Drainage Manual 6th Edition - Application Guide

Published by The South African National Roads Agency SOC Ltd, © 2013 48 Tambotie Avenue, Val de Grace, Pretoria, 0184, South Africa P.O. Box 415, Pretoria, 0001, South Africa www.sanral.co.za First edition in Afrikaans called “Handleiding vir Paddreinering” Pretoria, 1981 Second edition translated into English called “Manual on Road Drainage” Pretoria, 1983 Third partly revised edition Pretoria, 1986 Fourth partly revised edition Pretoria, 1993 Fifth Edition – Fully revised and called the “Drainage Manual” Pretoria, 2006 nd
2 print (including corrections up to 15 October 2007) Pretoria, 2007 Sixth Edition – Fully revised and extended Pretoria, 2013 ISBN 978‐0‐620‐55428‐2 (Drainage Manual) ISBN 978‐0‐620‐55429‐9 (Drainage Manual Application Guide – only available electronically) Copyright: Apart from any fair dealing for the purpose of research or private study, or criticism or review, as permitted under the Copyright Act, this publication may not be reproduced in whole, or in part, for commercial purposes. Additional copies for private use may, however, be printed off the PDF version, obtained from the website, www.sanral.co.za The copyright does not extend to the methods or intellectual property rights of any of the authors. In addition, photocopies of the whole, or parts of the publication may be made by academic institutions for students. Editor Edwin Kruger Sub‐editor Nuno Gomes, Fanie van Vuuren and Marco van Dijk Cover design Nitrogen Advertising & Design, Johannesburg Disclaimer: Although every effort has been made as to the accuracy and applicability of the information contained in this publication (including supporting flash drive/DVD and software), the publisher, The South African National Roads Agency SOC Ltd (SANRAL), and the authors, cannot accept any legal responsibility or liability for any errors, omissions or for any other reason whatsoever. FOREWORD
Water is often thought of as the source of civilization; hence the hypothesis that the development of
hydraulics is related to the evolution of ancient societies such as those of Mesopotamia and Egypt.
Owing to the structure of the early states, which entailed a closed system of absolute monarchy and
monopoly with only a small number of literate scholars, the pace of technological advancement was
cumbersome. The basket remained the only water-lifting device in Egypt until the sheduf was
introduced during the time of the New Kingdom – almost 3 500 years after the commencement of
agriculture in Egypt and 1 500 years after the rise of the nation-state. The development of the
waterwheel and the Archimedes clean water screw followed 1 000 years later in Alexandria.
Founded by the Egyptian ruler, during the Ptolemies dynasty (323 BC to AD 30), the Mouseion in
Alexandria hosted scholars such as Euclid and Archimedes (287 to 212 BC) who made significant
advances in mathematics of cones and cylinders as well as differential equations leading to major
advances in hydraulic engineering. These Alexandrian scholars laid the foundations of theoretical
hydrology in connection with practical applications. Around the same time the Persians too had
already made an ingenious contribution to hydraulic engineering by developing a water delivery
system known as qanats – a subterranean system of tunnels connecting wells. However, it is the
Romans who were instrumental in expanding the science of hydraulic engineering to various parts of
their empire.
Through the ages, civil engineers have always had to cope with unforeseen natural forces. The
external forces created by climatic change, and further exacerbated by human induced variables, can
unexpectedly and significantly influence the hydrological cycle with serious socio-economic effects.
Although mathematical analysis and modelling cannot cater for every eventuality, we can certainly
attempt to scientifically predict the behaviour of these natural forces and minimise their impacts on
our environment.
South Africa, for instance, is known for its low average annual rainfalls and large seasonal variations.
Despite the latter, abnormal rainfalls have historically had disastrous consequences. Although our
problems are not without precedent, societies are always inter-linked and local catastrophes could have
serious regional and national repercussions.
The channelling of water by societies for usage and development has remained an on-going challenge
since the days of the early mathematicians through to modern-day engineers. We trust that this
Application Guide, published as a guide to both students and practitioners will assist in meeting these
challenges. It must, however, be emphasised that it is merely an aid and should ultimately not replace
sound engineering analysis and judgement.
Nazir Alli
Chief Executive Officer
The South African National Roads Agency Limited
i
Drainage manual – Application Guide
ACKNOWLEDGEMENTS AND STRUCTURE OF THE DRAINAGE MANUAL
The South African National Roads Agency SOC Ltd (SANRAL) wishes to thank all parties involved
in extensively revising and updating the Road Drainage Manual (first published in 1981) and now
known as the Drainage Manual. The previous editors and authors of the original manual, J Bosman, A
Rooseboom, MS Basson, CH Loots, JH Wiggett, assisted by ZP Kovács and AM van Vuuren (neè
Mouton), is hereby also acknowledged.
In realising the goals of producing a manual of high standard the co-operation between authors and
reviewers to this and previous editions of the manual has been critical. All contributions, too numerous
to mention individually, both big and small is gratefully acknowledged. We have in the manual
endeavoured to take differing views into account which at times has proven to be a challenge. The
manual, we believe, is a summary of both historical and modern thought pertaining to drainage.
Feedback, comments and suggestions from users of the previous editions of the manual have been
incorporated where possible. This edition of the manual still covers all the previous background theory
but has been extended to include additional flood calculation methods, the analyses and design of
stormwater systems, the hydraulic assessment of existing culverts and the modelling of free surface
flows and flood line calculations. With the further expansion of the manual it was deemed necessary to
separate the manual into two distinct documents; the first being the Drainage Manual and the second
being the Drainage Manual Application Guide.
The front covers of the two documents are as shown below.
Thank you to my fellow editors, Professor Fanie van Vuuren, Marco van Dijk and Nuno Gomes for
their commitment and enthusiasm in updating the manual. The compilation and editing was not an
easy task but has been completed with passion and dedication.
Edwin Kruger
Editor
The South African National Roads Agency SOC Limited
Feedback:
Any positive feedback for possible incorporation into future editions will be appreciated. Please email
such comments/feedback to the Editor at bridges@nra.co.za
ii
Drainage manual – Application Guide
DRAINAGE MANUAL APPLICATION GUIDE
Table of Contents
Foreword
Acknowledgements
Table of Contents
List of symbols
1
2
3
4
5
6
7
8
9
i
ii
iii
v
CHAPTER 1 - INTRODUCTION ................................................................................. 1-1
1.1 Layout of the Drainage Manual Application Guide ................................................ 1-2
ECONOMIC EVALUATION OF DRAINAGE SYSTEMS ....................................... 2-3
2.1 Example 2.1 – Net Present Value ............................................................................ 2-3
2.2 Example 2.2 – Present Value .................................................................................. 2-3
2.3 Example 2.3 – Internal Rate of Return (IRR).......................................................... 2-4
FLOOD CALCULATIONS ............................................................................................ 3-5
3.1 Worked example 3.1 - Small catchment.................................................................. 3-5
3.1.1 Rational method.......................................................................................... 3-6
3.1.2 Unit Hydrograph method .......................................................................... 3-21
3.1.3 SDF method .............................................................................................. 3-29
3.1.4 SCS method .............................................................................................. 3-31
3.1.5 Empirical methods .................................................................................... 3-37
3.1.6 Comparison of solutions ........................................................................... 3-38
3.2 Worked example 3.2 - Large catchment................................................................ 3-39
3.2.1 Statistical method ..................................................................................... 3-42
3.2.2 SDF method .............................................................................................. 3-44
3.2.3 Empirical methods .................................................................................... 3-45
3.2.4 Comparisons of solutions ......................................................................... 3-46
HYDRAULIC CALCULATIONS ............................................................................... 4-48
4.1 Example 4.1 - Flow characterisation, energy gradient and normal depth ............. 4-48
4.2 Example 4.2 - Gradually varying river flow (backwater calculation – simple
sectional details) .................................................................................................... 4-50
4.3 Example 4.4 – Negligible energy losses (converging flow over short
distance) ................................................................................................................ 4-52
4.4 Example 4.4 – Transition losses ............................................................................ 4-53
4.5 Example 4.5 – Identification of acting controls .................................................... 4-54
SURFACE DRAINAGE................................................................................................ 5-56
5.1 Worked Example 5.1 - Flow depth on the road surface ........................................ 5-56
5.2 Worked Example 5.2 – Capacity of side channel.................................................. 5-58
5.3 Worked Example 5.3 – Capacity of drop grid inlet............................................... 5-59
5.4 Worked Example 5.4 – Kerb flow......................................................................... 5-60
5.5 Worked Example 5.5 – Scour velocity .................................................................. 5-61
5.6 Worked Example 5.6 – Protection measures ......................................................... 5-62
LOW LEVEL CROSSINGS ......................................................................................... 6-63
6.1 Worked Example 6.1 – Low level crossing........................................................... 6-63
LESSER CULVERTS AND STROMWATER PIPES............................................... 7-69
7.1 Example 7.1 - Determination of the required culvert size ..................................... 7-69
7.2 Example 7.2 - Erosion protection downstream from a culvert .............................. 7-78
BRIDGES AND MAJOR CULVERTS ....................................................................... 8-84
8.1 Worked Example 8.1 – Backwater at a bridge ...................................................... 8-84
8.2 Worked Example 8.2 – Scour at a bridge .............................................................. 8-90
STORMWATER ANALYSES AND DESIGN ......................................................... 9-101
9.1 Example 9.1 – Pipe flow ..................................................................................... 9-101
9.2 Example 9.2 – Introduction to using EPASWMM .............................................. 9-103
iii
Drainage manual – Application Guide
10 ASSESSMENT OF HYDRAULIC CAPACITY OF EXISTING DRAINAGE
STRUCTURES .......................................................................................................... 10-133
10.1 Example 10.1 – Level pool routing ................................................................... 10-133
10.2 Example 10.2 – Level pool routing trough a culvert (inlet controlled) ............. 10-136
11 FREE SURFACE FLOW DETERMINATION...................................................... 11-148
11.1 Basic flood line determination (HEC-RAS) ...................................................... 11-148
11.2 Setting-up a HEC-RAS model (river section, bridge and weir) and
performing unsteady flow analysis.................................................................... 11-182
12 SUB-SURFACE DRAINAGE................................................................................... 12-243
12.1 Example 12.1 - Herringbone drainage system .................................................. 12-243
APPENDICES
Appendix 3A
Appendix 3B
Appendix 3C
Appendix 3D
Appendix 3E
-
STATISTICAL ANALYSIS
STANDARD DESIGN FLOOD METHOD
STANDARD FLOOD CALCULATION FORMS
QT/QRMF RATIOS FOR DIFFERENT CATCHMENT AREAS
SCS-SA ADDITIONAL INFORMATION
iv
Drainage manual – Application Guide
LIST OF SYMBOLS
Chapter 2
F
i
IRR
n
NPV
r
=
=
=
=
=
=
future value
annual discount rate as a decimal fraction
internal rate of return technique
discount period in years
net present value
rate at which the left-hand and right-hand sides of the equation are equal, resulting
in a NPV of zero
Chapter 3
a
A
ARF
ARFiT
b
C
C
C1
C1D
C1T
=
=
=
=
=
=
=
=
=
=
C100
C2
C2
C3
CN
CNf
CNw
CN-II
=
=
=
=
=
=
=
=
CP
CS
CT
CV
D
F
FT
fiT
H
H
H0,10L
H0,85L
heiT
I
Ia
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
IT
K
KRP
KT
Ku
l
=
=
=
=
=
=
constant
area of catchment (km²)
area reduction factor (%)
area reduction factor (%)
constant
run-off coefficient (dimensionless)
catchment parameter with regard to reaction time
run-off coefficient for rural area with a value between zero and one
rural run-off coefficient incorporating the effect of dolomites
rural run-off coefficient incorporating the effect of dolomites and initial saturation
factor
calibration coefficient (SDF method)
calibration coefficient (SDF method)
run-off coefficient for urban area with a value between zero and one
run-off coefficient for lakes with a value between zero and one
Curve Number
Final Curve Number
Curve Number for wet conditions
retardance factor approximated by the initial Curve Number unadjusted for
antecedent soil moisture
run-off coefficient according to average soil permeability
run-off coefficient according to average catchment slope
combined run-off coefficient for T-year return period (dimensionless)
run-off coefficient according to average vegetal growth
storm duration (hours)
lag coefficient
adjustment factor for initial saturation for return period T
flood run-off factor (%)
height (m)
height of most remote point above outlet of catchment (m)
elevation height at 10% of the length of the watercourse (m)
elevation height at 85% of the length of the watercourse (m)
effective rainfall (mm)
rainfall intensity (mm/hour)
initial losses (abstractions) prior to the commencement of stormflow, comprising of
depression storage, interception and initial infiltration (mm)
average rainfall intensity for return period T (mm/h)
regional constant
constant for T-year return period
constant for T-year return period
dimensionless factor
hydraulic length of catchment along the main channel (m)
v
Drainage manual – Application Guide
L
L
LC
M
MAP
n
P
P
P
=
=
=
=
=
=
=
=
=
P1
PAvgT
PAvgiT
PiT
PT
Pt,T
qp
Q
Q
Qe
QiT
Qp
QRMF
QT
r
R
S
Sav
T
T
TC
TL
Tp
TSD
t
α
β
γ
qp
Q
D
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
30
=
hydraulic length of catchment (watercourse length) (km)
catchment lag time (h)
distance from outlet to centroid of catchment area (km)
2-year return period daily rainfall from TR102
mean annual precipitation (mm/a)
length of record (years)
mean annual rainfall (mm/annum)
probability (%)
daily rainfall depth (mm), usually input as a one-day design rainfall for a given
return period
probability of at least one exceedence during the design life
average rainfall over the catchment for the T-year return period (mm)
average rainfall for T-year storm duration (mm)
point intensity for the return period T (mm/h)
point rainfall for the return period T (mm)
the precipitation depth for a duration of t minutes and a return period of T years
peak discharge (m3/s)
peak discharge (m³/s)
stormflow depth (mm)
peak discharge of unit hydrograph (m³/s)
peak discharge for T-year return period (m³/s)
unit hydrograph peak discharge (m³/s)
regional maximum flood peak flow rate (m³/s)
peak discharge for T-year return period (m³/s)
roughness coefficient
average number of days per year on which thunder was heard (days/year)
potential maximum soil water retention (mm),
average slope (m/m)
time (hours)
return period (years)
time of concentration (hours)
lag time L (hours)
time to peak (hours)
storm duration (hours)
duration (minutes)
area distribution factor
area distribution factor
area distribution factor
peak discharge of incremental unit hydrograph (m3/s)
incremental stormflow depth (mm)
unit duration of time, used with the distribution of daily rainfall to account for
rainfall intensity variations (hours)
30-minute rainfall intensity for the 2-year return period (mm/h)
Chapter 4
A
A1
A2
B
C
E
Fr
=
=
=
=
=
=
=
sectional area (m²)
upstream sectional area (m²)
downstream sectional area (m²)
free surface width of cross section (m)
Chézy constant
specific energy (m)
Froude number
vi
Drainage manual – Application Guide
g
hl
hf
ks
L
P
q
Q
rc
R
Re
So
S
v
yc
yn
z
γ
Δx
ρ
υ
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
gravitational acceleration (m/s²)
transition loss (m)
friction losses (m)
measure of absolute roughness (m)
distance (m)
wetted perimeter (m)
discharge per unit width (m³/s/m)
discharge (m³/s)
centre line radius (m)
hydraulic radius i.e. area divided by wetted perimeter (m)
Reynolds number
Bed slope (m/m)
energy slope, which is equal to bed slope only when flow is uniform (m/m)
uniform channel velocity (m/s)
average velocity (m/s)
critical flow velocity (m/s)
depth of flow measured perpendicular to the streambed (m)
distance between water surface and centre of gravity of section (m)
critical flow depth (m)
normal/uniform flow depth (m)
bed level at point where depth of flow = y (m)
specific weight (value for water 9,8 x 103 N/m3)
distance (m)
mass density = 1 000 kg/m3 for water
kinematic viscosity (≈ 1,14 x 10-6 m²/s for water)
Chapter 5
A
A
B
C
C
CD
d
D
d1
d2
E
F
Fr
H
H
H
I
KL
Lf
n
n1
n2
P
Q
R
s
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
effective cross-sectional plan area of the opening (m²)
cross sectional area (m²)
total flow width (m)
inlet coefficient (0,6 for sharp edges or 0,8 for rounded edges)
Chézy constant
discharge coefficient
flow depth of water (mm)
depth of flow (m)
particle size (m)
side slope particle size (m)
specific energy (m)
blockage factor (say, 0,5)
Froude number
total energy head above grid (m)
energy head ≈ flow depth for upstream conditions (m)
head (m)
rainfall intensity (mm/h)
discharge coefficient
length of flow path (m)
Manning roughness value (s/m1/3)
road crossfall (%)
road gradient (%)
wetted parameter (m)
discharge (m³/s)
hydraulic radius i.e. area divided by wetted perimeter (m)
energy gradient (m/m)
v
vc
y
y
vii
Drainage manual – Application Guide
S
Sf
v
W
y
Chapter 6
Aover
Aeff
B
d
D
fi
Fr
g
LB
n
nconcrete
nriver
Pcell
Pconcrete
Peff
Pover
Priver
Q2
Qdesign
Qover
Qunder
R
S0
v under
x
Chapter 7
A
B
CB
Ch
D
D
Fr
h f 1 2
 h1 1 2
H1
H2
Kin
Kout
R
S0
Sc
v
yn
yc
=
=
=
=
=
bed slope (m/m)
slope of flow path (m/m)
average velocity (m/s)
width of roadway (m)
depth of flow at deepest point (m)
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
area of flow over structure at the flow depth selected (m²)
the effective inlet area through the structure (m²)
the width of the channel (or the length of the structure) (m)
depth of flow over the structure (m)
the height of the soffit of the deck above the river invert level (m)
a dimensionless factor related to the design level
Froude number
gravitational acceleration (9,81 m/s²)
the total width of the deck of the structure (m)
Manning n-value (s/m1/3)
Manning roughness coefficient of concrete (s/m1/3)
Manning roughness coefficient of the river bed (s/m1/3)
the total wetted perimeter of each cell (m)
the part of the wetted perimeter that has a concrete surface per cell (m)
Σ Pcell (effective wetted perimeter for the flow passing through the structure) (m)
wetted perimeter at the flow depth selected (m)
the part of the wetted perimeter that is made up by the riverbed per cell (m)
discharge with a 1:2 year return period (m³/s)
design discharge (m³/s)
discharge over the structure within the selected flow depth (m³/s)
discharge capacity of the openings through the structure (m³/s)
hydraulic radius (m)
slope in direction of flow (m/m)
average velocity of flow through the structure (m/s)
thickness of the deck (depending on the structural design outcome) (m)
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
cross sectional area (m²)
width (inside of culvert) (m)
inlet coefficient for culverts
inlet coefficient for culverts
inside diameter (m)
height (inside of culvert) (m)
Froude number
friction losses between cross-section 1 and 2 (m)
transition losses between cross-section 1 and 2 (m)
upstream energy level, relative to the invert level (m)
downstream energy level, relative to the invert level (m)
inlet secondary loss coefficients
outlet secondary loss coefficients
hydraulic radius i.e. area divided by wetted perimeter (m)
natural slope (m/m)
critical slope (m/m), where Fr = 1
average velocity (m/s)
normal flow depth (m)
critical flow depth (m)
viii
Drainage manual – Application Guide
Chapter 8
A1
A4
An
An2
B
Bn
Bn
b
C
Cb
D
d50
D50
davg
Dc
ds
Es
FD
Fr
Fr1
Fs
FSBP
g
h*
h*1A
ks
K*
K
K
K1
K1
K2
K3
K4
L
n
Q
Q
QT
Q2T
S
s
SF
q
q
V
vi
v1
v1
v1
v 2A
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
flow area at section 1 (m²)
flow area at section 4 (m²)
flow area at for normal flow conditions (m²)
projected flow area at constricted section 2 below normal water level (m²)
mean channel width (m)
mean channel width for normal flow conditions (m)
total flow width for the normal stage (m)
pier width (m)
Chézy coefficient
backwater coefficient
flow depth (m)
average particle diameter (m)
median size of bed material (m)
average depth in the main channel
critical particle size for the critical velocity Vc (m)
local scour depth at pier (m)
specific energy (m)
distance of the design flood, QT, below a deck soffit (underside of deck) (m)
Froude number
Froude number directly upstream of the pier
side factor to describe bank resistance to scour
freeboard to shoulder breakpoint (m)
gravitational acceleration (9,81 m/s2)
backwater damming height, afflux (m)
backwater damming height abnormal stage conditions (m)
absolute roughness of river bed (m)
secondary energy loss coefficient
pier shape coefficient (1,5 for round-nosed and 1,7 for rectangular piers)
factor applied for abutments
a factor defined
correction for pier nose shape
correction factor for angle of attack of flow
correction factor for bed condition
correction factor for armouring due to bed material size
pier length (m)
Manning’s coefficient of roughness (s/m1/3)
total discharge (m³/s)
equivalent steady discharge which would generate the channel geometry (m³/s)
design flood (m³/s)
twice the recurrence interval design flood (m³/s)
energy slope (m/m)
specific gravity of soil particles
required stability factor to be applied
discharge per unit width (m³/s.m)
discharge through the sub-channel (m³/s.m)
velocity on pier (m/s)
average velocity through sub-channel (a, b or c)
=
average velocity through Section 1 (m/s)
=
mean velocity upstream of the pier (m/s)
=
average approach velocity (m/s)
=
average velocity in constriction during abnormal stage conditions (m/s)
ix
Drainage manual – Application Guide
v 2c
=
average critical velocity in constriction (m/s)
v n2
va
=
average flow velocity at section 2 based on An2
y0
y1
y2
y2c
ys
Yt
Y0
Ys
α1
α2
θ
ρ
ρd
ρs
φ
τc
ν
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
average velocity in the main channel
shear velocity (m/s)
critical shear velocity (m/s)
approach velocity when particles at pier begin to move (m/s)
characteristic average velocity in the contracted section (m/s)
particle settling velocity (m/s)
velocity ratio
critical velocity for D50 bed material size (m/s)
critical velocity for D90 bed material size (m/s)
mean depth of flow (m)
depth of flow in the contracted bridge opening (m)
projected normal flow depth in the constriction (m)
depth upstream of pier (m)
flow depth directly upstream of pier (m)
flow depth under bridge (m)
critical depth in constriction (m)
scour depth (m)
total maximum scour depth (m)
maximum general scour depth (m)
local scour depth (m)
velocity coefficient
velocity head coefficient for the constriction
bank angle with the horizontal (°)
density of water (kg/m3)
dry bulk density (kg/m3)
saturated bulk density (kg/m3)
riprap angle of repose (°)
critical tractive stress for scour to occur (N/m²)
kinematic fluid viscosity (m²/s)
Chapter 9
A
A1, A2
D
g
h
=
=
=
=
=
hf1-2
hL
hl1-2
=
=
=
full-flow area (m²)
full-flow area for the inlet pipe and outflow pipe (m²)
pipe inner diameter (m)
gravitational acceleration (9,81 m2/s)
difference in elevation between the highest incoming pipe invert and the centreline
of the outlet pipe (m)
friction losses between cross-section 1 and 2 (m)
minor loss (m)
secondary losses between cross-section 1 and 2 (m)
k
ks
n
P
Q
R
S
v1, v2
yc
=
=
=
=
=
=
=
=
=
minor loss coefficient
absolute roughness of conduit (m)
coefficient of roughness (s/m1/3)
wetted perimeter (m)
flow rate (m³/s)
hydraulic radius (m) – A/P
slope of the energy grade line (m/m)
velocity of flow in the inlet pipe and outflow pipes (m/s)
critical depth (m)
V*
V*c
Vi
V
Vss
VR
Vc50
Vc90
y
y
y
x
Drainage manual – Application Guide
z1, z2
γ
ν
=
=
=
invert elevations of the inflow pipes relative to the outlet pipe invert (m)
specific weight (value for water 9,8 x 103 N/m3)
kinematic viscosity (m²/s)
=
vertical dimension of the existing culvert.
Chapter 10
D
dS
dt
I
N
O
O
QT0
=
the change in storage over the time step of dt (m3)
=
=
=
=
=
QC1
=
QC2
=
QT1
=
Q20
Q2T0
=
=
Q2T1
=
RC0
RC-1
=
=
S
S
T
Tc
Ts
=
=
=
=
=
VT1
=
Vstorm
=
x
=
ΔS
Δt
=
=
average inflow (m³/s)
auxiliary function (m³/s)
outflow through culvert (m³/s)
average outflow (m³/s)
design flood for the design return period which was obtained from the review of
the road classification, RC0 and the index flood, Q20 (m³/s).
maximum calculated existing inlet capacity of the culvert by limiting the total
energy head to 1,2D (m³/s)
maximum calculated current existing hydraulic capacity of the culvert by limiting
the total energy head to be equal to the shoulder brake point level (SBP) (m³/s)
design flood for the design return period which was obtained from the review of
the road classification, RC-1and the index flood, Q20 (m³/s)
index flood for the contributing catchment with a return period of 20 years (m³/s)
flow rate related to a return period twice that which was obtained for the design
flood, QT0 (m³/s)
flood rate related to a return period twice that which was obtained for the design
flood, QT1 (m³/s)
original road classification
reflects the selection of a road classification which is one class less than that
determined for the road
temporal storage or ponding volume (m³)
sum of the storage volume of the prism and the wedge (m3)
design return period
time of concentration (h)
total time during the routing of the flood when the upstream energy head is more
than 1,2D (h)
maximum storage volume upstream of the culvert assuming level-pool routing
conditions and an inflow hydrograph with a peak flow rate of QT1 and a triangular
distribution with a base width of 3Tc and the peak discharge occurring at Tc (m³)
calculated storm volume based on the assumption of an inflow hydrograph with a
peak flow rate of QT1 and a triangular distribution with a base width of 3Tc and the
peak discharge occurring at Tc (m³)
a dimensionless weighting factor indicating the relative importance of the inflow
(I) and the outflow (O) in determining the storage (S) in the reach
change in storage volume (m³)
time step that is used (s)
=
average volumetric inflow (m³)
=
average volumetric outflow (m³)
=
=
=
cross sectional flow area (m)
top width (m)
change in water depth (m)
I1  I 2
Δt
2
O1  O 2
Δt
2
Chapter 11
A
B
dy
xi
Drainage manual – Application Guide
dx
Esc
Fr
g
h
Q
S
Sc
Sf
S0
V
y
yc
yn
α
Es
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
distance over which change occurs (m)
specific minimum energy (m)
Froude number
gravitational acceleration (m/s²)
stage height (m)
flow rate (m³/s)
bed slope (m/m)
critical slope (m/m)
represents the slope of the total energy line
bed slope (m/m)
mean cross-sectional velocity
flow depth (m)
critical flow depth (m)
normal flow depth (m)
velocity coefficient
specific energy (m)
Chapter 12
A
Ag
At
AOS
B
B
Cu
d
D85
Dx
g
i
I
k
ks
kb
kt
L
L
n
nb
O95
P
q
q
S
S
So
t
T
tb
tb
W
ψ
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
surface area (m2)
geotextile area available for flow (m²)
total geotextile area (m²)
apparent opening size (mm)
a coefficient (dimensionless)
width of collector drain (m)
the uniformity coefficient
diameter of pipe (m)
soil particle size for which 85% of openings are smaller (mm)
the sieve size through which x% of the material passes (mm)
longitudinal slope of the road (m/m)
hydraulic gradient (m/m)
design infiltration rate (mm/h)
Darcy coefficient of permeability (m/s) and
permeability of material (m/day)
permeability of an open-graded layer (m/day)
permeability of the channel backfill (m/day)
length of the pipe (m)
length of paving (1 m wide) subject to infiltration (m)
Manning’s n (s/m1/3)
porosity of an open-graded layer
opening size in geotextile for which 95% of openings are smaller (mm)
1h duration/1 year return period rainfall intensity (mm/h)
drainage rate (mm/day)
discharge per meter width (m3/s.m)
spacing (m)
cross-slope of a drainage layer (m/m)
slope of the pipe (m/m)
depth of flow in material (mm)
drainage period for layer (h)
thickness of drainage layer (mm)
effective thickness of drain layer (mm)
width of the drainage layer (m)
geotextile permittivity
xii
Drainage manual – Application Guide
1
CHAPTER 1 - INTRODUCTION
The SANRAL Drainage Manual had a major update in 2006 which included additional chapters,
worked examples and links to applicable drainage software. SANRAL decided to revise and upgrade
the manual to be used as a user tool for all persons involved in the design of drainage structures and
systems. The purpose of the Drainage Manual (cover shown in Figure 1.1) is to provide a reference
document with regard to drainage and to demonstrate and reference some software for the modelling
and analysis of drainage problems.
The numerous worked examples were well received by industry as well as academia whom prescribe
the Drainage Manual as part of the Civil engineering curriculum that it was decided to expand this.
The document was split into the Drainage Manual and the Drainage Manual Application Guide (this
document).
Figure 1.1: SANRAL Drainage Manual
The Drainage Manual Application Guide contains the following:

