MEASUREMENT DEVICE - BUBBLER OR PURGE TECHNIQUE FOR
LEVEL MEASUREMENT
INDIRECT LIQUID LEVEL MEASUREMENTS
Hydrostatic Pressure Level Measurement Device
The hydrostatic pressure created by a liquid is directly related to the
height of the liquid column ( p =ρgh ). Therefore, a pressure gauge is installed
at the bottom or on the side of the tank containing the liquid (Fig. 28.1). The
rise and fall of the liquid level causes a corresponding increase or decrease in
the pressure p which is directly proportional to the liquid level h. The dial or
scale of the pressure gauge is calibrated in the units of level measurement.
These gauges function smoothly when the liquids are clean and non-corrosive.
For corrosive liquids with solid suspensions, diaphragm seals between the fluid
and the pressure gauge are generally employed.
Fig.28.1 Typical arrangements of hydrostatic pressure type level
measuring devices
Bubbler or Purge Technique for Level Measurement
In this method, the air pressure in a pneumatic pipeline is so regulated
that the air pressure in the bubbler tube, shown in Fig. 28.2, is very slightly in
excess over that of the hydrostatic pressure at the lowermost end of the
bubbler tube. The bubbler tube is installed vertically in the tank with its
lowermost open end at zero level. The other end of the tube is connected to a
134
regulated air supply and a pressure gauge. The air supply in the bubbler tube is
so adjusted that the pressure is just greater than the pressure exerted by the
liquid column in the tank. This is achieved by adjusting the air pressure
regulator until bubbles can be seen slowly leaving the open end of the tube.
Sometimes a small air flow meter is fitted in the line to control / check the
excessive flow of air. When the air flow is small and the density of the fluid is
uniform, then gauge pressure is directly proportional to the height of the liquid
level in the open tank. In practice, the gauge is directly calibrated in the units of
liquid level and if the tank is uniformly shaped, then the calibration may be in
the units of volume.
Fig.28.2 Bubbler or purge type of liquid level meter
135
LECTURE NO.29
CAPACITANCE
LEVEL
GAUGE
-
ULTRASONIC
LEVEL
GAUGE
-
NUCLEONIC GAUGE
Capacitance Level Gauge
A simple condenser / capacitor consist of two electrode plates separated
by a small thickness of an insulator (which can be solid, liquid, gas or vacuum)
called the dielectric. The change in liquid level causes a variation in the
dielectric between the two plates, which in turn causes a corresponding change
in the value of the capacitance of the condenser. Therefore, such a gauge is
also termed a dielectric level gauge.
The magnitude of the capacitance depends on the nature of the
dielectric, varies directly with the area of the plate and inversely with the
distance between them. The capacitance can be changed by any of these
factors.
In a parallel plate condenser which has identical plates each of area A
(cm2) separated by a distance d (cm) and an insulating medium with dielectric
constant K (K = 1 for air) between them, the expression for the capacitance is
given by
C (in µµ F ) = 0.0885
A
K
d
From the above equation it is observed that the capacitance varies
directly with the dielectric constant which in turn varies directly with the
liquid level between the plates. Figure 29.1 shows the schematic
arrangement of a capacitance level gauge. The capacitance would be at a
minimum when the tubes contain only air and at a maximum when the liquid
fills the entire space between the electrodes. The change in capacitance can
be measured by a suitable measuring unit such as a capacitive Wheatstone
bridge by either manual null balancing or automatic null balancing using the null
detecting circuit with a servo-motor that indicates the level reading.
136
Fig. 29.1 Dielectric liquid level gauge
For the measurement of level in the case of non-conducting liquids, the
bare probe arrangement may be satisfactory since the liquid resistance is
sufficiently high. For conducting liquids, the probe plates are insulated using a
thin coating of glass or plastic.
The capacitance type level gauge is relatively inexpensive, versatile,
reliable and requires minimal maintenance. These units have no moving parts,
are easy to install and adaptable to large and small vessels. Further, such
devices have a good range of liquid level measurement, viz. from a few cm to
more than 100 m. In addition, apart from sensing the level of the common
liquids, these gases find wide use in other important applications such as
determining the level of powdered or granular solids, liquid metals (high
temperatures), liquefied gases (low temperatures), corrosive materials (like
hydrofluoric acid) and in very high pressure industrial processes.