Hand calculations of typical problems.

Reference to applicable software utilities and user manuals for the programs.

Step-by-step worked examples using freeware software programs.
1-1
Introduction
1.1
Layout of the Drainage Manual Application Guide
The Drainage Manual Application Guide contains twelve chapters. The focuses in the different
chapters are:
Chapter 1: Provides an introduction to the Drainage Manual Application Guide.
Chapter 2: Review the economic considerations.
Chapter 3: Illustrate the various flood calculation methods for different recurrence intervals.
Chapter 4: Reflects basic hydraulic calculations.
Chapter 5: Demonstrates surface drainage design.
Chapter 6: Hydraulic analysis of low-level crossings.
Chapter 7: Contains analysis and design details for lesser culverts and storm water pipes.
Chapter 8: Focuses on bridges and major culverts and scour at these structures.
Chapter 9: Storm water analyses and design.
Chapter 10: Assessment of hydraulic capacity of existing drainage structures and the application of
flood routing.
Chapter 11: Free surface flow determination.
Chapter 12: Discusses sub-surface drainage.
It is trusted that the document will provide valuable assistance in the design of drainage systems.
References to all the figures and literature can be found in the Drainage Manual
1-2
Introduction
2
ECONOMIC EVALUATION OF DRAINAGE SYSTEMS
The following three simple examples have been included to illustrate the use of the economic
evaluation procedures. The supporting software is capable of determining the NPV, IRR and LCA for
more complex income and expenditure streams. It is suggested that the supporting software be used to
conduct sensitivity analyses.
2.1
Example 2.1 – Net Present Value
Evaluate which of the future income streams S1 or S2 is more favourable if the cost of capital is 10%
on a yearly basis and the amounts realize at the beginning of the year.
Year
1
2
3
4
5
S1
250
350
600
100
400
S2
100
400
350
600
250
Solution Example 2.1
If you assume year 1 to be the base year then the NPV’s of the two income streams are:
NPVS1 = R1 412.39
NPVS2 = R1 374.43
These calculations reflect that the income stream S1 is more favourable when comparing the Net
Present Values (NPV).
The NPV was calculated using the following formula:
F
NPV 
1  i n
…(2.1)
Where:
F
i
n
=
=
=
future value
interest rate
periods
Each future value was brought back to present values and accumulated to obtain the total NPV for
each income stream.
2.2
Example 2.2 – Present Value
Determine the current investment that should be made for the replacement of a R1,5 million
installation (current cost) after 15 years, if the expected CPIX is 15 % and the return on a fixed
investment is 8% p.a.
Solution Example 2.2
Firstly the future value (F) of the investment should be determined. The current installation (P) is
worth R1 500 000 and the escalation will be 15 % for a 15-year period.
F  P 1  i 
n
…(2.2)
2-3
Economic analysis
F  1 500 000 1  0,15  R12 205 592
15
Now the current investment (P) should be calculated by discounting the future required value (F) by
8% per annum for the 15-year period.
P
P
2.3
F
1  i n
12 205 592
1  0,0815
…(2.3)
 R3 847 712
Example 2.3 – Internal Rate of Return (IRR)
Determine the Internal Rate of Return (IRR) for the following cash flow.
Year
0
1
2
3
4
5
Cash flow
-1 300
250
350
600
100
400
Solution Example 2.3
The internal rate of return is the rate where the NPVincome = NPVexpenditure
250
350
600
100
400




1
2
3
4
1  i 1  i 1  i 1  i 1  i5
1300
NPVexpenditure 
1  i 0
NPVincome 
…(2.4)
…(2.5)
Equation (2.11) = Equation (2.12)
250
350
600
100
400
1300





1
2
3
4
5
1  i 1  i 1  i 1  i 1  i 1  i0
Solving from this equation for “i”
IRR = 9,525%
2-4
Economic analysis
3
FLOOD CALCULATIONS
The main aim of this section is to provide the reader with a step-by-step explanation of the procedures
used to calculate flood magnitudes for different return periods.
In the two paragraphs below, flood peaks will be calculated for a small as well as a large catchment
using the various relevant deterministic, statistical and empirical methods.
3.1
Worked example 3.1 - Small catchment
The first worked example reflects the flood calculation for a small bridge on the Moretele Spruit,
which runs through the eastern part of Pretoria in a north-westerly direction (see Figure 3.1).
The small bridge, as shown in Figure 3.2, is located in Pretoria East (location indicated on Figure
3.1). The flooding of the bridge has to be analysed for the 1:20 year and 1:50 year recurrence interval
flood peaks to determine the risk of flooding Hans Strijdom Drive, which has become an important
artery in the eastern suburbs of Pretoria.
Figure 3.1: Moretele Spruit catchment area (shown on a 1:50 000 topographical map)
3-5
Flood calculations
Figure 3.2: Small Bridge across the Moretele Spruit (Hans Strijdom Drive)
3.1.1
Rational method
Data requirements
The Rational method requires the following data:




Area of catchment
Length of longest watercourse and average slope to calculate time of concentration
Catchment characteristics to calculate run-off coefficients
Mean annual precipitation and rainfall region to determine average rainfall intensity
Calculation procedure
Step 1: Determine the catchment area (km²).
Topographical maps (1: 50 000) are normally used to determine the area of a catchment.
However, the accuracy and contour intervals on these maps are not always as required and it
is often useful to obtain 1: 10 000 maps, if available. Ortho-photographs should also be
used, if available. Use graph paper or a planimeter to determine the total catchment area,
which will contribute to the peak flow. Pans or areas that are artificially isolated should thus
be excluded.
The use of Geographical Information Systems (GIS) has permeated almost every field in the
engineering, natural and social sciences. GIS do not inherently have all the hydrological
simulation capabilities that complex hydrological models do, but are used to determine many
of the catchment parameters that hydrological models or design flood estimation methods
require. Other software applications such AutoCAD could also be used to determine the
catchment area.
3-6
Flood calculations
The catchment area of the Moretele Spruit up to the small bridge is 28,5 km² as shown in
Figure 3.3.
Figure 3.3: Determined catchment area
Step 2: Determine the length of the longest watercourse (km).
For the defined catchment area as required for Step 1, the longest watercourse and its length
are determined. The length of the watercourse for this example is L = 7,25 km.
Step 3: Determine the average slope of the longest watercourse.
Utilising the 10-85 method (m/m) as developed by the US Geological Survey, and tested by
the UK Institute of Hydrology, calculate the average slope. A longitudinal profile of the
Moretele Spruit along the longest watercourse is shown in Figure 3.4.
Sav 
H 0,85L  H 0,10L
… (3.1)
1 0000,75L
where:
Sav = average slope (m/m)
H0,10L = elevation height at 10% of the length of the watercourse (m)
H0,85L = elevation height at 85% of the length of the watercourse (m)
L
= length of watercourse (km)
The elevation at 10% of the length of the longest watercourse is H0,10L = 1 412,1 m and at
85% of the length the elevation is H0,85L = 1 528,8 m.
The calculated average slope for this example is 0,02146 m/m.
3-7
Flood calculations
Figure 3.4: Longitudinal profile of the Moretele Spruit
Step 4: Calculate the time of concentration from catchment characteristics. The recommended
empirical formula for calculating the time of concentration in natural channels has been
developed by the US Soil Conservation Services.
0,385
 0,87L2 

Τ C  
 1 000 S av 
where:
TC
= time of concentration (hours)
L
= length of watercourse (km)
Sav = average slope (m/m)
… (3.2)
In most cases the longest water path includes both overland and channel flows. In large
catchments the channel flow is usually dominant, but in small catchments it may be
necessary to determine TC as the sum of the flow times for both the overland and channel
flow stretches. To obtain a broad indication, it may usually be accepted that a defined
watercourse exists when the average slope of the catchment is greater than 5 per cent and the
catchment itself is larger than 5 km².
The time of concentration of the Moretele Spruit up to the specific point is TC = 1,338 hours.
Step 5: Obtain the mean annual precipitation (MAP), from the South African Weather Service or
from the simplified Figure 3.5.
When there are two or more rainfall stations in the catchment area the Thiessen method or
weighted area method can be used to determine the representative rainfall for the catchment.
The catchment area in this example contains one rainfall station within the catchment and
two adjacent as shown in Figure 3.6.
3-8
Flood calculations
Figure 3.5: Mean Annual Precipitation
Figure 3.6: Rainfall stations used in determining the representative MAP
3-9
Flood calculations
The weighted area method was used to determine the representative mean annual
precipitation as shown in Table 3.16 based on the applicable areas. All the stations in this
example are located in a straight line and thus the Thiessen method could not be utilized in
this example.
Table 3.1: Mean annual precipitation of catchment area
Weather Service rainfall
Latitude
Longitude
MAP
station
D M
D M
(mm)
0513529 – Garsfontein
25° 49'
28° 18'
771,8
0513531 - Rietvlei Agr.
25° 51'
28° 18'
714,0
0513528 - Constantia Park
25° 48'
28° 18'
702,5
746,6
Total
Area
(km²)
16,53
9,69
2,28
28,5
Also determine the rainfall region in which the catchment falls.
The mean annual precipitation (MAP) for this catchment is 746,6 mm (see Table 3.1) and
the catchment is located in the inland region.
Historically there have been a number of ways in which the rainfall intensity could be
determined. These alternative methods have been retained in this document although the latest
method using the Design Rainfall Estimation Software is recommended (Alternative 3).

Alternative 1 – Original method using Depth-Duration-Frequency Diagram.

Alternative 2 – The TR102 representative rainfall data and the modified Hershfield equation
is used (in the past this was referred to as the Alternative Rational Method).

Alternative 3 – The design rainfall from the Design Rainfall Estimation software is used to
determine the point rainfall of the catchment.
Alternative 1
Step 6a: Determine the point rainfall values (PT) (mm) for the required return periods. Based on the
mean annual precipitation (MAP), the rainfall region, the time of concentration (TC) and the
required return period, Figure 3.7 can be used to determine the point rainfall. As shown in
Figure 3.7 the point rainfall for the 1:20 year and 1:50 year return periods are determined
using the co-axial Depth-Duration-Frequency diagram.
The point rainfall for the 1:20 and 1:50 year return periods is P20 = 78 mm and P50 = 104 mm
respectively.
Step 7a: Calculate the point intensity (mm/hour)
The point intensity (PiT) is the point rainfall divided by the time of concentration (if TC >
0,25 hours). If TC ≤ 0,25 hours divide by 0,25 hours.
PiT 
PT
TC
where:
PiT
PT
TC
… (3.3)
=
=
=
point intensity for the different return periods (mm/h)
point rainfall (mm)
time of concentration (hours)
The point intensities for the 1:20 and 1:50 year return periods are Pi20 = 58,3 mm/h and
Pi50 = 77,7 mm/h respectively.
3-10
Flood calculations
Figure 3.7: Determining the point rainfall utilizing Depth-Duration-Frequency diagram
Step 8a: Determine the area reduction factors (ARF) for the different return periods.
In this example the catchment area is small and thus Figure 3.8 is used. The resulting ARFs
are ARF20 = 94% and ARF50 = 91% for the 1:20 and 1:50 years return periods respectively.
3-11
Flood calculations
Figure 3.8: Expected percentage run-off as a function of point intensity (small areas), ARF
Step 9a: Determine the average rainfall intensity or effective catchment precipitation.
 ARFT 
I T  PiT 

 100 
… (3.4)
where:
IT
=
ARFT =
PiT
=
rainfall intensity averaged over the catchment in millimetres/hour
for the return period T.
area reduction factor as a percentage for return period T (should be
smaller than 100%)
point intensities for the different return periods (mm/h)
The average rainfall intensities are I20 = 54,79 mm/h and I50 = 70,71 mm/h.
3-12
Flood calculations
Alternative 2
Step 6b: Determine the representative rainfall from the available TR102 South African Weather
Service stations in and around the catchment (see Table 3.2).
Table 3.2: Representative rainfall station from TR102
Pretoria (The Willows)
Weather Service station
513524
Weather Service station no
647 mm
Mean annual precipitation
25° 44' 28° 18'
Coordinates
Duration
Return period
(days)
2
5
10
20
50
100
60
83
101
121
150
175
1 day
75
105
129
155
192
224
2 days
83
117
143
171
211
245
3 days
110
160
199
241
303
355
7 days
200
202
259
282
412
Step 7b: Based on the calculated time of concentration and representative rainfall, determine the
precipitation depth. In this example the time of concentration is 80 minutes, in other words
less than 6 hours, and thus the modified Hershfield relationship will be used.

Pt,T  1,130,41  0,64lnT  0,11  0,27lnt  0,79M 0,69 R 0,20
where:
Pt,T
t
T
M
R

… (3.5)
= precipitation depth for a duration of t minutes and a return period of T
years (mm)
= duration (minutes)
= return period
= 2-year return period daily rainfall from TR102
= average number of days per year on which thunder was heard (days/year)
(Figure 3.9)
The average number of days on which thunder was heard (R) is equal to 61 and M is
60 (from Table 3.2). The calculated precipitation depths are:
Pt20 = 85,55 mm and Pt50 = 107,10 mm
Step 8b: Calculate the point intensity (mm/hour)
The point intensity (PiT) is the point rainfall divided by the time of concentration (if TC >
0,25 hours). If TC ≤ 0,25 hours, divide by 0,25 hours.
PiT 
PtT
TC
where:
PiT
PtT
TC
… (3.6)
= point intensity for the different return periods (mm/h)
= precipitation depth for a duration of t minutes and a return period of T
years (mm)
= time of concentration (hours)
The point intensity for the 1:20 and 1:50 year return periods is Pi20 = 63,93 mm/h and
Pi50 = 80,04 mm/h respectively.
3-13
Flood calculations
Figure 3.9: Average number of days per year on which thunder was heard
Step 9b: Determine the area reduction factors (ARF) for the different return periods from Figure 3.10
or equation 3.7.
0,4
… (3.7)
ARF  90000  12800lnA  9830ln 60TC 
where:
ARF
A
TC
=
=
=
area reduction factor as a percentage (should be less than 100%)
catchment area (km²)
time of concentration (hours)
The resulting ARF = 96 % for the 1:20 and 1:50 years return periods.
Step 10b: Determine the average rainfall intensity or effective catchment precipitation
 ARFT 
… (3.8)
I T  PiT 

 100 
where:
IT
= rainfall intensity averaged over the catchment (mm/h) for the
return period T.
ARFT
= area reduction factor as a percentage for return period T (should
be smaller than 100 %)
PiT
= point intensities for the different return periods (mm/h)
The average rainfall intensities are I20 = 61,4 mm/h and I50 = 76,9 mm/h.
3-14
Flood calculations
Figure 3.10: Area reduction factors
Alternative 3
This is the preferred method of obtaining point rainfall data for use in the
Rational Method procedure.
Step 6c: The design rainfall from the Design Rainfall Estimation software is the recommended
method to determine the point design rainfall of a catchment (see Figure 3.11). Utilising the
Design Rainfall Estimation in South Africa software application the representative weather
station or coordinates as shown in Figure 3.12 can be entered. A summary of all the closest
rainfall stations as well as the n-day rainfall values as shown in Figure 3.13 is obtained. The
software enables the estimation of design rainfall for durations ranging from 5 minutes to 7
days and for 2 to 200 year return periods at any 1' latitude x 1' longitude point in South
Africa.
Enter the coordinates or station and click on the proceed button (Figure 3.12) to obtain a
summary of all the closest rainfall stations as well as the n-day rainfall values (see Figure
3.13).
3-15
Flood calculations
Figure 3.11: Snapshot of design rainfall database
Figure 3.12: Design Rainfall estimation software
3-16
Flood calculations
Figure 3.13: Design Rainfall estimation results
Step 7c: Based on the calculated time of concentration and representative rainfall, determine the point
rainfall values (see Figure 3.14) for the catchment area.
The calculated precipitation depths are Pt20 = 57 mm and Pt50 = 70 mm.
Step 8c: Calculate the point intensity (mm/hour)
The point intensity (PiT) is the point rainfall divided by the time of concentration (if TC >
0,25 hours). If TC ≤ 0,25 hours, divide by 0,25 hours.
PiT 
PtT
TC
where:
PiT
PtT
TC
… (3.9)
= point intensity for the different return periods (mm/h)
= precipitation depth for a duration of t minutes and a return period of T
years (mm)
= time of concentration (hours)
The point intensity for the 1:20 and 1:50 year return periods is Pi20 = 42,6 mm/h and Pi50 = 52,3 mm/h
respectively.
3-17
Flood calculations
Figure 3.14: Gridded point rainfall values
Now that the intensities have been calculated using three alternative methods the run-off
coefficient can now be determined.
Step 10: Identify the catchment characteristics to determine the run-off coefficient.
The run-off coefficient in the rational method is an integrated value representing the many
factors influencing the rainfall run-off relationship.
There is no objective theoretical method for determining C and as a result the subjective
elements of experience and engineering judgement play a very important role in the
successful application of this method.
Table 3.3 provides recommended values of C for the calculation of the run-off coefficient.
The Moretele Spruit catchment is classified as 40% rural and 60% urban based on the latest
information available (i.e. topographical maps and confirmed by a visit to the catchment (see
Figure 3.3) i.e. α = 0,4; β = 0,6 and γ = 0,0.
Based on the available data from the catchment, the following tables were compiled to
characterise the catchment (Table 3.4 and Table 3.5).
3-18
Flood calculations
Table 3.3: Recommended values of run-off factor C for use in the rational method
Rural (C1)
Component
Classification
Urban (C2)
Mean annual rainfall (mm)
600 < 600
> 900
900
Use
Factor
Surface
slope
(Cs)
Vleis and pans (<3%)
Flat areas (3 to 10%)
Hilly (10 to 30%)
Steep areas (>30%)
0,01
0,06
0,12
0,22
0,03
0,08
0,16
0,26
0,05
0,11
0,20
0,30
Lawns
- Sandy, flat (<2%)
- Sandy, steep (>7%)
- Heavy soil, flat (<2%)
- Heavy soil, steep (>7%)
0,05 - 0,10
0,15 – 0,20
0,13 – 0,17
0,25 – 0,35
Permeability
(Cp)
Very permeable
Permeable
Semi-permeable
Impermeable
0,03
0,06
0,12
0,21
0,04
0,08
0,16
0,26
0,05
0,10
0,20
0,30
Residential areas
- Houses
- Flats
0,30 – 0,50
0,50 – 0,70
Thick bush and
plantation
Light bush and farm
lands
Grasslands
No vegetation
0,03
0,04
0,05
Industry
- Light industry
- Heavy industry
0,50 – 0,80
0,60 – 0,90
0,07
0,11
0,15
0,17
0,26
0,21
0,28
0,25
0,30
Business
- City centre
- Suburban
- Streets
- Maximum flood
0,70 – 0,95
0,50 – 0,70
0,70 – 0,95
1,00
Vegetation
(Cv)
Table 3.4: Catchment characteristics (Rural)
Rural (C1)
Component
Classification
%
Surface slope
(CS)
Permeability
(CP)
Vegetation
(CV)
Vleis and pans (<3%)
Flat areas (3 to 10%)
Hilly (10 to 30%)
Steep areas (>30%)
Very permeable
Permeable
Semi-permeable
Impermeable
Thick bush and plantation
Light bush and farm lands
Grasslands
No vegetation
20
70
10
0
0
50
50
0
0
45
50
5
Utilising Table 3.4 the run-off coefficient for the rural area is calculated using the following formula:
C1  C S  C P  C V
where:
=
run-off coefficient with a value between zero and one
C1
CS
=
run-off coefficient according to average catchment slope
=
run-off coefficient according to average soil permeability
CP
CV =
run-off coefficient according to average vegetal growth
… (3.10)
The average rainfall falls between 600 and 900 mm, and thus:
3-19
Flood calculations
C1  0,20 x 0,03  0,70 x 0,08  0,10 x 0,16
 0,50 x 0,08  0,50 x 0,16
 0,45 x 0,11  0,50 x 0,21  0,05 x 0,28
C1  0,3665
If it is estimated that up to 10% (D%) of the area could be dolomitic, then the run-off factor should be
reduced as described earlier in this chapter. Based on the defined slopes, the following factors (Dfactor)
are used to adjust the run-off coefficient.