Ultrasonic Level Gauge
A schematic diagram of the ultrasonic level gauge is shown in Fig. 29.2.
Sound waves are directed towards the free surface of the liquid under test from
an ultrasound transmitter. These waves get reflected from the surface of the
liquid and are received by the receiver. In this technique, liquid level variations
are quite accurately determined by detecting the total time taken by the wave to
travel to the liquid surface and then back to the receiver. The longer this time
interval, the farther away is the liquid surface, which in turn is a measure /
indication of the liquid level.
137
Fig. 29.2 Schematic of ultrasonic liquid level gauge
It may be noted that the operating principle of this instrument is quite
simple. But the actual instrument is expensive and requires a high degree of
experience and skill in operation. However, its main advantage is a wide range
of applications in level measurement for different types of liquid and solid
substances.
Nucleonic Gauge
The working principle of the nucleonic gauge or gamma ray liquid level
sensor is that the absorption of gamma rays varies with the thickness of the
absorbing material (i.e. height of liquid column) between the source and the
detector. The higher the height of the liquid column, greater is the absorption of
gamma rays and consequently lower is the detector output. The output is
measured and correlated with the level of liquid in the tank using the following
exponential type of expression applicable in such an arrangement:
I = I o e −µρ x
where
I is the intensity of radiation falling on the detector
Io is the intensity of radiation at the detector with absorbing
material not present
e is base of natural logarithm = 2.71
µ is the mass absorption coefficient in m3/kg (constant for a
given source and absorbing material)
138
ρ is the mass density of the test material in kg/m3
x is the thickness of absorbing material in m (i.e. height of liquid
column in the present case).
The schematic of the liquid level gauge is shown in Fig. 29.3. The
instrument consists of a radioactive source (which may be either Ce-137, Am241 or Co-60), a radiation detector (of ion is at ion chamber type) and
electronic circuits incorporating the amplifiers and read-out instrument or
recorder-controller.
Fig.29.4 Schematic of gamma ray liquid level gauge
Nuclear gauges cover a wide range of applications for recording the
level of a wide variety of liquid as well as solid substances. They are quite
suitable for large reservoirs of 30-40 m diameter and can give continuous
measurements of heights of 20 m or more with repeatability of ± 1%. Like the
ultrasonic gauge, this is also a non-contact device and the level measurement
is not affected by conditions of high or low temperatures, pressure, viscosity,
corrosion, abrasion, etc. Further, these gauges are quite rugged and can
withstand severe operating conditions. The main drawback in these gauges is
the risks involved due to radiation effects. Therefore, adequate shielding to limit
the radiation field intensity well below the Atomic Energy Commission (AEC)
tolerances has to be provided for.
139
LECTURE NO.30
CONTROL SYSTEMS- INTRODUCTION- BASIC COMPONENTS OF THE
CONTROL SYSTEM- CLASSIFICATION OF CONTROL SYSTEMS – OPEN
LOOP SYSTEM - CLOSED LOOP SYSTEM - SERVO MECHANISMS
CONTROL SYSTEMS
Introduction
Automatic control is the maintenance of a desired value of quantity or
condition by measuring the existing value, compare it with the desired value
and employing the difference to initiate action for reducing this difference.
Automatic control systems are used in practically every field of our life.
Since, nowadays it has become a tendency to complete the required work or a
task automatically by reducing the physical and mental effort. The different
applications of automatic control systems are:
1. Domestically they are used in heating and air conditioning.
2. Industrial applications of automatic control system includes:
(i) Automatic control of machine tool operations.
(ii) Automatic assembly lines.
(iii) Quality control, inventory control.
(iv)In process industries such as food, petroleum, chemical, steel,
power etc. for the control of temperature, pressure, flow etc.
(v) Transportation systems, robotics, power systems also uses
automatic control for their operation and control.
(vi) Compressors, pumps, refrigerators.
(vii) Automatic control systems are also used in space technology
and defence applications such as nuclear power weapons, guided
missiles etc.