Vleis and pans (slopes <3%) 0,10

Flat areas (3 to 10%)
0,20

Hilly (10 to 30%)
0,35

Steep areas (slopes >30%)
0,50
C1D  C1 1  D %   C1 D %  D factor x C S% 
C1D  0,36651  0,1  0,36650,10,10 x 0,20  0,20 x 0,70  0,35 x 0,1
C1D  0,337
C1D is the rural run-off coefficient that incorporates the effect of the dolomitic area.
The influence of initial saturation is incorporated by means of an adjustment factor. Using these
adjustment factors (FT) for rural areas, the run-off coefficients (C1D) for the 1:20 and 1:50 year return
periods are adjusted as follows with F20 = 0,67 and F50 = 0,83.
… (3.11)
C1T  C1D x FT
Thus C1(20) = 0,2258 and C1(50) = 0,2797
The run-off coefficient for the urban area (C2) is calculated using the defined catchment
characteristics (Table 3.5) and the most conservative coefficients of Table 3.5 (for this
example).
C 2  0,20 x 0,10  0,10 x 0,20 
 0,40 x 0,50  0,05 x 0,70 
 0,05 x 0,80 
 0,10 x 0,70  0,10 x 0,95
C 2  0,48
The combined run-off coefficient is calculated as follows:
C T   C 1T   C 2   C 3
With α = 0,4; β = 0,6 and γ = 0,0.
C20 = 0,3783
C50 = 0,3999
3-20
… (3.12)
Flood calculations
Table 3.5: Catchment characteristics (Urban)
Urban (C2)
Use
%
Lawns
- Sandy, flat (<2%)
- Sandy, steep (>7%)
- Heavy soil, flat (<2%)
- Heavy soil, steep (>7%)
Residential areas
- Houses
- Flats
Industry
- Light industry
- Heavy industry
Business
- City centre
- Suburban
- Streets
- Maximum flood
20
10
0
0
40
5
5
0
0
10
10
0
Step 11: Determine the peak flow for each of the required return periods utilising the simple linear
relationship and for this example the various methods used to calculate the average rainfall
intensity (Alternatives 1 to 3):
C I A
… (3.13)
QT  T T
3,6
where:
QT =
peak flow rate for T-year return period (m³/s)
CT
=
combined run-off coefficient for T-year return period
IT
=
average rainfall intensity over catchment for a specific return
period (mm/hour)
A
=
effective area of catchment (km²)
3,6 =
conversion factor
The peak flow rates based on the rational method for the 1:20 year and 1:50 year return periods
(calculated by means of equation 3.13) are:
Peak flood
Q20
Q50
3.1.2
Alternative 1
164 m³/s
224 m³/s
Alternative 2
184 m³/s
243 m³/s
Alternative 3
128 m³/s
166 m³/s
Unit Hydrograph method
Step 1: The first three steps of the Rational method described above are also applicable to the Unit
Hydrograph method, thus A = 28,5 km2, L = 7,25 km and S = 0,02146 m/m.
Step 2: Determine the veld-type zone in which the catchment is located from Figure 3.15. The
catchment of the Moretele Spruit falls in Zone 8.
3-21
Flood calculations
Figure 3.15: Regions with generalised veld types in South Africa
Step 3: Calculate the catchment index by means of the following formula:
L LC
… (3.14)
Index 
S
where: L
=
hydraulic length of catchment (km)
LC
=
distance between outlet and centroid of catchment (km)
S
=
average slope (as for Rational method in m/m)
The measured length from the catchment outlet along the watercourse and then
perpendicular to the centroid is LC = 4,65 km. The calculated catchment index is 230,1.
Step 4: Determine the lag time in hours from Figure 3.16 based on the catchment index and
veld-type zone. The Lag time (TL) equals 1,35 hours.
3-22
Flood calculations
Figure 3.16: Ratio of lag time to catchment index
Step 5: From Table 3.6 obtain the value of KU for the specific veld-type. For this example Ku =
0,367.
Table 3.6: Values of KU for various veld types
Regional number
Generalised veld type
(Figure 3.15)
1
Coastal tropical forest
2
Schlerophyllous bush
3
Mountain sourveld
4
Grasslands of interior plateau
5
Highland sourveld and Dohne sourveld
5a
As for Zone 5 – but soils weakly developed
6
Karoo
7
False Karoo
8
Bushveld
9
Tall sourveld
Factor Ku
0,261
0,306
0,277
0,386
0,351
0,488
0,265
0,315
0,367
0,321
Step 6: The peak flow rate for the unit hydrograph according to the regional classification given in
Table 3.6 in zone 8 is calculated using the following formula:
A
… (3.15)
Qp  K u
ΤL
where:
=
peak flow rate of unit hydrograph (m³/s)
QP
A
=
size of catchment (km²)
=
Lag time (hours)
TL
The unit hydrograph peak discharge is 7,75 m³/s.
Step 7: Obtain the mean annual precipitation (MAP), as described for the Rational method. The
determined MAP for this catchment is 746,6 mm/a.
Step 8: This step has to be repeated for different storm durations as well as for different return
periods. The main aim is to determine the effective rainfall (heiT) for the different storm
durations with which the dimensionalised unit hydrograph peak flow could then be
multiplied.
3-23
Flood calculations
Step 8.1:
Determine the point rainfall for the required return periods (PT) based on the mean
annual precipitation (MAP), the rainfall region, and the storm duration (TSD). Point
precipitation for various durations, normally shorter than or equal to the lag time, is
obtained. Figure 3.5 may be used to determine the point rainfall although it is
preferred that the Design Rainfall software utility is used (see Figure 3.12). The
probable maximum flood can also be calculated using the Unit hydrograph method,
see the Drainage Manual Chapter 3 for more details.
For this example the point rainfalls for the 0,25 hour, 0,5 hour, 1 hour and 2 hour
storms have been determined for the different return periods 1:20 and 1:50 year (see
Table 3.7).
Step 8.2:
Calculate the point rainfall intensity (mm/hour). The point intensity (PiT) is the point
rainfall divided by the storm duration (TSD).
P
… (3.16)
PiT  T
TSD
where:
PiT =
point intensities for the different return periods (mm/h)
PT
=
point rainfall (mm)
TSD =
storm duration (hours). If duration < 0,25 hours use 0,25 hours.
See solution in Table 3.7.
Step 8.3:
Determine the area reduction factors (ARFiT) for the different return periods based on
the catchment area and different storm durations from Figure 3.8. The determined
ARFiT values are shown in Table 3.7.
Step 8.4:
Calculate the average rainfall (PAvgiT) for the different return periods and storm
durations. This is the area reduction factor (ARFiT) multiplied by the point rainfall
(PT). The average rainfall values are shown in Table 3.7.
Step 8.5:
Determine the flood run-off factor from Figure 3.17. This factor is based on the
average rainfall, veld-type zone and catchment area. The flood run-off factors (fiT) are
given in Table 3.7.
Step 8.6:
Calculate the effective rainfall (heiT) for each return period and selected storm duration
by multiplying the flood run-off factors (fiT) with the average rainfall values (PAvgiT).
Table 3.7: Calculation of effective rainfall values (heiT)
Return period
Description
Storm duration (TSD)
Point rainfall (PT)
Point intensity (PiT)
Area reduction factor (ARFiT)
Average rainfall (PAvgiT)
Flood run-off factor (fiT)
Effective rainfall (heiT)
Unit
hours
mm
mm/hour
%
mm
%
mm
1:20
0,25
41
164
84
34,44
12
4,13
0,5
63
126
88
55,44
16
8,87
3-24
1
84
84
92
77,28
19
14,68
1:50
2
97
48,5
95
92,15
22
20,27
0,25
50
200
80
40,00
13
5,20
0,5
77
154
85
65,45
18
11,78
1
102
102
90
91,80
22
20,20
2
118
59
94
110,92
24
26,62
Flood calculations
Figure 3.17: Average storm losses
Step 9: The maximum flood peak is obtained by multiplying the effective rainfall for specific storm
durations with the unit hydrograph peak flow. The duration of storms that cause the
maximum peak discharge is obtained by trial and error. Since the standard duration of a unit
hydrograph is one hour (from the one-hour rainfall), the duration should be increased or
decreased to make provision for other rainfall durations.
An S-curve is obtained by staggering a number of unit hydrographs by the unit duration and
then summing them as shown Figure 3.18. It is recommended that an S-curve be constructed
in all cases.
Once the S-curve has been drawn, lagging an identical second S-curve by the duration and
then subtracting one from the other provides a unit hydrograph of the lagged duration. The
resulting values only need to be multiplied by a proportionate factor to obtain a new unit runoff hydrograph. This unit hydrograph could again be dimensionalised using the values of
QP and TL. It is thus advisable to calculate the run-off values for the original unit hydrograph
at such time intervals that the duration of the required hydrographs will be divisible by these
time intervals.
3-25
Flood calculations
Figure 3.18: Illustration of S-curve
The dimensionless one-hour unit hydrograph for veld-type zone 8 is shown in Figure 3.19,
obtained from Table 3.8, and the constructed S-curve in Figure 3.20. The rising and falling
limbs of the unit hydrograph used to construct the S-curve are not equal. If the ordinates of
the staggered unit hydrographs are summed, the constructed S-curve is not constantly
increasing until it reaches the maximum value thereof. As illustrated in this example, this
leads to an uneven S-curve as shown in Figure 3.20. It is suggested that this be rectified as
shown by preventing the S-curve values for example (Q/Qp)t being less than (Q/Qp)t-1. This
approach is conservative, which could probably lead to an over-estimation in calculating the
volume of discharge, but should provide a conceptually correct answer in terms of the flood
peak value.
Figure 3.19: Dimensionless one-hour unit hydrograph for veld type Zone 8
3-26
Flood calculations
Table 3.8: Dimensionless one hour unit hydrographs for various veld zone regions
Time as
T/TL
1
2
3
0
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
1,40
1,45
1,50
1,55
1,60
1,65
1,70
1,75
1,80
1,85
1,90
1,95
2,00
2,05
2,10
2,15
2,20
2,25
2,30
2,35
2,40
2,45
2,50
2,55
2,60
2,65
2,70
2,75
2,80
2,85
2,90
2,95
3,00
3,05
3,10
3,15
3,20
3,25
3,30
3,35
3,40
3,45
3,50
3,55
3,60
3,65
3,70
3,75
3,80
3,85
3,90
3,95
4,00
4,05
4,10
4,15
4,20
4,25
0,000
0,035
0,070
0,112
0,163
0,228
0,306
0,414
0,524
0,709
0,921
0,983
0,996
0,998
0,964
0,893
0,826
0,758
0,700
0,652
0,605
0,563
0,525
0,491
0,463
0,437
0,411
0,387
0,362
0,341
0,321
0,302
0,283
0,265
0,252
0,238
0,226
0,215
0,204
0,194
0,183
0,174
0,165
0,157
0,149
0,142
0,135
0,128
0,121
0,116
0,110
0,105
0,100
0,096
0,091
0,087
0,082
0,078
0,074
0,070
0,066
0,062
0,057
0,054
0,050
0,047
0,043
0,039
0,036
0,032
0,029
0,025
0,022
0,019
0,016
0,012
0,009
0,005
0,003
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,012
0,024
0,036
0,052
0,072
0,091
0,121
0,152
0,198
0,258
0,342
0,472
0,676
0,940
0,991
0,995
0,973
0,888
0,807
0,741
0,678
0,622
0,567
0,513
0,467
0,425
0,394
0,364
0,338
0,313
0,291
0,272
0,253
0,236
0,220
0,206
0,192
0,181
0,171
0,160
0,152
0,143
0,136
0,130
0,123
0,118
0,114
0,108
0,104
0,100
0,096
0,093
0,089
0,085
0,081
0,078
0,074
0,070
0,066
0,063
0,060
0,056
0,053
0,050
0,047
0,044
0,040
0,037
0,034
0,031
0,027
0,024
0,021
0,018
0,015
0,011
0,008
0,005
0,002
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,010
0,023
0,039
0,057
0,074
0,106
0,139
0,184
0,261
0,376
0,518
0,670
0,809
0,970
1,000
0,990
0,935
0,840
0,755
0,675
0,612
0,546
0,500
0,460
0,424
0,395
0,368
0,347
0,325
0,305
0,290
0,276
0,264
0,252
0,238
0,228
0,216
0,208
0,200
0,194
0,186
0,178
0,171
0,165
0,158
0,152
0,147
0,142
0,139
0,132
0,128
0,124
0,120
0,114
0,111
0,107
0,103
0,099
0,095
0,091
0,087
0,084
0,081
0,078
0,075
0,071
0,068
0,064
0,062
0,059
0,056
0,051
0,048
0,046
0,043
0,040
0,037
0,035
0,032
0,029
0,027
0,024
0,021
0,011
0,000
Run-off as Q/QP for veld-type regions
4
5
5a
6
0,000
0,011
0,024
0,038
0,041
0,070
0,089
0,111
0,138
0,175
0,220
0,350
0,700
0,980
1,000
0,987
0,885
0,760
0,670
0,580
0,530
0,470
0,430
0,393
0,364
0,336
0,310
0,288
0,271
0,252
0,235
0,218
0,201
0,187
0,172
0,159
0,147
0,136
0,125
0,115
0,108
0,098
0,089
0,081
0,074
0,068
0,062
0,056
0,052
0,047
0,043
0,039
0,035
0,032
0,029
0,026
0,023
0,021
0,019
0,017
0,016
0,012
0,011
0,009
0,008
0,006
0,004
0,003
0,002
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,018
0,038
0,063
0,095
0,142
0,220
0,315
0,500
0,685
0,810
0,936
0,985
1,000
0,960
0,800
0,675
0,588
0,524
0,473
0,432
0,397
0,365
0,340
0,315
0,295
0,276
0,260
0,242
0,228
0,214
0,200
0,187
0,174
0,163
0,152
0,143
0,134
0,126
0,120
0,112
0,106
0,100
0,094
0,088
0,084
0,079
0,074
0,070
0,066
0,062
0,058
0,055
0,051
0,048
0,045
0,042
0,039
0,036
0,033
0,030
0,027
0,025
0,022
0,020
0,018
0,016
0,013
0,011
0,010
0,008
0,006
0,004
0,002
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
3-27
0,000
0,004
0,011
0,019
0,027
0,037
0,05
0,064
0,083
0,107
0,140
0,210
0,425
0,885
0,958
0,993
0,991
0,955
0,740
0,535
0,440
0,385
0,340
0,300
0,265
0,235
0,209
0,187
0,169
0,152
0,140
0,128
0,116
0,105
0,097
0,088
0,081
0,074
0,067
0,061
0,055
0,050
0,046
0,041
0,038
0,034
0,031
0,028
0,025
0,023
0,021
0,019
0,017
0,015
0,013
0,012
0,011
0,010
0,009
0,008
0,006
0,004
0,003
0,002
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,024
0,052
0,087
0,140
0,260
0,700
0,983
1,000
0,970
0,915
0,848
0,795
0,754
0,714
0,678
0,641
0,605
0,572
0,540
0,514
0,488
0,465
0,443
0,422
0,402
0,382
0,365
0,347
0,330
0,315
0,300
0,287
0,274
0,260
0,249
0,237
0,225
0,214
0,203
0,193
0,183
0,173
0,164
0,155
0,147
0,138
0,130
0,122
0,115
0,109
0,102
0,097
0,090
0,085
0,080
0,075
0,069
0,064
0,059
0,054
0,049
0,044
0,040
0,036
0,031
0,027
0,022
0,018
0,013
0,010
0,005
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
7
8
9
0,000
0,006
0,014
0,024
0,032
0,044
0,058
0,074
0,095
0,121
0,160
0,275
0,480
0,700
0,950
0,975
0,993
1,000
0,995
0,980
0,900
0,805
0,730
0,655
0,590
0,530
0,477
0,432
0,388
0,350
0,308
0,280
0,255
0,232
0,211
0,194
0,177
0,164
0,152
0,140
0,130
0,120
0,111
0,102
0,094
0,087
0,081
0,075
0,069
0,063
0,058
0,053
0,049
0,045
0,041
0,039
0,036
0,033
0,030
0,029
0,026
0,023
0,021
0,019
0,017
0,015
0,013
0,011
0,010
0,008
0,006
0,005
0,004
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,006
0,014
0,025
0,035
0,050
0,069
0,100
0,150
0,245
0,655
0,905
0,980
0,994
0,991
0,966
0,860
0,755
0,655
0,565
0,500
0,440
0,392
0,355
0,322
0,294
0,270
0,250
0,231
0,215
0,200
0,186
0,174
0,164
0,155
0,146
0,137
0,130
0,122
0,115
0,110
0,103
0,098
0,091
0,086
0,081
0,075
0,070
0,066
0,062
0,058
0,054
0,050
0,047
0,044
0,041
0,038
0,035
0,032
0,029
0,026
0,024
0,022
0,020
0,019
0,017
0,015
0,013
0,011
0,009
0,007
0,005
0,004
0,002
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,011
0,027
0,043
0,065
0,093
0,142
0,225
0,350
0,570
0,772
0,930
0,982
1,000
0,985
0,945
0,900
0,814
0,750
0,670
0,600
0,530
0,472
0,413
0,364
0,316
0,280
0,260
0,241
0,225
0,210
0,198
0,188
0,176
0,168
0,158
0,151
0,144
0,137
0,131
0,124
0,119
0,113
0,108
0,103
0,097
0,093
0,087
0,085
0,079
0,075
0,071
0,070
0,063
0,061
0,055
0,053
0,049
0,045
0,041
0,038
0,035
0,030
0,027
0,022
0,018
0,014
0,010
0,007
0,004
0,002
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
Flood calculations
Step 10: The 0,25, 0,5 and 2-hour unit hydrograph peaks are obtained by multiplying the maximum
obtained values from the previous step with the peak flow rate of the unit hydrograph (Qp),
see Table 3.9.
Step 11: The last step is to calculate the peak flows for the different return periods and storm
durations. The maximum peak flow for each return period is then used as the design peak
flood for that specific return period as shown in Table 3.9. The peak values are adjusted as
indicated for QPiT/QP < 1; in this case 0,9923.
Figure 3.20: S-curve for veld type Zone 8 and lagged by 0,25 hour
Table 3.9: Peak flows utilising the discharge unit hydrograph method
Return period
1:20
1:50
Variable
Unit
Storm duration
hours
0,25
0,5
1
2
0,25
0,5
1
(TSD)
Effective rainfall
mm
4,13
8,87
14,68
20,27
5,20
11,78
20,20
(heiT)
Unit hydrograph peak
m³/s
24,52
14,48
7,68
4,77
24,52
14,48
7,68
(QPiT)
Peak flow
m³/s 101,34 128,42 112,73 96,64 127,50 170,56 155,05
(QiT)
Adjusted for QPiT/QP < 1
m³/s 102,12 129,42 113,60 97,39 128,49 171,88 156,26
2
26,62
4,77
126,91
127,89
The peak flow rates, based on the unit hydrograph method, for the 1:20 year and 1:50 year return
periods are:
Q20 = 129 m³/s and Q50 = 172 m³/s
3-28
Flood calculations
3.1.3
SDF method
The calculation sequence to determine the flood peaks based on the SDF method is as follows:
Step 1: Identify the drainage basin in which the site is located from Figure 3.21. The catchment falls
in drainage basin number 1.
Step 2: Determine the area of the catchment. In this example it has already been calculated as
A = 28,5 km².
Step 3: Determine the length of the main channel. In this example it has already been calculated as
L = 7,25 km.
Step 4: Determine the average slope of the catchment as described for the Rational method. The
calculated average slope (S) for this example is 0,02146 m/m.
Figure 3.21: Standard Design Flood drainage basins
Step 5: Apply the US Soil Conservation Service formula to determine the time of concentration
TC (hours) as suggested in HRU1/72 (3.23).
0,385
 0,87L2 
TC  

1000S av 
The time of concentration is as calculated earlier, i.e. TC = 1,338 hours.
3-29
… (3.17)
Flood calculations
Step 6: Convert TC (hours) to t (minutes) and determine the point precipitation depth PtT (mm) for
the different the return period T (years). In this example the modified Hershfield equation
will be used.

Pt,T  1,130,41  0,64lnT  0,11  0,27lnt  0,79M 0,69 R 0,20
where:
M
=
R
=

… (3.18)
mean of the annual daily maxima from Table 3B.1 (in Appendix B)
equals 56 mm.
average number of days per year on which thunder was heard from
Table 3B.1 equals 30.
Table 3.10: Calculating point precipitation
1:20
1:50
Return period
PtT (mm)
70,84
88,69
Step 7: Multiply the point precipitation depth PtT (mm) by the area reduction factor ARF (%) to
determine the average rainfall over the catchment for the required return period (PAvgT). The
corresponding rainfall intensity IT (mm/h) is obtained by dividing this value by the time of
concentration.
0,4
… (3.19)
ARF  90000  12800lnA  9830lnt
Table 3.11: Calculating point intensity
1:20
1:50
Return period
ARF (%)
96
96
PAvgT (mm)
68,00
85,14
IT (mm/hour)
50,83
63,63
Step 8: The above steps constitute the standard procedures used in the conventional rational method.
The SDF uses calibrated run-off coefficients C2 (2-year return period) and C100 (100-year
return period) from Table 3B.1 instead of determining these from catchment characteristics.
The run-off coefficients for the range of return periods are derived by applying the return
period factors YT in Table 3.12, using the equation below:
CT 
C 2  YT  C100 C 2 




100  2,33  100 100 
… (3.20)
Table 3.12: Return period factors
T
2
5
10
20
50
100
200
YT
0
0,84
1,28
1,64
2,05
2,33
2,58
With the calibrated coefficients being C2 = 10 % and C100 = 40 %, and the return period factors Y20 =
1,64 and Y50 = 2,05 the run-off coefficients are calculated for the 1:20 and 1:50 year return periods:
C20 = 0,3112 and C50 = 0,3639
Step 9: Finally, the flood peak QT (m³/s) for the required return period is calculated as follows:
C I A
… (3.21)
QT  T T
3,6
3-30
Flood calculations
Table 3.13: Calculating flood peaks
Return period
CT
IT (mm/hour)
QT (m³/s)
1:20
0,3112
50,83
125
1:50
0,3639
63,63
183
Step 10: The SDF hydrograph is triangular in shape with the duration of the rising limb equal to the
time of concentration TC (hours), and that of the falling limb equal to twice the time of
concentration. Use linear interpolation between these two values.
3.1.4
SCS method
The SCS method requires a minimum input of catchment area, the catchment response time (Time of
Concentration), design rainfalls and soils and land cover classification. The catchment can be divided
into sub-areas or Hydrological Response Units (HRUs) which are areas with similar soils and land
cover and hence have a relatively similar hydrological response to rainfall.
Step 1: Catchment information
The following information is provided or has been calculated above:
Table 3.14: Previously determined information
Moretele Spruit
Catchment name
25 o 47,75'
Latitude
Longitude
28 o 17,95'
Total catchment area - A
28,5
(km2)
1,334
(h)
Catchment time of concentration - Tc
The catchment is 40% rural and 60 % urban.
Step 2: Initial Curve Number determination
From the ISCW images of soil Land Types, the following Land Types are found in the
catchment: Ib7, Ba3 and Ba9. For each of the Land Types, the dominant terrain unit was
assumed to represent the entire HRU. Similarly, the dominant land class and soil series
within a terrain unit was assumed to respresent the entire unit and, where more than one soil
series is grouped to form the land class, the median SCS soil classification was used. For
each soil series representing each HRU, the appropriate SCS soil classification was
determined using tables from the Visual SCS-SA User Manual. The classification determined
as described above is summarised in Table 3.15, with the catchment divided into four HRUs.
For each HRU in Table 3.15 the soil and land cover classification is used to determine the
initial CN using information contained in Table 3E.3 (in Appendix 3E). From the initial
CN, values of S can be determined using Equation 3.22.
S
25400
 254
CN
…(3.22)
3-31
Flood calculations
Table 3.15: Determination of initial CN and S
SOIL
HRU
Area
(%)
Ai
Form
Series
1
30
Glenros
2
30
3
20
4
20
LAND COVER
Initial
CN
S
(mm)
30% imp
77
75,9
25% imp
75
84,7
264,
4
84,7
Cover
Cover
Class
(S/I/D)
Practice/
Treatment
B/C
Urban
I
SaClLm
B/C
Urban
I
Msinga
SaClLm
A
Veld
I
Moderate
49
Trevanian
SaClLm
B/C
Veld
I
Moderate
75
Texture
SCS
Group
Trevanian
SaClLm
Glenros
Trevanian
Hutton
Glenros
Stormflow
potential
Step 3: Lag estimation
The catchment lag is computed from the time of concentration for the catchment using
Equation 3.23.
L  0,61,334  0,8 hours
… (3.23)
Step 4: Areal reduction factor (ARF)
Given that the SCS method is primarily intended to estimate peak discharge from small
catchments, over which a uniform daily rainfall may be assumed, the reduction of point to
catchment rainfall by means of an ARF is generally not applied. However, to be consistent
with the example, an ARF20 = 94% and ARF50 = 91% for the 20 and 50 year return periods
respectively is used.
Step 5: One-day design rainfall estimation
The SCS method requires the input of one-day design rainfalls which can be estimated using
a number of different methods. The Visual SCS-SA software includes the following options:
(i) User estimated design rainfalls computed directly from raingauge data.
(ii) Design rainfall extracted for a selected station from Adamson’s TR102 report.
(iii) Using at-site design rainfall calculated from the representative rainfall stations used to
represent the rainfall in each of the 712 hydrological zones.
(iv) Design rainfall estimated using the regional method developed by Smithers and
Schulze (2003).
Given the regional approach used and the longer periods of record from all available stations
used in the analysis compared to all previous studies, it is recommended that the regional,
scale invariance approach to design rainfall estimation developed for South Africa by
Smithers and Schulze (2003) be used to estimate the one-day design rainfall.
The results from the application of this approach at the location of the three rain gauges
located in and close to the catchment are summarised in Table 3.16. Given the relatively
small differences in design rainfall between the values computed from the at-site data and
the RLMA&SI methodology, as well as between the different locations, the RLMA&SI
values for Garsfontein were used in the estimation of the design floods. These were then
reduced by the areal reduction factors of 94 % and 91 % for the 20 and 50 year return period
events respectively in order to determine the catchment design rainfalls.
3-32
Flood calculations
Table 3.16: Estimation of one-day design rainfalls at stations around the Moretele Spruit
catchment used in this example
Location
Return period (years)
20
50
At-site RLMA&SI At-site RLMA&SI
(mm)
(mm)
(mm)
(mm)
0513529 – GARSFONTEIN
Latitude: 25o 49'
110,5
118,6
135,4
145,7
Longitude: 28o 17'
0513531 – RIETVLEI
Latitude: 25o 51'
121,4
114,6
148,8
140,5
Longitude: 28o 18'
0513528 - CONSTANTIA PARK
Latitude: 25o 48'
*
120,4
*
147,7
o
Longitude: 28 18'
* No at-site values available
Step 6: Catchment one-day design rainfall
The ARF is used to calculate the catchment design rainfall, as shown in Table 3.17.
Table 3.17: Calculation of one-day catchment design rainfall
20
50
Return period (years)
Areal reduction factor - ARF (%)
94
91
Design daily rainfall depth - PD (mm) 118,6 145,7
Catchment design rainfall
111,5 132,6
Step 7: Design stormflow depth estimation
For each sub-area or HRU which the catchment has been divided into, the stormflow is
calculated using Equation 3.24, as shown in Table 3.18. For example, the computation for
the 20 year return period stormflow from HRU 1 is:
(P  Ia) 2
Q
for P > Ia
…(3.24)
P  Ia  S
where
Q = stormflow depth (mm),
P = daily rainfall depth (mm), usually input as a one-day design rainfall for a
given return period,
S = potential maximum soil water retention (mm),
 index of the wetness of the catchment's soil prior to a rainfall event,
Ia = initial losses (abstractions) prior to the commencement of stormflow,
comprising of depression storage, interception and initial infiltration (mm)
= 0,1S (recommended for use in South Africa)
Q 20 
111,5  (0,1  75,9)2
111,5  (0,1  75,9)  75,9
3-33
 60,0 mm
Flood calculations
Table 3.18: Calculation of stormflow depth (mm)
Return period (years)
20
50
Design stormflow depth
Sub-Area
(mm)
HRU 1
60,0
77,8
56,5
73,8
HRU 2
HRU 3
20,7
30,4
HRU 4
56,5
73,8
Step 8: Total stormflow depth
The stormflow from each sub-area is area weighted to calculate an equivalent stormflow
depth from the entire catchment using Equation 3.25 with the results shown in Table 3.19.
Q
N
Q A
i
… (3.25)
i
i 1
where
Q =
Qi =
Ai =
N =
average stormflow depth from entire catchment (mm)
stormflow depth (mm) from i-th sub-area calculated using Equation 3.24
fraction of sub-area of total catchment area for i-th sub-area
number of sub-areas
Table 3.19: Calculation of total stormflow depth
Return period (years)
20
50
Total runoff depth (mm) 50,4 66,3
Step 9: Total runoff volume
The stormflow volume from the catchment is calculated using Equation 3.26 and is given in
Table 3.20.
QA
1000
where
V =
stormflow volume (m3x106)
Q =
stormflow depth (mm)
A =
catchment area (km2)
… (3.26)
V
Table 3.20: Calculation of total stormflow volume
Return period (years)
20
50
Total runoff volume (m3x106)
1,4
1,9
Step 10: Peak discharge estimation
The peak discharge from the catchment is calculated using Equation 3.27.
q 
p
0,2083AQ
1,83L
… (3.27)
3-34
Flood calculations
For the 20 year return period, the peak discharge is calculated as:
0,208328,550,4  204,5 m³/s
q 
p
1,830,8
Results
The computed peak discharge for the 20 and 50 year return periods are summarised in Table 3.21 for
both the manual calculation method, as summarised above, and computed by the Visual SCS-SA
software. The differences in the calculated peak discharge by the two methods are a result of:
(i)
(ii)
No adjustment of the initial CNs into final CNs is included in the manual method. In the
Visual SCS-SA method, the median condition method was used to adjust the initial CNs into
final CNs, thus accounting for typical soil moisture conditions.
The manual method does not use the incremental unit hydrograph approach and does not take
into account the regionalised typical rainfall hyetographs, both of which are used in the Visual
SCS-SA software.
Table 3.21: Computed peak discharge
20
Return period (years)
50
Peak discharge (m3/s): Manual method 204,5 268,9
Peak discharge (m3/s): Visual SCS-SA
181,7 245,0
A standard calculation sheet is included in Appendix 3C for the manual method. The output from the
Visual SCS-SA software is shown in Figure 3.22 and Figure 3.23. The manual method outlined in this
guide is a simplified version of the adaptations to the SCS method for South Africa. The full
adaptations can be performed manually using the SCS-based design runoff user manual developed by
Schmidt and Schulze (1987b). The full adaptations are incorporated into the Visual SCS-SA software,
including the estimation of design rainfall using the RLMA&SI developed by Smithers and Schulze
(2003).
300
Discharge (m3/s)
250
200
150
100
50
0
600
700
800
900
1000
1100
1200
Time (minutes)
20 Year
50 Year
Figure 3.22: Hydrographs generated by Visual SCS-SA
3-35
Flood calculations
CATCHMENT NAME
PROJECT NO
RUN NO
TOTAL CATCHMENT AREA (km2)
STORM INTENSITY DISTRIBUTION TYPE
CATCHMENT LAG TIME (h)
COEFFICIENT OF INITIAL ABSTRACTION
CURVE NUMBERS:
Sub-catchment 1
Sub-catchment 2
Sub-catchment 3
Sub-catchment 4
Initial
77
75
49
75
:
:
:
:
:
:
:
Garsfontein
Example
1
28.50
3
0,80
0,10
Final
72,1
70,4
49,0
70,4
RETURN PERIOD (YEARS)
20
50
DESIGN DAILY RAINFALL DEPTH (mm)
111
132
DESIGN STORMFLOW DEPTH (mm)
Sub-catchment 1
Sub-catchment 2
Sub-catchment 3
Sub-catchment 4
51,4
48,6
20,5
48,6
67,8
64,5
30,1
64,5
43,8
58,6
439,3
415,2
116,8
276,8
579,5
551,4
171,7
367,6
1,2
1,7
67,3
67,1
181,7
245,0
TOTAL RUNOFF DEPTH (mm)
DESIGN STORMFLOW VOLUME
(thousands m3)
Sub-catchment 1
Sub-catchment 2
Sub-catchment 3
Sub-catchment 4
TOTAL STORMFLOW VOLUME
(millions m3)
COMPUTED CURVE NUMBER
PEAK DISCHARGE (m3/s)
Figure 3.23 : Output from Visual SCS-SA
3-36
Flood calculations
3.1.5
Empirical methods
Peak discharges for return periods less than or equal to 100 years can be determined by means of an
empirical deterministic method developed by Midgley and Pitman. The formula reads:
Q T  0,0377KT PA 0,6C 0,2
… (3.28)
where:
QT = peak flow for T return period (m³/s)
KT = coefficient based on veld-type region (see Figure 3.24 and Table 3.22).
P
= mean annual precipitation over catchment (mm/a) (see Figure 3.5 or utilise Design
Rainfall software for the catchment (see Figure 3.11).
Α S
and C 
(Catchment parameter with regard to reaction time) … (3.29)
L LC
where:
A
S
L
LC
=
=
=
=
area of catchment (km²)
average slope of stream (m/m)
hydraulic length of catchment (km)
distance between outlet and centre of gravity of catchment (km)
Table 3.22: Constant values of KT for different veld types
Return period T in years
10
20
Zone number and Generalized Veld type
(Figure 3.15)
1
50
100
Coastal tropical forest
0,17
0,23
0,32
0,40
Schlerophyllous bush
0,42
0,83
0,52
1,04
0,68
1,36
0,80
1,60
3
Mountain sourveld
0,29
0,40
0,55
0,70
4
Grasslands of interior plateau
0,59
0,68
0,95
1,20
0,59
0,80
1,11
1,40
0,59
0,68
0,95
1,20
Karoo
0,33
0,67
0,45
0,91
0,63
1,26
0,80
1,60
7
False Karoo
0,67
0,91
1,26
1,60
8
Bushveld
0,42
0,57
0,79
1,00
9
Tall sourveld
0,50
0,68
0,95
1,20
2
Winter
All year
Highland sourveld and Dohne
sourveld
As for Zone 5 – but soils weakly
developed
5
5A
6
Winter
All year
With the catchment being in veld-type zone 8, the KT values are 0,57 and 0,79 for the 1:20 and 1:50
year return periods respectively. The calculated catchment parameter C with regard to reaction time is
0,1238.
The flood peaks as determined with the empirical method for the 1:20 and 1:50 year return periods are
78,85 m³/s and 109,28 m³/s respectively.
3-37
Flood calculations
Figure 3.24: Regions with generalised veld types in South Africa
3.1.6
Comparison of solutions
Table 3.23 summarises the results for the five methods used in this example.
Table 3.23: Comparison of solutions
Return period
Method
1:20
1:50
Rational (Alternative 1)
164
224
Rational (Alternative 2
184
243
Rational (Alternative 3)
128
166
Unit Hydrograph
129
172
SDF
125
183
SCS-SA
205
269
Empirical
79
109
3-38
Flood calculations
3.2
Worked example 3.2 - Large catchment
The second worked example is a design flood calculation for a new low-level bridge across the Tsitsa
River, which runs through the Eastern Cape in a south-easterly direction (see Figure 3.25). The
position of the proposed Tsitsa low-level river bridge is shown on Figure 3.25.
Figure 3.25: Proposed Tsitsa low-level river bridge position
The catchment characteristics were determined (see Table 3.24 ), and are used in the calculation of the
flood peaks for various recurrence intervals.
Table 3.24: Catchment characteristics
Description of characteristic
Determined value
Comment
Catchment area (see Figure 3.25)
4318 km²
Catchment area may be clearly defined
Starts at Antelope Spruit, joins the
Length of longest watercourse
Tsitsana River and further downstream
179,5 km
(see Figure 3.27)
joins the Ixnu River to form the Tsitsa
River
Height difference
Total height difference equals 1 814 m,
(1085-method)
500 m
very steep slopes along the upper reaches
(See Figure 3.28)
of the water course
Average catchment slope
0,37%
See detailed description below
Distance to catchment centroid
85 km
SDF Drainage basin number
23
Based on calculated average from a
Average rainfall
860 mm
number of weather stations in the T35
drainage basin
Catchment area falls within regions K5
RMF K-factor
5,0 – 5,2
and K6 (assume highest value).
(See Figure 3.26)
3-39
Flood calculations
Description of characteristic
Description of catchment run-off
characteristics
Generalised veld type zone
(Figure 3.24)
Gauging station (see Figure 3.29)
Determined value
Rural area only with a
combination of flat and hilly
zones, steep slopes along
perimeter of catchment and
pans with slopes <3%;
permeability varying from
permeable
to
semipermeable, light bush and
cultivated lands, as well as
grasslands.
Comment
Zone 5
T3H016 Tsitsa River
Xonkonxa
Latitude: 31°14’13’’
Longitude: 28°51’15’’
@ This gauging station is close to the
N2 river bridge approximately
5 km upstream of the proposed
bridge site
Figure 3.26: Maximum flood peak regions in southern Africa from Kovács
3-40
Flood calculations
Figure 3.27: Catchment area and longest watercourse (3.21)
Figure 3.28: Watercourse profile and average slope
3-41
Flood calculations
Figure 3.29: Gauging station (T3H016 Tsitsa River @ Xonkonxa)
3.2.1
Statistical method
There is a gauging station approximately 5 km upstream of the proposed bridge site, and flow data
from 1951/52 until 1997/98 are available. Historical flood data for the gauging station were obtained
from the Department of Water Affairs and Forestry. The gauging station, T3H016, is situated at the
N2-Bridge. The data unfortunately contain periods, full hydrological years and parts thereof, during
which the flow was not measured. The hydraulic capacity of the structure, which is 1091 m³/s, was
exceeded on at least three occasions. The data as used in the statistical analysis are shown in Table
3.25.
The flood peak of March 1976 measured at the Tsitsa River gauging station was one of the flood peaks
used in the derivation of the Francou-Rodier K-values for this specific region.
The historical data indicated that the flood peak was higher than 1091 m³/s, which is the maximum
capacity of the gauging station. In a technical report entitled, “Maximum flood peak discharges in
South Africa: An empirical approach”, Report No. TR105, by Kovács, a peak flow of 1 699 m³/s was
used in deriving the Francou Rodier K-value. The maximum recorded water level was 3,48 m. This
represented the highest peak flow recorded up to March 1976. The other high peak flow of February
1972 was less than this peak flow (i.e. between 1 091 and 1 699 m³/s), and it was estimated as
1 364 m³/s.
Another peak flow event, during which the measuring weir was overtopped, occurred in October 1976.
It is estimated that this peak flow was 1347 m³/s.
3-42
Flood calculations
Year
1951/52
1952/53
1953/54
1954/55
1955/56
1956/57
1957/58
1958/59
1959/60
1960/61
1961/62
1962/63
1963/64
1964/65
1965/66
1966/67
1967/68
1968/69
1969/70
1970/71
1971/72
1972/73
1973/74
1974/75
1975/76
1976/77
1977/78
1978/79
1979/80
1980/81
1981/82
1982/83
1983/84
1984/85
1985/86
1986/87
1987/88
1988/89
1989/90
1990/91
1991/92
1992/93
1993/94
1994/95
1995/96
1996/97
1997/98
1998 - 2004
Table 3.25: Historical annual maximum flood peaks for T3H016
Discharge
Comment
Description
Adopted peak flow
(m³/s)
value (m³/s)
60
112
120
197
126
188
188
274
185
52
338
788
488
322
343
492
111
380
303
660
1091
229
326
297
1091
1091
926
82
97
-1
-1
-1
295
851
443
332
881
904
672
90
301
110
580
273
995
486
709
-1
Incomplete year
Incomplete year
Includes summer period
Too short year
Incomplete year
Too short year
Incomplete year
Incomplete year
Includes summer period
Too short year
Rating limit exceeded
From TR105
Rating limit exceeded
Rating limit exceeded
From TR105
From TR105
Incomplete year
Incomplete year
Missing data
Missing data
Missing data
Too short year
Includes summer period
Incomplete data
Incomplete data
Incomplete data
Missing data
Includes summer period
Includes summer period
Includes summer period
60
112
120
-1
126
188
188
274
185
-1
338
788
488
322
343
492
111
380
-1
660
1364
229
326
297
1699
1347
926
-1
97
-1
-1
-1
295
851
443
332
881
904
672
90
301
110
580
273
995
486
709
-1
Based on the historical flow records the results from statistical analyses are shown in Table 3.26.
Equations and statistical tables are included in Appendix 3A.
3-43
Flood calculations
Table 3.26: Statistical analyses for Tsitsa river gauging station T3H016 (missing data excluded)
Return Extreme value
General
Log Pearson
Log extreme
Log normal
period
Type 1
extreme value
Type 3
value
2
421
414
352
358
307
5
766
758
714
719
645
10
994
991
1035
1022
1057
20
1214
1221
1401
1359
1696
50
1497
1527
1980
1850
3126
100
1710
1764
2507
2286
4953
The frequency distribution curve that fitted the data the best was the Log Pearson Type 3 curve (LP3)
(see Figure 3.30).
Figure 3.30: Log Pearson Type 3 fit through historical data points
The following gauge record information relates to Figure 3.30.
YT (record length in years) = 53
NA (peaks ≥ high threshold) = 1
NB (peaks between thresholds excluding missing data) = 39
LW (non-zero peaks below low threshold) = 0
ZR (zero flows) = 0
NC (missing data) = 13
3.2.2
SDF method
The calculation sequence to determine the flood peaks has been described in the first worked example,
and will therefore not be repeated here. The main results are presented in Table 3.27. In this example
the point precipitation is obtained from the weather service station selected for this basin from TR102;
i.e. Station nr. 180439 @ INSIZWA.
3-44
Flood calculations
Description
Area (km²)
L (km)
S (m/m)
TC (hours)
M (mm)
R (days)
C2 (%)
C100 (%)
Return period
PtT
ARF (%)
PavgT (mm)
IT (mm/hour)
CT
QT (m³/s)
3.2.3
Table 3.27: Results of SDF calculation
Answer obtained
4318
179,5
0,0037
31,16
60
45
10
80
1:10
1:20
1:50
116,81
144,32
180,69
80
80
80
93,23
115,19
144,21
2,99
3,70
4,63
0,485
0,593
0,716
1739
2628
3974
1:100
208,20
80
166,17
5,33
0,80
5117
Empirical methods
Peak discharges for return periods less than or equal to 100 years could be determined by means of an
empirical deterministic method developed by Midgley and Pitman. The formula reads:
Q T  0,0377K T PA 0,6 C 0,2 … (3.30)
where:
QT
KT
P
= peak flow for T return period (m³/s)
= coefficient based on veld-type region (see Figure 3.24 and Table 3.22).
= mean annual precipitation over catchment (mm/a) (see Figure 3.5 or utilise Design
Rainfall database for the catchment (see Figure 3.11).
Α S
(Catchment parameter with regard to reaction time)
… (3.31)
and C 
L LC
where:
A
= area of catchment = 4318 km²
S
= average slope of stream = 0,0037 m/m
L
= hydraulic length of catchment = 179,5 km
LC
= distance between outlet and centroid of catchment = 85 km
In this example the catchment falls within Zone 2 (All year) with KT values of K10 = 0,83,
K20 = 1,04, K50 = 1,36 and K100 = 1,60
The calculated catchment parameter C with regard to reaction time is 0,01721.
The flood peaks as determined using the empirical method (Equation 3.30) for the different return
periods are shown in Table 3.28.
Table 3.28: Flood peaks based on empirical method
Return period
Peak flows (m³/s)
10
1 812
20
2 270
50
2 969
100
3 493
3-45
Flood calculations
The regional maximum flood may be calculated as follows using the Francou-Rodier relationship:
 Α 
Q RMF  10  8 
 10 
1  0,1K
6
…(3.32)
where:
QRMF =
K
=
106
108
=
=
regional maximum flood peak flow rate (m³/s)
regional constant (Obtainable from the regional classification detailed
in Figure 3.26 and simplified in Table 3.29)
total world MAR (m³/s)
total world catchment area (km²)
Step 1: Determine the catchment area: 4318 km².
Step 2: Identify the region in which the site is located (Figure 3.26). In this example, as shown in
Table 3.24, the region is K6 (higher K-value). Note that the regions on the map refer to the
location of the site and not to the catchment. Only if the site is located near a boundary
between regions would it be necessary to consider adjusting the K-factor.
Step 3: Utilise the equation provided in Table 3.29 to calculate the RMF as 8059 m³/s
Kovács
region
K
K1
K2
K3
K4
K5
K6
K7
K8
2,8
3,4
4,0
4,6
5,0
5,2
5,4
5,6
Table 3.29: RMF region classification in southern Africa
Transition zone
Flood zone
Number
of
Area range
QRMF
Area range
QRMF
floods #
(km²)
(m³/s)
(km²)
(m³/s)
6
1 – 500
30A0,262
500 – 500 000
1,74A0,72
12
1 – 300
50A0,265
300 – 500 000
5,25A0,66
0,34
26
1 – 300
70A
300 – 300 000
15,9A0,60
55
1 – 100
100A0,38
100 – 100 000
47,9A0,54
155
1 – 100
100A0,50
100 – 100 000
100A0,50
0,56
61
1 – 100
100A
100 – 30 000
145A0,48
34
1 – 100
100A0,62
100 – 20 000
209A0,46
25
1 – 100
100A0,68
100 – 10 000
302A0,44
Notes: # Recorded flood data are reflected in the DWAF report TR105
3.2.4
Comparisons of solutions
Comparing the calculated flood peaks below (Table 3.30) provides an overview of the range of
expected floods. Based on the flood calculations above, a structurally sound low-level bridge structure
was designed to withstand the high floods and provide a safe crossing during the lower floods (Figure
3.31 and Figure 3.32). Further analysis was also performed on the historical flow data to ensure that
the bridge will not be inundated for prolonged periods, cutting off communities from each other.
Table 3.30: Comparison of calculated peak flows (m³/s)
Return
Empirical
Standard
Regional
Statistical
period
design flood
maximum
(LP3)
flood (RMF)
1 812
1 739
1 022
10
2 270
2 628
1 359
20
2 969
3 974
3 951*
1 850
50
3 493
5 117
4 796*
2 286
100
8 059
*Using QT/QRMF ratios as detailed in Appendix 3D.
3-46
Flood calculations
Figure 3.31: Tsitsa crossing downstream view
Figure 3.32: Tsitsa crossing
3-47
Flood calculations
4
HYDRAULIC CALCULATIONS
4.1
Example 4.1 - Flow characterisation, energy gradient and normal depth
Problem description Example 4.1
The total discharge through a channel section is 477 m³/s. The dimensions and absolute roughness
values for the channel are shown below (Figure 4.1).
Figure 4.1: Cross-section of channel
Determine:
(i)
(ii)
(iii)
(iv)
(v)
The energy gradient (Sf).
Whether the flow is sub- or supercritical.
The average velocity through section 3.
Whether the flow is laminar or turbulent.
The normal flow depth.
Solution Example 4.1
Divide the channel as shown above and derive the following details (Table 4.1):
Table 4.1: Channel characteristics (Example 4.1)
Section
Parameter
1
2
3
Area (A)
28,5 m²
9,0 m²
49,25 m²
Wetted perimeter (P)
12,24 m
3,0 m
15,42 m
Hydraulic radius (R = A/P)
2,33 m
3,0 m
3,19 m
Absolute roughness (ks)
0,3 m
0,7 m
0,7 m
Chézy
 12R 