140
(viii) Even the control of social and economic systems may be
approached from theory of automatic control.
The term control means to regulate, direct or command. A control
system may thus be defined as: "An assemblage of devices and components
connected or related so as to command, direct or regulate itself or another
system".
In general the objectives of control system are to control or regulate the
output in some prescribed manner by the inputs through the elements of the
control system.
Basic components of the control system are:
(i) Input i.e. objectives of control. It is the excitation applied to a control
system from external source in order to produce output.
(ii) Control System Components. Devices or components to regulate direct or
command a system that the desired objective is achieved.
(iii) Results or Outputs. The actual response obtained from a system.
Fig. 30.1 Block diagram of control system.
Classification of Control Systems:
There are two basic types of control Systems:
1. Open Loop System (Non-feed Back)
2. Closed Loop System (Feed Back)
Open Loop System (Non-feed Back)
The elements of an open loop system can usually be divided into two
parts : the Controller and the Controlled process as shown in Fig.30.2.
141
Fig.30.2 Open loop system
 An input signal or command r (t) is applied to the controller which
generates the actuating signal u(t).
 Actuating signal u(t) then controls (activates) the process to give
controlled output c(t). In simple cases, the controller can be an amplifier,
mechanical linkage, filter, or other control element, depending on the
nature of the system. In more sophisticated cases the controller can be a
computer such as microprocessor.
 The control action has nothing to do with output c (t) i.e. there is no any
relation between input and output.
 There is no feed back hence it is known as non-feedback system.
Examples of open loop System:
1. Traffic control signals at roadway intersections are the open loop
systems. The glowing of red and green lamps represents the input.
When the red lamp grows the traffic stops. When green lamp glows, it
directs the traffic to start.
The red and green light travels are predetermined by a calibrated
timing mechanism and are in no way influenced by the volume of traffic
(output).
2. Automatic washing machine: In washing machine, input is dirty
clothes, water, soap and output is clean cloths. Soaking, washing and
rinsing operations are carried out on a time basis. However, the machine
does not measure the output signal, namely the cleanliness of the
clothes.
Advantages of Open Loop System:
1. Simple in construction.
2. Economic.
142
3. More stable.
4. Easy maintenance.
Disadvantages of Open Loop System:
1. Inaccurate and unreliable.
2. It is affected by internal and external disturbances, the output may
differ from the desired value.
3. It needs frequent and careful calibrations for accurate results.
4. Open loop systems are slow because they are manually controlled.
5. There is no feed back control. The control systems are rather
unsophisticated.
Closed Loop System
A closed loop control system measures the system output compares it
with the input and determines the error, which is then used in controlling the
system output to get the desired value.
In closed loop system for more accurate and more adaptive control a link
or feedback from the output to the input of the system is provided. The
controlled signal c(t) is fed back and compared with the reference input r(t), an
actuating signal e(t) proportional to the difference of the input and the output is
send through the system to correct the error and bring the system output to the
desired value. The system operation is continually correcting any error that may
exit. As long as the output does not coincide with the desired value, there is
likely to some kind of actuating signal.
Thus, the closed loop systems correct the drifts of the output which may
be present due to external disturbance or due to deterioration of the system
itself.
The closed loop system may have one or more feedback paths. Fig.30.3
shows the general block diagram of closed loop system.
143
Fig. 30.3 Closed loop system
r(t) = reference input
e(t) = error or actuating signal
b(t) = feedback signal
m = manipulation
Advantages of Closed Loop System:
 These systems can be used in hazardous or remote areas, such as
chemical plants, fertilizer plants, areas with high nuclear radiations, and
places at very high or very low temperatures.
 Increased productivity
 Relief of human beings from hard physical work and economy in
operating cost.
 Improvement in the quality and quantity of the products.
 They are more reliable than human operators.
 A number of variables can be handled simultaneously by closed loop
control systems.
 In such systems there is reduced effect of non-linearities and distortions.
 Closed loop systems can be adjusted to optimum control performance.
 Such systems senses environmental changes, as well as internal
disturbances and accordingly modifies the error.
 Satisfactory response over a wide range of input frequencies.
Disadvantages of Closed Loop Control System:
 It is more complex and expensive.