C  18 log 
35,4 m½/s
30,8 m½/s
31,3 m½/s
 ks 

The energy gradient (Sf )
By assuming uniform flow conditions the local slope of the channel, S0, may be set equal to
the energy slope, Sf. Continuity of mass and energy (Chézy equations) combined provide the
following relationships:
4-48
Hydraulic calculations
Q total 
Q
Q total  A1 C1 R 1Sf  A 2 C 2 R 2Sf  A 3 C 3 R 3Sf


Q total  28,535,4 2,33  9,030,8 3,0  49,2531,3 3,19 Sf
Q total  (1541 480  2754) Sf
Sf 

Q 2total
4776 2
 0,01 m/m (Energy gradient)
Determine the flow regime
Q 2 B 477  25,5 

 Fr  0,952  1,0 thus subcritical
gA 3 9,81(86,75) 3
2
(Froude)² =

Determine the average velocity through section 3
Q 3 2754 477


 5,59 m/s
A 3 4776 49,25
v3 

Identify the flow type
Calculate the Reynolds Number
vR
Re 
υ
477
Q 
v
 5,50 m/s
 A 28,5  9  49,25
R
86,75
A 
 2,83 m
 P 12,24  3,0  15,42
υ
Re 

= 1,14 x 10-6 m²/s (kinematic viscosity of water)
vR 5,502,83

 13,65  10 6
υ
1,14 x 10 6
Re >> 2000  Highly turbulent
Calculation of normal flow depth
The normal (uniform) flow depth for a given discharge is calculated by the same procedure,
except that the flow depth is the unknown quantity and the energy gradient, Sf, is equal to the
average (near constant) bed slope, S0.
Q total  477,0  A1 C1 R 1Sf  A 2 C 2 R 2Sf  A 3 C3 R 3Sf
As shown above, the area, wetted perimeter and hydraulic radius can be written in terms
of the unknown depth, Y. If Y is the depth in section 3, then the variables may be written
as shown in Table 4.2.
4-49
Hydraulic calculations
Table 4.2: Channel characteristics written in terms of unknown flow depth (Example 4.1)
Section
Parameter
1
2
3
2
Y

1 2

 9Y  2 
Y  6Y  14
3Y - 2 
Area (A) (m2)
2
 4

Wetted perimeter (P) (m)
Hydraulic radius (R = A/P)
(m)
Absolute roughness (ks) (m)
Chézy
 12R 
½
 (m /s)
C  18 log 
 ks 
3,0

5 
 8 7
Y 

4


(A/P) *
Y - 2 
(A/P) *
0,3
0,7
0,7
*
*
*
8 

2 Y  2 
Note: * The relationship is not shown, but could be obtained from the combination of the given relationships.
With a known slope, S0, and flow rate, Q, Y can be solved. In this case Y = 5 m.
4.2
Example 4.2 - Gradually varying river flow (backwater calculation – simple sectional
details)
Problem description Example 4.2
Determine the flood level at section 3 for a river of trapezoidal section with side slopes 1:2 and
varying bed width. The characteristics of the cross-sections are reflected in Table 4.3.
Q50 = 43,3 m³/s
Section
1
2
3
4
5
Table 4.3: Characteristics of the river cross-sections
Base width
Bed level
Chainage
Manning, n
(m)
(m)
(m)
(s/m1/3)
6
1203,02
0
0,032
4,8
1203,24
65
0,026
5,6
1203,75
147
0,024
5,4
1203,99
214
0,028
5,6
1204,42
280
0,024
Remark
Downstream
Site
Upstream
Using the principle of conservation of mass and energy would solve this problem. It is assumed that
the flow rate is constant at 43,3 m³/s. It is necessary to determine the type of flow to establish the
control, and then to work away from the control.
Although the assumption that uniform flow will be present at the cross-sections is incorrect,
calculation of the “normal flow depth” at each section will give an indication of the type of flow. In
Table 4.4 the “normal flow depths” have been calculated. This is not the solution to the problem but
merely a way to establish the type of flow!
Solution Example 4.2
From Table 4.4 it could be concluded (Fr < 1) that the flow will be subcritical and hence that the
control will be downstream.
4-50
Hydraulic calculations
Section
ID
a*
1
2
3
4
5
Position
ID
b
Downstream
Site
Upstream
Invert
(m)
c
3,02
3,24
3,75
3,99
4,42
Table 4.4: Flow characteristics (Example 4.2)
Calculation based on uniform flow assumption
Slope (local)
Yn
A
P
R
Cal Q
(m/m)
(m)
(m²)
(m)
(m)
(m³/s)
d
e
f
g
h
i
0,003
1,980
19,718
14,854
1,327
43,3
0,006
1,653
13,403
12,194
0,973
43,3
0,004
1,725
15,614
13,316
1,027
43,3
0,007
1,622
14,026
12,656
0,958
43,3
Fr
j
0,589
0,952
0,792
0,908
Note: * Refer to the legend table (Table 4.6)
Now start with the assumption of a flow depth at section 1 (downstream) and work upstream by
applying the continuity of energy as shown in Table 4.5. Assume that the secondary losses will be
negligible.
The flow depth at section 1 is assumed to be 2,258 m. The total energy level at this section is then
equal to 2,427 m.
Table 4.5: Flood level calculations
Section
ΔX
ID
a
1
(m)
k
H total
Fr
energy
(m)
l
m
1205,246 0,589
Area
P
Velocity
E1
Sf
(m²)
n
19,718
(m)
o
14,854
(m/s)
p
2,196
(m)
(m/m)
q
r
1205,246 0,00338
1205,544 0,675
17,499
13,709
2,474
1205,544 0,00299
65
2
1205,832 0,904
14,105
12,765
3,070
1206,195 0,692
17,282
13,829
2,506
1206,195 0,00366
(m)
t
3,031
1206,505 0,00459
-0,000622 1205,833
66
5
(m/m)
s
0,002349 1205,545
1205,832 0,00475
67
4
E2'
0,000198 1205,245
82
3
(So-Sf)avg
0,002394 1206,195
1206,505 0,889
14,286
12,832
Δ(E2'-E1) Water
level
(m)
(m)
u
v
1205,00
-0,001
1205,23
0,000
1205,35
0,001
1205,87
0,000
1206,04
Notes: A brief description of the columns content for the above tables is listed in Table 4.6
Table 4.6: Legend table
Column ID Description of the variable
a
Section identification
b
Description of the position
c
Invert level (m)
Local slope calculated from the level difference between that of the section and the
d
upstream section divided by the distance between the sections
e
Yn is the calculated flow depth assuming that uniform flow characteristics will occur
f
Calculated area for the given Yn
g
Calculated wetted perimeter for the given Yn
h
Calculated hydraulic radius for the given Yn
i
Calculated flow rate
j, m
Froude number
k
Distance between the sections
n
Calculated area
o
Calculated wetted perimeter
4-51
Hydraulic calculations
Column ID
p
q
r
s
t
u
v
4.3
Table 4.6: Legend table (continued)
Description of the variable
Calculated velocity
Calculated total energy
Calculated energy slope
Calculated difference of the energy slope and the channel slope
Specific energy
Difference in the specific energy
Calculated water level
Example 4.4 – Negligible energy losses (converging flow over short distance)
Problem description Example 4.4
A concrete chute with a stream width of 0,6 m conveys water down the side of an embankment 3,0 m
high with a slope of 1,5 vertical to 1,0 horizontal, see Figure 4.2. The discharge is 0,1 m³/s and the
water flows away from a trough in the road profile. Calculate the flow velocity, depth of flow and
Froude number at the toe.
Figure 4.2: Concrete chute down embankment
Solution Example 4.3
Since the water has to dam in order to run off, a control is created at the upper end (Fr = 1)
Q2Β
 3 1
gΑ c
With:
Q
=
B
=
Ac =
g
=
=
yc
vc =
0,1 m³/s
0,6 m
Bcyc = 0,6yc
9,81 m/s²
0,141 m
1,178 m/s
2
2
and E c  y c  v c  0,141  1,178   0,212 m
2g
29,81
Since the channel is very steep, the energy losses will be small in relation to the change in level.
4-52
Hydraulic calculations
Consequently H  3,0  0,212  y 2 
v 22
can be assumed.
2g
q  v 2 y 2  0,167 m 3 /sm
v2
v 2 = 7,9 m/s; y2 = 0,021 m and Fr2 
gy 2
 17
The actual velocity will be slightly lower. (If H>> y2, then v2  2gH )
4.4
Example 4.4 – Transition losses
Problem description Example 4.5
The normal (uniform) flow depth in a long 2 m wide, rectangular canal is 2 m and the normal flow
velocity 2 m/s. The Manning n-value is 0,02 s/m1/3. There is a 90° bend with a centre-line radius of
7 m. Calculate the Froude number for uniform flow conditions.
Solution Example 4.4
Calculate the flow depths just upstream and just downstream of the 90° bend.
Frn 
vn
gy n

2,0
9,812,0
 0,452 (based on the normal flow depth)
Downstream control and hence the depth just downstream of the bend will be 2 m.
Energy head loss through bend: h  
2,0 2,0 2,0   0,1165 m
2B v 2
.

7,0 2 9,81 
rc 2g
2
Energy equation:
Upstream energy head: H 1  H 2  h l 
H1 
v2
 y2  hl
2g
2,02  2,0  0,1165  2,321 m
29,81
v12
 2,321 m
2g
Write the velocity in terms of the upstream flow depth (y1) using continuity:
 y1 
v1 
Q 2,02,0  2,0 4,0


y1 2,0
A1
y1
2
 4,0 


y1 

 y1 
 2,321 m . Solving the only unknown term - y1
29,81
y1 = 2,143 m (depth upstream of bend)
4-53
Hydraulic calculations
4.5
Example 4.5 – Identification of acting controls
Problem description Example 4.5
Water flows across a 16 m wide road. The road has cross-falls of 2%. Calculate the discharge per unit
width that would flow across the road when the adjacent level rises 0,5 m above the shoulder, see
Figure 4.3.
Figure 4.3: Flow across the road
Solution Example 4.5
Assume that the control (point of release) occurs at the crown (B). If there are no energy losses
between A and B, the specific energy at the top of the crown will be 0,5 – 0,16 = 0,34 m and the
critical depth yc = 0,227 m (two thirds of the specific energy).
The corresponding discharge per unit width:
3
2
c
q  v c y c  g y  0,338 m 3 /s.m
q2
 0,209 m
g
yc  3
and
Ec 
Assume that the actual discharge is 0,3 m³/s.m
3
y c  0,314 m
2
With this discharge, the normal flow depth (Manning) will be given by:
5
1
y 3S 2
q
n
With a Manning n-value = 0,013 s/m1/3
5
1
y 3 0,02  2
0,3 
0,013
y n  0,116 m  y c  0,209 m
The slope of 2% is thus hydraulically steep and the control is indeed at B. If yn was found to be greater
than yc this would mean that the control was at C, and the depth there would be yc, from which point
calculations would then progress upstream. Because the depths of flow are small, one should test to
see whether the flow is indeed turbulent.
Re 
vy
0,3

 2,6  10 5  2000 , indicating the flow is turbulent.
6
υ 1,14  10
Now determine the depth yA at A.
4-54
Hydraulic calculations
0,5  y A 
v A2
v2
 0,35 A
2g
2g
(Energy equation with provision for transition losses)
and y A v A = 0,3 (continuity)
Thus yA = 0,472 m
The depth varies from 0,209 to 0,472 m and since the cross-sectional areas differ by more than 40%,
more than one increment should be used. Use three increments; i.e. depths of: 0,209; 0,297; 0,384 and
0,472 m (see Figure 4.4), and Table 4.7.
Figure 4.4: Increments of flow depth across the road
dE
 So  Sf (Energy equation for prismatic channels)
Δx
x 
dE
So  Sf
So = -0,02 m/m (uphill)

v2  
v2 
dE   y 1  1    y 2  2 
2g  
2g 

Sf 
v2n 2
y
y
(m)
0,209
0,297
0,385
0,472
4
3
Table 4.7: Calculation table (Example 4.5)
E
Sf
Sf(average)
Δx
(m)
(m/m)
(m/m)
(m)
0,314
0,002792
0,001831
1,60
0,349
0,000870
0,000619
3,23
0,416
0,000368
0,000277
3,81
0,493
0,000185
ΣΔx = 8,64 m
ΣΔx = 8,64 > 8,0 thus the discharge per unit width should be less (i.e. q should be smaller).
Choose smaller q and repeat until ΣΔx ≈ 8,0 m for a more accurate answer.
4-55
Hydraulic calculations
5
SURFACE DRAINAGE
A number of typical problems are explained below.
5.1
Worked Example 5.1 - Flow depth on the road surface
Problem description Example 5.1
Determine the depth of flow if the rainfall intensity is 100 mm/h on a roadway with a width of 10 m
and a cross-fall of 2%. The road gradient is 6%.
The aim should always be to limit the flow depth on the road surface to a maximum of 6 mm to
prevent hydroplaning.
Solution Example 5.1
Figure 5.1 provides the relationship between the road gradient and road cross-fall, width of the
roadway, the energy slope and the flow depth.
5-56
Surface drainage
Figure 5.1: Depth of sheet flow on road surface (Laminar flow conditions assumed)
Figure 5.1 could be used to determine the flow depth by starting with the road gradient (n2) and
moving anti-clockwise on the nomograph.
Sf, the energy slope is dependent on n1 and n2 and may be calculated as follows:
Sf  n 12  n 22
2
Sf  2  6
…(5.1)
2
Sf  6,32%
Calculate the flow path length, Lf:
1


n2 2
6 2
L f  W 1  22   10 1  2

n1 
2 


1
2



…(5.2)
5-57
Surface drainage
L f  31,62



 31,62100
d  4,6x102 L f I
d  4,6x102
5.2
0,5
S 
0.2
f
0,5
…(5.3)
0,06320.2  4,49 mm
Worked Example 5.2 – Capacity of side channel
Problem description Example 5.2
Determine the flow capacity in a side channel cross section shown in Figure 5.2, and the dimensions
provided below.
Figure 5.2: Channel cross section
Manning roughness, n = 0,015 s/m1/3
Flow depth, Y = 100 mm
Y1 = 40 mm
1/ZA = 1/20
1/ZB = 1/40
Road gradient = 5 %
Solution Example 5.2
The following relationships could be obtained for geometry (units in mm):
X = ZA(Y – Y1)
…(5.4)
X = (20)(100 – 40)
X = 1200
ZBY1 = (40)(40)
ZBY1 = 1600
Top width, T = 1200 + 1600 = 2800 mm
T
Z
Y
Q = QA+ QB
see calculations in Table 5.1.
S = 0,05 m/m
Manning n = 0,015 s/m1/3
Parameter
Table 5.1: Channel flow characteristics
Section A
5-58
Section B
Surface drainage
Cross-sectional area (m²)
Wetted perimeter (m)
A A  0,50,1  0,041,2
A B  0,5 0,040 1,6 
A A  0,084
A B  0,032

PA  0,1  0,06   1,2 
2

2 0,5
PA  1,302
Hydraulic radius (m)

PB  1,6 0,04   0,001
2

2 0,5
0,04
PB  1,6001
RA = 0,06454
RB= 0,020
QA = 0,2015
QB = 0,03514
Flow rate from Manning (m3/s)
Q
R 0,667S0,5
n
A
The total capacity of the channel is:
Qtotal = 0,2366 m3/s
5.3
Worked Example 5.3 – Capacity of drop grid inlet
Problem description Example 5.3
Determine the flow capacity of a drop grid inlet, dimensions of 0,9 by 0,6 m and a submergence of
0,2 m if the approaching flow is subcritical. For comparison with Figure 5.6 assume that the inlet
coefficient = 0,8 and the blockage factor, F = 0,5.
Solution Example 5.3
Figure 5.3 provides the relationship of flow rate for an orifice control or a broad-crested weir.
Figure 5.3: Section through outlet: Drowned conditions
Q  CFA 2gH
where:
C
F
A
H
=
=
=
=
…(5.5)
inlet coefficient (0,6 for sharp edges or 0,8 for rounded edges)
blockage factor (say 0,5)
effective cross-sectional plan area of the opening (m²)
total energy head above grid (m)
5-59
Surface drainage
Figure 5.4: Example of type of grid inlet
From Equation 5.5:
Q  1,77A
H
A  0,90,6  0,54 m²
Q  1,77 0,54  0,2
Q = 0,427 m3/s
The calculation of the flow rate was based on the orifice equation.
5.4
Worked Example 5.4 – Kerb flow
Problem description Example 5.4
Determine the kerb flow rate if the flow depth is 100 mm and the road gradient is 4%. The road crossfall is 2% and the Manning roughness is 0,015 s/m1/3.
Solution Example 5.4
The Manning equation may be used.
5
1 A3
Q
n 2
P3
A
S
1
YT  0,5 0,1 5,0  0,25 m²
2
5-60
Surface drainage
P  Y  Y 2  T 2  0,1 
S
0,12  5,02
 5,101 m
4
 0,04 m/m
100
5
0,25 3
1
Q
0,015 5,101 23
0,04  0,446 m³/s .
Strictly speaking, the very wide section with variable velocities should be subdivided into narrower
sections.
5.5
Worked Example 5.5 – Scour velocity
Problem description Example 5.5
Determine the maximum flow depth and velocity in a wide channel with a slope, S is 2%. The channel
is lined with stones (relative density 2,65) and representative size (more than 50% by mass) of
250 mm.
Solution Example 5.5
For a wide channel it is known that:
R=D=y
where:
R
D
=
=
hydraulic radius (m)
y = flow depth (m)
From Chezy:
 12R 
 RS
V  18log 
k
s