144
 Installation and adjustment is intricate.
 Maintenance is difficult as it involves complicated electronics. Moreover
trained persons are required for maintenance.
 Due to feed back, system tries to correct the error time to time.
Tendency to over correct the error may cause oscillations without bound
in the system.
 It is less stable as compared to open loop system.
Table 30.1 Comparison between open loop and closed loop systems
Open Loop System
Closed Loop System
1
No feed back
1
Feed back is present
2
No error detector
2
Error detector is included
3
Simple in construction, easy to 3
built
Complex design, difficult to built
4
Disturbances occurring in the 4
process are not controllable
Disturbance do not affect the
process, they can be controlled
automatically
5
It is more stable
5
It is less stable
6
Economical
6
Expensive
7
Less accuracy
7
Accurate
8
Response is slow
8
Response is fast
9
Examples: Two way traffic 9
control,
automatic
toaster,
coffee maker, hand drier
Examples: Human being, automatic
electric irons, automatic speed
control system, centrifugal watt
governor etc
Servo Mechanisms
A servo mechanism is an automatic control system (closed loop system)
in which the controlled variable is a mechanical position (displacement), or a
time derivative of displacement such as velocity and acceleration. The name
servo mechanism or regulator may describe a complete system that
provides automatic control of an object or quantity as desired. Such a
system may include many electrical, mechanical or hydraulic devices, by their
use a person can control large power with greater speed and accuracy than
that person alone can provide.
145
The output is designed to follow a continuously changing input or
desired variable. The servo mechanisms are inherently fast acting (small time
lag with response time in the order to milliseconds) as usually employ electric
or hydraulic actuations. These systems are essentially used to control the
position or speed of a mechanism which is either too heavy or too remote to be
controlled manually. e.g. power assisted steering and control in large cars, air
crafts, ships etc. The complete automation of machine tools together with
programmed instructions is another notable example of servo mechanism.
Servos are used in defence, navigation as well as in industry. They are
used in industry in the automatic follow-up control of precision machine tools,
the remote handling of dangerous materials, the automation of production lines
etc.
Fig.30.4 A block diagram of servo showing its basic parts.
146
LECTURE NO.31
CONTROLLERS AND CONTROL ACTION - PNEUMATIC CONTROLLER HYDRAULIC CONTROLLERS - ELECTRIC CONTROLLERS
CONTROLLERS AND CONTRL ACTION
An automatic controller compares the actual value of the plant output
with the desired value of output, determines the deviation and produces a
signal which will reduce the deviation to zero or to a small value.
The manner in which the automatic controller produces the control signal
is called control action. The control action may operate through mechanical,
pneumatic, hydraulic or electrical means.
Fig. 31.1 Classification of control actions
Controllers can be in the form of (i) Pneumatic (ii) Hydraulic (iii) Analog or
digital
The choice of the control action for a particular operation depends upon:
 The nature of the plant
 Operating conditions
 Size and weight
 Availability and cost
 Accuracy and reliability and
 Safety etc
Control Actions
147
ON-OFF or two position control action
The controller is ON when the measured value is below set point and the
output is at maximum level. When the measured value is above the set point
the controller is OFF and the output is minimum i.e. zero.
These are relatively simple and economical. ON -OFF controllers are
widely used in both industrial and domestic control systems. These controllers
are not suitable for complex systems. The examples of their applications are:
Room heaters, Refrigerators, mixers or food processors, level control of water
tanks etc.
Proportional Control Action (P)
Proportional control action is a continuous mode of operation. In
proportional control, the output changes with proportional change of input. It is
widely used control action where the output of controller is a linear function of
error signal.
The proportional control follows the law :
m(t ) =kp e (t ) +P0
where,
m(t ) = controller output
e (t ) =error signal
kp =gain
of controller
P0 =output of controller when error is zero
The proportional controller may be thought of as an amplifier with high
and adjustable gain.
Composite Control Action
Composite control action means combination of two continuous control action:
1. Proportional Plus Integral Control Action (P + I)
148
The proportional control action produces off set in the system whenever
load change occurs. This offset can be eliminated by adding integral action to
the proportional control action. The output is
m(t ) =kp e (t ) +
kp
Ti
T
∫ e(t ) .dt
+ P0
0
2. Proportional Plus Derivative (PD) Control Action
In a derivative control mode, the magnitude of the controller output is
proportional to the rate of change of the actuating error signal. The control
action in which derivative control action is added to the proportional control
action is called PD control action.
The governing equation of PD control action is
m(t ) =kp e (t ) + kp . Td
d e(t )
+ P0
dt
Advantages: Improves damping ratio and reduces maximum overshoot.
3. PID Control Action: It is powerful but complex control action. In a PID
control action, the output m(t) is a linear combination of input e(t), the time rate
of change of input and the time integral of input. The control is thus an additive
combination of proportional action, derivative action, and integral action.
The equation of PID control action is given by
m(t ) =kp e + kp . Td
de
kp
+
dt
Td
∫ e dt +P
0
PNEUMATIC CONTROLLER
Pneumatic controllers use air medium (or other gases in special
situations) to provide an output signal which is a function of an input error
signal. Regulated pressurized air supply at about 20 psg is used as a input
signal. Air medium has the advantage of being non-inflammable and having
almost negligible viscosity compared to the high viscosity of hydraulic fluids.
The danger of explosion existed due to electrical equipment is avoided by
pneumatic controller.
149
Fig.31.2 Schematic of a pneumatic control system
Advantages and Limitations of Pneumatic Controllers:
Advantages
 The danger of explosion is avoided.
 For operating the final control elements relatively high power
amplification is obtained.
 Due to availability of free supply of air it is relatively inexpensive.
 Comparatively simple and easy to maintain.
Limitations:
 Slow response and longer time delays.
 The lubrication of mating parts create difficulty.
 Compressed air pipe is necessary throughout the system.
 In pneumatic system there is a considerable amount of compressibility
flow so that the systems are characterized by longer time delays
Hydraulic Controllers
In hydraulic controllers power is transmitted through the action of fluid
flow under pressure. The fluid used is relatively incompressible such as
petroleum base oils or certain non-inflammable synthetic fluids. Fig. 31.3 shows
a schematics of a hydraulic control system.
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Fig.31.3 Schematic of a hydraulic controller
The major components of a hydraulic controller are:
an error detector
an amplifier
a hydraulic control valve, and
an actuator.
Advantages of hydraulic controllers
 High speed response.
 High power gain.
 Long life due to self lubricating properties of fluid.
 Simplicity of actuator system
 Easy maintenance.
Limitations of hydraulic controllers
 Hydraulic fluids require careful maintenance to remove impurities,
corrosive effects etc.
 Seals should be properly maintained to prevent leakage of hydraulic
fluids.
Electric controllers
Electrical control devices are most widely used because of their
accuracy and fast response with easy handling techniques. Electric controller
for proportional, proportional plus integral and proportional + integral +
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derivative actions may be divided into two types: (1) The null balance type in
which an electrical feedback signal is given to the controller from the final
elements.
(2) The direct type in which there is no such feedback signal.
As with the pneumatic controller, the various control actions are
accomplished by modifying the feed back signal. This is done by adding
properly combined electrical resistances and capacitances to feedback circuit
just as restrictions and bellows were added in the pneumatic circuit.
A very simple form of two step controller is the room-temperature
thermostat. Fig.31.4 show simple type of electrical two position control. The U
shaped bimetal strip fixed at one end of the thermostat frame deflects when
heated, its free and moving in such a direction as to separate the fixed and
moving contacts. When the bimetal strip cools the two contacts are once more
brought in contact. The small permanent magnet ensures the opening and
closing of the contacts with a snap action to minimize the damage caused by
arcing. The adjusting screw varies the small range of temperature, sometimes
called the differential gap between contacts opening on rising temperature and
closing on falling temperature.