…(5.6)
From Shields (Equation 5.7) it follows that for a stable channel:
d1 > 11 DS
Dy
0,25 1,14
110,02
…(5.7)
m
Now the velocity can be calculated using Equation 5.6:
 121,14 
 1,140,02
v  18 log
 0,25 
v = 4,71 m/s
5-61
Surface drainage
5.6
Worked Example 5.6 – Protection measures
Problem description Example 5.6
Determine the required diameter of stones to protect the sides and bottom of a trapezoidal channel
with side angles of 25° and a flow depth of 1,8 m. The stones are slightly angular and have an angle of
repose of 30°. The channel slope is 0,1%.
Solution Example 5.6
For a stable bed the particle size (d1) should at least be:
d 1  11DS  11 1,8  0,001  0,0198 m
For stable side slopes the particle size (d2) should at least be:
8,3Ds
d2 
cosθ 1 
tan 2 θ
tan 2 φ
…(5.8)
where:
θ
Ø
=
=
angle of slope of sides of the channel (°)
angle of repose of stone material (°)
Figure 5.5: Required sizes of the stone for erosion protection of loose bed channels
(The side slope, θ, should always be smaller than the angle of repose, Ø, to ensure stability.)
From Equation 5.8:
d2 
8,3 1,8 0,001
tan 2 25 
cos 25  1 
tan 2 30 
 0,028 m
5-62
Surface drainage
6
LOW LEVEL CROSSINGS
6.1
Worked Example 6.1 – Low level crossing
Problem description Example 6.1
A river crossing structure is to be provided for a tertiary road linking rural settlements on both
banks of a river. No structure exists and vehicles such as tractors, four-wheel drive vehicles, LDVs
and donkey carts cross via the sandy riverbed. The route is not accessible for motorcars. Motorcars use
an alternative route via the main road with a length of 45 km. Although the current traffic volume is 50
vehicles per day, it is expected to increase to 300 vehicles per day, should a proper river crossing
structure be provided. The expected traffic growth rate for the next 20 years is 2% per year.
At the point of the crossing the river has a catchment area of 360 km². The 1:2 year flood has been
determined as 120 m³/s.
Test pits were excavated in the sandy riverbed. Solid rock was encountered at depths varying between
1,2 m and 2,0 m. Rock is also day lighting in places.
The approach gradients of the road are moderate and there is no horizontal curvature. The preliminary
design of the vertical alignment of the road across the structure to be provided has also been done. The
straight section in the middle (L2) has a length of 20 m, and K1 and K3 are both 4 m (refer to Figure
6.1). The slope of the road on the southern bank is - 5,6%, and on the northern bank 7,0%.
Figure 6.1: Definition of symbols for the flow over the structure
The deck thickness is taken as 500 mm, and the soffit of the deck is on average 1 400 mm above the
riverbed.
Solution Example 6.1

Design flow rate
The design level is determined as per Section 6.3.3. Design level 1 is taken as the initial choice.
Because of the expected traffic volume of 300 vehicles per day exceeding the suggested 250 vehicles
per day, the design level is increased to level 2. This is supported by the availability of an alternative
route of length less than the suggested 50 km. As the criteria suggested for design level 3 are not met,
design level 2 is selected.
6-63
Low level crossings
The design flow rate is determined from Equation 6.1:
…(6.1)
Q design  f i Q 2
From Table 6.1 follows that f2 is 0,50 and Q2 is the discharge with a 1:2 year return period (120 m³/s).
Design
level
1
Table 6.1: Levels of design for low-level structures*
Average no of times flow can be
Average length of period flow is
exceeded (hours)
Dimensionless expected to be exceeded per year
factor, fi
Min
Max
Average
Min
Max
Average
value
value
value
value
value
value
0,25
0,0
4,2
1,3
0,0
30
9,0
2
0,50
0,0
2,4
0,8
0,0
13
5,5
3
1,00
0,0
1,4
0,5
0,0
6
3,4
Note: * Based on observed data from the Northern Province
Qdesign = 0,5 x 120 m³/s
= 60 m³/s

Cross-section
With a design period of 20 years and 2% growth in traffic per year, the anticipated 300 vehicles per
day is expected to increase to 446 vehicles per day after 20 years. Because of this being less than the
suggested 500 vehicles per day and visibility being good, a single-lane structure is opted for. The
cross-fall in the direction of flow is taken as 2%.

Selection of structure
Because of good, but uneven founding conditions a low-level bridge is opted for. Six spans of 6 m
each fit the river cross-section well. Piers are 300 mm thick.

Hydraulic calculations
The capacity of the structure is determined as the sum of the flow that can be accommodated over the
structure and through the structure.
Flow over the structure
Assume supercritical flow and decide on a maximum flow depth of 0,1 m (d). The flow that can be
accommodated over the structure is determined from Equation 6.2.
Q over 
1/2
A 5/3
over S 0
2/3
n Pover
…(6.2)
A over  A 1  A 2  A 3 , or
1
1
A over  d 800K1d  dL 2  d 800K 3 d
3
3
and
…(6.3)
6-64
Low level crossings
Pover  P1  P2  P3 , or
Pover 
1
1
800K 3 d
800K 1d  L 2 
2
2
…(6.4)
where:
Qover
= the discharge that could be accommodated over the structure within the
selected flow depth (m3/s)
Aover
= area of flow over structure at the flow depth selected (m²)
S0
= slope in direction of flow, for example 0,02 or 0,03 m/m
n
= Manning n-value. For a concrete deck nconcrete
= wetted perimeter at the flow depth selected (m)
Pover
A1, A2, A3 = the areas defined in Figure 6.1 (m2)
d
= depth of flow over the structure (m)
K1
= the geometric K value for vertical curve 1
K2
= the geometric K value for vertical curve 3
With K being a vertical road alignment parameter, defined as the horizontal length of
road required for a 1% change in the gradient of the road.
S0 is 0,02 (2% as above) and Manning n roughness parameter for concrete is 0,016 s/m1/3. The crosssection area of flow is determined using Equation 6.2.
1
1
A over  d 800K1d  dL 2  d 800K 3 d where K1 and K3 are both 4 and L2 is 20 m (Equation 6.3)
3
3
Aover = 3,19 m2
Pover 
1
1
800K 3 d = 37,89 m (equation 6.4)
800K 1d  L 2 
2
2
From Equation 6.2:
A 5/3 S1/2 3,19 5 3 0,02 1 2
Q over  over2/3 0 
n Pover
0,016 37,89 2/3
Qover = 5,42 m³/s
Establish whether flow is indeed supercritical by calculating the Froude number (Equation 6.5):
Fr 
2
Q over
B
g A 3over
…(6.5)
where:
B =
g =
L1 + L2 + L3 (m), the width of the channel (or the length of the structure)
9,81 m/s², the gravity constant
and L1 
1
1
800K 3 d
800K 1d and L 3 
2
2
B = L1 + L2 + L3, L1 = L3 = 8,94 m and L2 is 20 m, giving B equal to 37,89 m
Fr = 1,87, which is > 1,0 m, confirming supercritical flow over the deck of the structure.
Flow passing through the structure
6-65
Low level crossings
Assume outlet control, then:
Q under  v under A eff
…(6.6)
v under is determined from Equation 6.7, for which the following is required:
v under 
H1  H 2
2
LB
C n eff

4/3
2g
R
…(6.7)
where:
Aeff
=
LB
v under
C
=
=
=
the effective inlet area through the structure (m²) = ΣAcell (the effective
inlet area through the structure)
the total width of the deck of the structure (m)
the velocity of flow through the structure (m/s)
factor that reflects the transition losses (Equation 6.8)
C   K inl  K out each cell
…(6.8)
Kinl and Kout are determined as follows for rectangular sections:
Kinl at outlet control:
Sudden transition:
Gradual transition:
Kinl =
Kinl =
0,5
0,25
Kout at outlet control:
Sudden transition:
Gradual transition:
Kout =
Kout =
1,0
1,0 for 45º < θ < 80º
0,7 for θ = 30º
0,2 for θ = 15º
Figure 6.2: Definition of symbols
6-66
Low level crossings
By applying the conservation of energy principle, determine the depth upstream of the structure, h as
shown in Figure 6.2, that is required to pass the flow rate, Qover:
h
v 22
d
2g
H1 = h + x + D
where:
x
D
=
=
…(6.9)
…(6.10)
the thickness of the deck (depending on the structural design outcome) (m)
the height of the soffit of the deck above the river invert level (m)
…(6.11)
H 2  D  L BS0
where:
LB
S0
= the total width of the deck of the structure (m)
= slope of the conduit underneath the structure (m/m)
Determine the depth upstream of the structure, h, that is required to pass the flow rate, Qover using
Equation 6.9.
v2
h  2  d , where v 2 = Qover/Aover = 1,70 m/s
2g
h = 0,247m
From Equation 6.10:
H1 = h + x + D, where h is as above, x = 0,5 m and D = 1,4 m
H1 = 2,147 m
From Equation 6.11:
H2 = D – LB S0, where LB = (4,0) + (2)(0,25) = 4,5 m (for the guide-blocks)
H2 = 1,4 – (4,5) (0,02)
H2 = 1,31 m
Assume Kinl = 0,5 and Kout = 1,0 (both sudden transitions), then
C = 6 x (0,5 + 1,0), see Equation 6.8.
C=9
Pcell is the total wetted perimeter of each cell (m).
Pcell = (5,7)( 2) + (1,4)(2) = 14,2 m
P
n
P n
n cell  concrete concrete  river river and assume nriver to be 0,03 s/m1/3
Pcell
Pcell
n cell 
5,7  21,40,016 5,70,03
14,2

14,2
1/3
ncell = 0,022 s/m
Peff = ΣPcell = (6)(14,2) = 85,2 m
 n cell Pcell 
n eff 
Peff
60,02214,2
n eff 
85,2
neff = 0,022 s/m1/3
6-67
Low level crossings
R = Aeff/Peff where
Aeff = (6)(5,7)(1,4) = 47,88 m2
R = 0,562 m
v under from Equation 6.7 is:
v under 
H1  H 2
2
LB
C n eff

4/3
2g
R

2,147  1,31
0,022  4,5
9

2(9,81)
0,562 4/3
2
v under = 1,344 m/s
Also from Equation 6.6 Q under  v under A eff = 64,35 m³/s
Design discharge
The capacity of the structure at the design level Qover + Qunder = 69,8 m³/s
As Qover + Qunder is larger than Qdesign (60 m³/s), the design is complete as the structure is adequate. If
this was not the case, the level of the deck would have to be adjusted, and the calculation be redone.
6-68
Low level crossings
7
LESSER CULVERTS AND STROMWATER PIPES
7.1
Example 7.1 - Determination of the required culvert size
Problem description Example 7.1
A culvert size needs to be determined which would handle the design flood (QD). The calculated 1:20
year flood (Q20) is 85 m3/s and the road can be assumed to be a Class 3 road. From Figure 7.1 the
design flood frequency is determined as T = 15 years and the calculated 1:15 year flood (Q15) is
44,5 m3/s.
Figure 7.1: Design flood frequency estimate
No significant debris is anticipated since the catchment area consists mainly of grassland. The client
favours the use of circular (pipe) culverts. The final level of the roadworks across the river will be at a
level of 2,5 m above the riverbed.
The absolute roughness, ks, for the trapezoidal river channel is 0,1 m. The cross-sectional details are
provided in Figure 7.2. The natural slope of the river, S0, is 0,0015 m/m upstream from the culvert and
it is 0,004 m/m downstream from the culvert. The culvert will be placed at the same slope as the
upstream river section. The submergence of the culvert should be limited to a H/D ratio of about 1,2.
7-69
Lesser culverts and stormwater pipes
Figure 7.2: Cross-sectional details of the natural channel
Solution Example 7.1
First calculate the normal flow depth, Yn and flow conditions in the channel upstream and downstream
of the planned culvert.

Determine the upstream normal flow depth
For a uniform channel the relationship of Chèzy can be used.
QC RS A
…(7.1)
where:
Q
C
R
A
Yn upstream
=
=
=
=
=
flow rate (m3/s)
Chèzy constant
hydraulic radius (m)
area (m2)
Y = upstream normal flow depth (notation used here) (m)
 12R 
 RS A
44,5 18 log
 ks 
 12A  AS

A
44,5  18 log 
k
P
s

 P
Substituting the values for A, P, S and ks in the above equation provides:

 (12) 8Y  (2)(0,5)(Y 2 )(2)
44,5  18 log
(0,1)(8  (2) 5 Y)

  8Y  (2)(0,5)(Y


2

)(2) (0,0015)
(8  (2) 5 Y)
8Y  (2)(0,5)(Y
2
)(2)

Solve the upstream normal flow depth Y in the above equation.
Y = 2,0 m and A = 24,0 m2, hence V = 1,851 m/s.
The flow type can be determined by calculating the Froude number,
Q2B
Fr 2 
 0,2327 and Fr = 0,482
gA 3
7-70
Lesser culverts and stormwater pipes
The flow is thus subcritical (Fr < 1) and therefore the cross-sectional area of the river may be reduced,
resulting in a deceleration of the flow and some damming upstream from the intended structure (Note:
In the case of supercritical flow it is not allowed to decelerate the flow, because it might lead to the
creation of a hydraulic jump that might breach the downstream structure).

Determine the downstream normal flow depth
In a similar way as above, the downstream normal flow depth can be determined. In this case
the downstream normal flow depth, Yds = 1,541 m, Frds = 0,841 and the flow is subcritical.
2
Total energy head upstream of the culvert, H 1  v  Y  2,175 m
2g

Determine the size of the culverts to manage the flow
The height difference between the river bed and the final road level is 2,5 m. If the optimum H/D ratio
of 1,2 is used the maximum vertical dimension of the culvert (D) is 2,5/1,2 = 2,08. Based on Figure
7.4 multiples of 1,8 m diameter pipe culverts will be used.
For a culvert with a diameter of 1,8 m and the downstream flow depth of 1,541 m, the flow will
probably be inlet controlled (to be verified) and the flow can be evaluated based on the relationship for
inlet control (Table 7.1).
Table 7.1: Relationships for the flow rate under inlet control
ROUND CULVERTS
RECTANGULAR CULVERTS
D = inside diameter (m)
D = height (inside) (m)
B = width (inside) (m)
For:
For :
0 < H1/D < 0,8
S 
 0,48 0 
gD
 0,4 
Q
D
2
0,05
0 < H1/D ≤ 1,2
 H1 
D
 
And for: 0,8 < H1/D ≤ 1,2 *
1,9
2
2
gH1
Q  C B BH1
3
3
Where: CB = 1,0 for rounded inlets (r > 0,1B)
CB = 0,9 for square inlets
And for: H1/D > 1,2
1,5
Q  C h BD 2gH 1  C h D 
 S0   H1 
 0,44    
2
D gD
 0,4   D 
Where: Ch = 0,8 for rounded inlets
(S0 = slope of culvert bed with slight
Ch = 0,6 for square inlets
effect on capacity)
Note:
* For H1/D > 1,2, the orifice formulae
D

applies Q  C D A 2 g  H 1   with
2

CD ≈ 0,6
Q
In this example, the maximum
0,05
H 1 2,5

 1,39 and the flow rate through a culvert can be determined.
D 1,8
7-71
Lesser culverts and stormwater pipes
Table 7.1 reflects that for a circular pipe culvert, under submerged conditions with H/D ≥ 1,2, the
flow rate can be determined as follows:
D

Q  C D A 2g H 1  
2

…(7.2)
2
1,8   1,8 


  8,55 m³/s
Q  0,6 29,81 2,5  π
2  
4 

The number of pipes required = 44,5/8,55 = 5,20.
Determine if it is practical to install 6 pipe culverts in the cross-section of the river.
Assume the distance between the pipes is 100 mm and the wall thickness of the pipes is about 78 mm,
then the total width of six culverts will be = (6)[1,8+(2)(0,078)] +(5)(0,1) = 12,236 m. With some
groundwork it is possible to place the culverts as is shown in Figure 7.3.
Figure 7.3: Positioning of the 6 pipe culverts
There are, however, also box culverts that could have been used here.
Figure 7.4 reflects the required culvert size for a given (design) flow rate and a H/D ratio of 1,2.
Reference to pipe and portal (box) culverts are reflected here.
By means of Figure 7.4 and by assuming that a portal (box) culvert could be used as an alternative to
the calculation above, the required culvert size for Inlet Control conditions could be obtained.
Assume that 5 culverts will be used, the flow per culvert = 44,5/5 = 8,9 m³/s.
7-72
Lesser culverts and stormwater pipes
Figure 7.4: Diagram for the determination of sizes of culverts and storm water pipes
Using Figure 7.4 for a square culvert and following the lines for Inlet Control (clockwise), the value
for H1 = 2,4 m for the flow of 8,9 m³/s, a 1800 x 1800 mm portal culvert could be selected (as shown
in Figure 7.5). The H/D ratio will however be 1,33 and the capacity of the 5 culverts needs to be
verified.
This result can be checked with the following formula (Table 7.1):
Q  C h BD 2gH1  C h D 
…(7.3)
Where Ch = 0,8 for rounded inlets and Ch = 0,6 for square inlets.
Q  0,61,81,8 29,812,4  0,61,8 = 9,893 m³/s
and hence 5 culverts will be sufficient.
7-73
Lesser culverts and stormwater pipes
Figure 7.5: Determining culvert size (inlet control)
7-74
Lesser culverts and stormwater pipes