Fig. 31.4 Electrical two position control
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LECTURE NO.32
DATA
TRANSMISSION
TRANSMISSION
ELEMENTS
ELEMENTS
-
-
ELECTRICAL
PNEUMATIC-TYPE
TYPE
DATA
TRANSMISSION
ELEMENTS - POSITION-TYPE DATA TRANSMISSION ELEMENTS - RADIOFREQUENCY (RF) TRANSMISSION SYSTEM
DATA TRANSMISSION ELEMENTS
When the measured variables have to be transmitted over long
distances from the measuring points to a location for display or recording of
data, data transmission elements are employed. These are classified into two
categories:
1. Land-line or cable type transmission elements.
2. Radio-frequency (RF) type data transmission elements.
In the former units, data is transmitted by wires or pipes while in the
latter it is transmitted by radio waves. The former finds applications in data
transmission in process plants, power generating stations, etc. and includes
electrical, pneumatic and position type elements while the latter is used in
aero-space systems.
Electrical Type Data Transmission Elements
In these elements, the input measured variable, usually a motion signal,
is made to change an electrical quantity, the effect of which is transmitted by
wires to the receiving end, for record or display.
Figure 32.1 shows two such elements. In Fig. 32.1(a), the position of
contact C on a variable resistance AB is adjusted by the input motion, changing
the value of the current through the lines. The current at the receiving end is a
measure of the input variable. In this type, resistance changes due to
temperature changes introduce errors. In Fig. 32.1(b), instead of measuring the
current at the receiving end a potentiometer is used, which is balanced so that
no current flows, as indicated by G. Thus, the setting of the potentiometer gives
an indication of the input signal. In this case, the effect of change of line
resistance due to temperature, etc. is eliminated.
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Fig.32.1 Data transmission by change of electric quantity
Pneumatic-Type Transmission Elements
These are also a land-line type. A typical arrangement is shown in Fig.
32.2, and uses the flapper-nozzle arrangement. The signal to be transmitted is
converted into the form of a motion signal x. With change in x, pressure P2
changes as shown. The pressure P2 gets transmitted to the receiving end and
may, by use of an elastic element, be converted to motion for recording.
Fig.32.2 Pneumatic transmitter
Figure 32.3 shows a flow transmitter of the pneumatic type, employing a
system similar to that of Fig.32.2. The flow signal results in a pressure
difference across the restrictor (which may be an orifice or venturi or a nozzle).
The pressure difference results in the deflection of an elastic diaphragm and
the motion signal is transmitted, by being converted to the pressure signal P2.
These elements are not linear, as shown in Fig. 32.2 (b).
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Fig.32.3 Pneumatic flow transmitter
Another type of pneumatic transmission system called force-balance
type, has better linearity characteristics. This is shown in Fig.32.4.
The input signal is in the form of a force signal F applied at the end of a
pivoted lever (a motion input signal may be applied through a spring, resulting
in force F). Application of F rotates the level clockwise as shown, decreasing
the gap between the level extension and the nozzle and thus increasing
pressure P2 till the lever balances and no further building up of pressure occurs.
At balance,
p 2 A d 2 =Fd 1
---------------(32.1)
Fig.32.4 Force-balance type pneumatic transmitter
A being the area of the diaphragm shown and d1 and d2, the distances
from the pivot. Equation (32.1) shows that P2 is linearly related to the input F.
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In pneumatic type transmitters, there is a pressure drop in transmission
piping, resulting in a reduction in the signal transmitted. In practice, these are
used for transmitting the signal over a few hundred meters.
Position-Type Data Transmission Elements
In these types, the motion signal (like rotation of a pointer) is transmitted
over long distances, by use of synchros. Two synchros - a transmitter and a
receiver are employed (Fig.32.5). A synchro consists of a stator with three coils
at 120°, inside which is a rotor, which is free to rotate within the stator windings.
The transmitting synchro is energized by an ac power source. If the two rotors
are in identical positions, the voltages in stators have the same magnitude but
opposite sense and no current flows in the stator wires. If the input rotor is
turned, making the two rotor positions different, current flows in the stator wires
producing a resulting torque which would align the two rotors making θo =θi
.Thus, the angular motion θi is transmitted to the receiving end.
Fig. 32.5 Synchros for data transmission
Radio-Frequency (RF) Transmission System
Such data transmission systems use radio-frequency waves for data
transmission and no wires or cables are needed between the transmitting and
receiving ends. In large systems like aero-space systems, a number of input
signals like temperature, pressure, vibrations, etc. may be transmitted by such
units.
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