Evaluation of the same problem with the upstream slope equal to the downstream slope
It follows from the new slope details (S0 upstream and S0 downstream is 0,0015 m/m) that the upstream and
downstream normal flow depths will be 2,0 m, as was determined before. If the upstream water level
is limited to a maximum of 2,5 m to prevent the inundation of the road, the culvert flow rate can be
determined as follows.
For inlet control conditions the length, roughness, slope and hydraulic radius of the culvert have no
influence on the discharge rate. For outlet control these variables do influence the flow rate and have
to be considered.
Assume that the following information is still valid:
Slope of the culvert, S0 = 0,0015 m/m
Roughness of the culvert, ks = 0,002 m
Diameter of the culvert, D = 1 800 mm
Length of the culvert, L = 25 m
By assuming that 6 culverts will be used the flow rate per culvert = 44,5/6 = 7,417 m³/s.
It was reflected above that the upstream flow is subcritical, i.e. Fr = 0,482, hence downstream control
will be experienced in the channel prior to the placing of the culvert.
By applying the energy equation between the upstream/inlet (Position subscript 1) and the
downstream/outlet (Position subscript 2) (as represented in Figure 7.6) the required upstream energy,
H1, can be determined by using the energy principle.
Figure 7.6: Energy components of flow through a culvert
H1  S0 L  H 2  h l1 2  h f1 2
…(7.4)
(between Position 1 (upstream) and Position 2 (downstream))
For the flow of 7,417 m³/s the flow velocity in the pipe culvert can be determined as follows:
v
7,417
 2,915 m/s
π( 0,9) 2
The secondary losses, hl, can be determined as follows:
h l1- 2 = hl inlet + hl outlet
h l1- 2  (K inlet  K outlet )
2,915 = 0,649 m
v
 0,5  1
2g
29,81
2
…(7.5)
2
7-75
Lesser culverts and stormwater pipes
The friction losses, hf, can also be determined, assuming that full bore flow conditions in the culvert
will prevail:
hf 
λLv 2
2gD
…(7.6)
For rough turbulent flow conditions,
1
λ
 2log(
3,7D
)
ks
…(7.7)
λ  0,02015
h f1 2 = 0,121 m
For outlet control conditions, the upstream conditions can now be determined (Equation 7.4):
H1  H 2  Z1  h l1 2  h f1 2
H1 = (2,0 + 0,175 ) - 0,0015(25) + 0,649 + 0,121
H1 = 2,908 m
The value of H1 for outlet control is greater than the maximum allowable damming height of 2,5 m,
hence outlet control will be maintained through the culvert. The only way to reduce the upstream flow
depth is to consider more culverts of similar dimension in parallel or larger culverts.
Assume that seven culverts will be used. With the flow of 44,5/7 = 6,357 m³/s ( v = 2,498 m/s) and the
value of the losses, H L  h l1 2  h f1 2 = 0,477 + 0,089 = 0,566 m, the upstream conditions can now be
determined.
H1 = H2 - Z1 + HL
H1 = (2,0 + 0,175) - 0,0015(25) + 0,566
H1 = 2,704 m (which is still greater than the allowable upstream damming height)
To illustrated the use of Figure 7.4, start at Q = 6,357 m³/s (flow rate in each of the 7 culverts) and
HL = 0,566 m, then it can be seen that the 1 800 mm pipe culvert is still insufficient to transport the
flow (Figure 7.7). Figure 7.4 could thus be used to consider other culvert sizes.
Placing the seven culverts in parallel will also however result in a section width of about
(7)[1,8+(2)(0,078)] +(6)(0,1) = 14,3 m, which is much wider than the river base of 8,0 m.
The number of 1,8 m pipe culverts required to prevent overtopping of the road will be eight (although
still marginally undersize). Alternatively portal culverts with a larger vertical dimension (2,1 m) could
be used following the same procedure as above.
An economic/technical assessment of the alternatives i.e. re-alignment of the road against provision of
a practical culvert design have to be conducted to select the solution for implementation without
changing the risk of failure.
7-76
Lesser culverts and stormwater pipes
Figure 7.7: Determining culvert size (outlet control)
7-77
Lesser culverts and stormwater pipes
7.2
Example 7.2 - Erosion protection downstream from a culvert
Problem description Example 7.2
In Example 7.1 it was indicated that for inlet control it is possible to convey 8,9 m3/s (for H/D = 1,2)
through a 1,8 m diameter circular culvert. You are now requested to design the protection works for a
single 1,8 m diameter culvert, functioning under inlet control conditions with H/D = 1,2. The concrete
culvert is 28 m long with an estimated absolute roughness of 0,003 m. The culvert will be installed at a
slope of 0,01 m/m.
The flow releases into a natural trapezoidal river section with a base width of 2,0 m and side slopes of
1V:2H. The natural slope of the river is 0,004 m/m and the roughness is 0,05 m. Details of the crosssection are given in Figure 7.8.
Figure 7.8: Upstream view of the culvert
Solution Example 7.2
The uniform flow equations of Manning and Chezy can only be used if uniform flow occurs. Uniform
flow will occur if the cross-sectional parameters, roughness and slope remain constant. With the
culvert length of only 28 m it is unlikely that the normal flow depth will be reached within the culvert.
By assuming that the normal flow depth will be reached, the analysis is conservative, resulting in a
flow depth that is less (for the slope steeper that the critical slope, S0 > Sc) or the flow depth will be
greater for a subcritical slope (S0 < Sc).
Firstly the normal flow depth, yn, downstream from the culvert in the river is determined by using the
Chezy formula:
v  C RS
Q

vA

18



log
12R
k
s



…(7.8)
…(7.9)
RS
A
where:
Q
= flow rate (m3/s)
= average velocity (m/s)
v
R
= hydraulic radius (m)
ks
= absolute roughness (m)
S
= slope of the river section (m/m)
Table 7.2 reflects the cross-sectional parameters for a circular pipe.
7-78
Lesser culverts and stormwater pipes
Firstly the normal flow depth, yn, downstream from the culvert in the river is determined by using the
Chezy formula:
v  C RS
…(7.8)

12R 
 RS A
Q  vA  18  log
…(7.9)
k s 

where:
Q
= flow rate (m3/s)
= average velocity (m/s)
v
R
= hydraulic radius (m)
= absolute roughness (m)
ks
S
= slope of the river section (m/m)
Table 7.2: Sectional parameters for a circular cross-section
Variable
Y < D/2 (θ < π radials)
Y > D/2 (θ > π radials)
Cross-sectional view
Area,
A (m2)
Wetter perimeter,
P (m)
Hydraulic radius,
R (m)
θ
πR 2  (R 2 θ)  20,5R  y Sin R
 2
θ
R 2 θ  20,5 R  y Sin  R
2
R2π  θ
R θ 
A
P
By substituting the known values:
12R 

8,9  18  log
 R 0,004 A
0,05 

with:
A  2 y n   20,5 y n  2y n 
P  2  2  5 y n 
R
where:
yn
A
P
=
the unknown normal flow depth (m)
Solving for yn:
yn = 1,068 m
This indicates that the normal flow depth in the river section downstream from the culvert will have no
backwater influence on the culvert flow (yn < D).
7-79
Lesser culverts and stormwater pipes
Now the flow depth at the outlet of the culvert is determined. (Refer to the reasoning above where the
influence of assuming uniform flow in the culvert was explained.)
The critical slope in the culvert can be determined. Critical conditions will occur when Fr = 1, and the
critical slope Sc can be determined for full flow conditions as follows:
v2
Q2
Sc  2  2 2
…(7.10)
C R C A R
Sc = 0,00792 m/m
This indicates that the flow depth in the culvert will reduce downstream from the position where
critical flow occurs near the inlet of the culvert because S0 > Sc.
If it is assumed that the flow depth in the culvert Y is more than D/2, solve for a potential flow depth,
Y.
It is found that:
y = 1,330 m; A = 2,015 m² ; B = 1,582 m (top width of flow); v = 4,417 m/s and Fr = 1,25
(subcritical).
y/D = 1,330/1,8 = 0,739
Figure 7.9 can now be used to select the appropriate erosion protection.
In this example the appropriate protection falls in the Type III. Figure 7.10 can now be used to obtain
dimensions for outlet erosion protection.
7-80
Lesser culverts and stormwater pipes
.
Figure 7.9: Limiting values for different methods of erosion protection at culvert outlets
7-81
Lesser culverts and stormwater pipes
Calculated dimensions:
D50 = 0,258 m
C = 10,8 m
A = 9,0 m
B = 9,0 m
D = 0,517 m
E = 1,8 m
F = 0,9 m
Figure 7.10: Dimensions for the outlet erosion protection
Using Figure 7.11 with a flow of 8,9 m³/s in a circular culvert the values of Froude and the flow depth
can also be obtained which will correspond with the calculated values.
7-82
Lesser culverts and stormwater pipes
Figure 7.11: Diagram for the determination of outlet velocities for steep culverts and storm
water pipes (Only H1/D = 1,2, So > Sc)
7-83
Lesser culverts and stormwater pipes
8
BRIDGES AND MAJOR CULVERTS
8.1
Worked Example 8.1 – Backwater at a bridge
Problem description Example 8.1
Determine the backwater caused by a proposed bridge across the Broekspruit. Details of the bridge
are shown below in Figure 8.1.
Design discharge
Average bed slope
Angle of skew
Bridge span on skew
Projected bridge span
No of rows of piers
Projected width of pier
Q
So
ø
bs
b
Np
Wp
=
=
=
=
=
=
=
150 m3/s
0,00082 m/m
15º
17,6 m
17,0 m
1
2,00 m
Figure 8.1: Upstream view of the bridge
Determine:
(i)
(ii)
(iii)
(iv)
(v)
Characteristics of the unconstricted flood state
The flow type
Bridge opening ratio
Velocity head coefficients
Calculate backwater
Solution Example 8.1
(i)
Characteristics of the unconstricted flood state:
First determine the normal flow depth, yn.
8-84
Bridges and major culverts
Table 8.1: Sub-section details
ni
Ai (m2)
Pi (m)
Sub-section
1
2
3
0,035
0,030
0,035
1,602y2
18,61y
1,163y2
(y2 + 10,26 y2)0,5
18,61
2
(y + 5,41 y2)0,5
Utilising the Manning equation the normal flow depth can be calculated, yn = 3,157 m.
Table 8.2: Sub-section flow characteristics
(ii)
qi
(m3/s)
10,59
1,51
17,17
1,08
58,75
18,61
3,61
120,69
2,05
11,59
7,99
1,45
12,14
1,05
86,30
37,19
Ai
(m2)
Pi
(m)
1
15,96
2
3
This result in the:
Flood stage level
Width at flood stage
qi
Ai
(m/s)
Ai
Pi
(m)
Subsection
=
=
Ri 
vi 
150,00
84,56 m
36,06 m
Determine flow type:
Frn
1
=
 Q2B 


 gA 3 
n 

=
0,359 < 1
2
 150 2 36,06  

 
3 
 9,8186,30  
1
2
Flow is Type I or Type II.
Calculate specific energy (Esn) of unconstricted normal flow:
with yn = 3,157 m (Flood stage level – river bed level)
vn
=
Q
150

A n 86,30
=
1,738 m/s
2
vn

1,738
yn 
 3,157 
2g
29,81
3,311 m
2
Esn
=
=
8-85
Bridges and major culverts
Calculate specific energy (Esc) of constricted flow critical depth:
3
 150 2
 Q2 
 2   
 9,8117 2
 gb 

Q
150

y 2c b 2,817 17 
1
y2c
=
v 2c
=
Esc
=




1
3
= 1,995 m
= 4,424 m/s
v 2c
4,4242
 1,995 
2g
29,81
2
y 2c 
= 2,992 m <
Esn indicating Type I flow (see
Figure 8.2).
Figure 8.2: Type I flow with substantial damming and does not reach critical conditions
Because the values of Esn and Esc are fairly close, and other losses are so far ignored, it would be
prudent to check Type I and Type II flow.
(iii)
Calculate bridge opening ratio:
Qb
=
=
(iv)

17 

 17  1,61 
110,25 m3/s
120,69
M
=
Q b 110,25

Q
150
=
0,735
Calculate velocity head coefficients:
 qv 
2
α1
=
α2
=
=
2
Qv n
1,20
1,15 (from Figure 8.3)
8-86
Bridges and major culverts
Figure 8.3: Estimation of the velocity coefficient, α2 (generic example)
(v)
Calculate backwater
For Type I flow:
Determine secondary energy loss coefficient K* from Figure 8.4:
Figure 8.4: Chart to determine the backwater coefficient, K*
8-87
Bridges and major culverts
Projected area of piers in flow direction and projected area below normal water level.
Ap
J
=
Wp y n
=
=
(2)(3,157)
6,314 m²
Ap
An2
=
=
=
6,314
A n2 51,84
0,122 (use J = 0,1 from Figure 8.4)
=
1
=
0,56
=
=
(bcosø)(yn)
17cos15 3,157
o
51,84 m²

Eccentricity
e
Qa
1
Qc
12,14

17 

17,17  120,69 1 
 17  1,61 
From Figure 8.4 and with ø = 15º:
K*
=
0,80
Approximate backwater (to estimate A1 in Equation 8.1):
2
 A  2  A  2  v 2
v n2
*
*
h1  K α 2
 α 1  n2    n2   n2
2g
 A 1   2g
 A 4 
where:
=
secondary energy loss coefficient
K*
α1, α2 =
velocity coefficients
v n2
…(8.1)
v n2
=
Q (m/s) where Q = design discharge (m³/s)
A n2
An2
=
A1
=
A4
=
projected flow area at constricted section 2 below normal water level of the
river section (m²)
flow area at section 1, including the influence of the backwater on the flow
depth (m²)
flow area at section 4 (m²)
=
=
Q
150

A n2 51,84
2,894 m/s
2
h1*1
=
v
K α 2 n2
2g
h1*1
=
0,801,15 2,894
29,81
=
0,393 m
=
=
A n  h 1*1 B  86,3   0,393 36,06 
100,46 m²
A1
*
…(8.2)
2
8-88
Bridges and major culverts
Final estimate of backwater (Equation 8.1):
h1*1
 A
h  α 1  n2
 A 4
*1
1
=
=
For Type II flow:
Cb



2
v 2
 n2
 2g
 51,84  2  51,84  2   2,894 2 
0,393  1,20  
  
  

 86,30   100,46    29,81 
0,441 m
=
bc
2
  A n2
  
  A1
=
b   W   17,0  2,0
=
15,0 m
=
0,152 from Figure 8.5
p
Figure 8.5: Estimation of the Backwater Coefficient, Cb
1
y2c
=
=
y
=
=
 Q 2  3  150 2
 

 gb 2   9,81152
c
 

2,168 m
1
3



A n2 51,84

b
17
3,050 m
In 1st iteration, assume
v1
=
Q
150

A n 86,30
=
1,738 m/s
for v 2c based on the net width:
v 2c
=
=
gy2c 0,5  9,812,1680,5
4,612 m/s
8-89
Bridges and major culverts
2
h1*1
2
v 2c
v
C b  1  α1 1  y 2c  y
2g
2g
=
α2
=
1,154,6122 0,152  1  1,201,7382  2,168  3,050
29,81
29,81
=
=
1,436 - 0,185 + 2,168 - 3,050
0,371 m
Adjust result for improved value of v1 :
A1
=
=
v1
=
h1*1
A n  h 1*1 B  86,30   0,371 36,06 
99,67 m²
=
150
99,67
1,505 m/s
=
1,436 
=
0,417 m
1,201,5052  2,168  3,050
29,81
Although the difference in this case is negligible, to be conservative, the higher value should be used.
From the calculations h1*1 for Type II flow was 0,417 m which is less than the backwater calculated
for Type I flow, thus Type I flow prevails i.e. h1*1 = 0,441 m.
Note that this example was also modelled in HEC-RAS (provided on the supporting flash drive/DVD)
and that the highest backwater was obtained by the Standard Step Energy Method. The backwater is
300 mm, which is less than the value of 441 mm obtained above. However, in this model the
ineffective flow area option had been used. The model was then re-run, with this option switched off
and a higher backwater of 580 mm was obtained in the revised model.
Users of HEC-RAS should therefore carefully consider the option where the bridge approach
conditions are “smoothed”, thereby reducing the backwater.
8.2
Worked Example 8.2 – Scour at a bridge
Problem description Example 8.2
Consideration is being given to construct a bridge across the Sand River, which is some 730 m wide at
the proposed bridge site. The potential scour at the bridge should be determined. This problem was
also evaluated with HEC-RAS, and the data files are included with the data files as Example2.prj.
Figure 8.6 shows a plan view (obtained from the HEC-RAS problem evaluation) and the position of
the bridge relative to the other cross-sections. The cross-sectional information for all the sections is
available. The bridge will be positioned at cross-section 6.5 (downstream from cross-section 7 and
upstream of cross-section 6).
8-90
Bridges and major culverts
Figure 8.6: General layout of the cross-sections and the position of the bridge
The bridge data is described below and the bridge cross-section is shown in Figure 8.7.
The bridge opening between the sloping abutments is approximately 126,61 m wide and the bridge is
supported by five piers, each with a width of 1,5 m (equally spaced). The high (road surface) and
low cord (bridge soffit) values for the bridge deck on the upstream side are 6,7 and 5,5 m respectively.
The user can open the project (Example2.prj) in HEC-RAS and by selecting the appropriate icons,
review the bridge data which is not repeated here in detail.
The design flow rate for which the scour analyses have to be conducted is the 1:100 year flood (Q100),
which has been determined to be 850 m³/s.
The flow in the river is downstream control and the normal flow depth, yn, could be calculated at the
bridge, assuming a representative slope of 0,002 m/m.
Bed material characteristics
The sieve analyses (percentage passing) of the bed material revealed the following:
D50 = 0,0020 m
D90 = 0,0045 m
8-91
Bridges and major culverts
Figure 8.7: Upstream and downstream bridge cross-section from the HEC-RAS analysis
Cross-section details
The cross-section details are given in the Table 8.3 below. These details can be obtained from
analysis of the surveyed cross-section information, using software such as HEC-RAS, or computing
the variables by hand, as illustrated in Example 8.1.
Slope of the river
The general slope of the river is 0,2 %.
Determine
(i)
(ii)
(iii)
(iv)
(v)
Short-term general scour
Contraction scour
Local scour at the piers and abutments
Total scour
Verify the scour depth with the method based on the principle of applied stream power.
Solution Example 8.2
For this analysis the design flood discharge of 850 m3/s will be used (Chapter 3 describes procedures
to determine the design flood).
The contracted width at the bridge will be 126,61 m. This will result in a discharge per unit width of
850/126,61 = 6,713 m3/s.
8-92
Bridges and major culverts
The normal flow depth (fixed bed), yn, of the river can be determined by the assumption of the energy
slope to be equal to the bed slope 0,002 m/m and by using the Chezy or Manning equations.
It is estimated that the bed roughness under flood conditions will be 0,002m, equal to D50 the
representative sediment material size.
Table 8.3: Details of cross-section 6.5 (Obtained from HEC-RAS analysis)
Wetted perimeter
Section
yn (m)
Area (m²)
Flow rate (m3/s)
(m)
Left bank
209,97
288,17
168,75
Main channel
258,73
126,67
542,60
2,98
Right bank
185,40
283,48
138,65
Total
654,10
698,32
850,00
R = 0,937 m and v = 1,299 m/s
Top flow width = 698,2 m for the calculated normal flow depth of 2,98 m.
It is assumed that the bed material consists of deep alluvial sand with no cohesion.
(i)
Short-term general scour
The regime equations are applied to establish equilibrium conditions at the design flow:
0,25
B  14Q 0,5 D 50
Fs0,5
where:
B
y
Q
q
=
=
=
=
D50 =
Fs =
…(8.3)
mean channel width (m)
mean depth of flow (m)
equivalent steady discharge which would generate the channel geometry (m3/s)
discharge per unit width (Q/B) (m3/s.m) (Note: To estimate channel geometry
conditions under flood conditions the design flood flow may be used.) (8.9)
median size of bed material (m)
side factor to describe bank resistance to scour (Table 8.4)
Table 8.4: Side factors
Bank type
Value of Fs
Sandy loam
0,1
Silty clay loam
0,2
Cohesive banks
0,3
With Fs = 0,1 from Table 8.4 for sandy loam, the width B can be calculated.
B = 273 m, which is wider than the proposed bridge of 126,61 m.
Use Equation 8.4 to determine the mean flow depth at the equilibrium width:
y  0,38q
0,67
 0,17
D 50
where:
y
=
D50 =
…(8.4)
mean depth of flow (m)
median size of bed material (m)
8-93
Bridges and major culverts
q = 850/273 = 3,114 m³/s.m
Mean depth y = 2,34 m. The maximum depth, Ymax = 1,25y = 2,92 m.
The maximum live-bed depth, Ymax, is slightly less than the fixed bed depth, yn of 2,98 m, which
reflects that no general short term scour will occur.
(ii)
Contraction scour
It has been indicated that contraction scour can be determined by applying either the regime
equations (Equations 8.4 for the case of an alluvial channel) or the contraction equations (Equations
8.5 with 8.6 or 8.7).
The depth of scour is given by:
 v 22  v12
 2g
d s  y 2  y 1   1  K  




…(8.5)
Sediment-laden flow
y2  Qt 


y1  Q c 
6/7
 B1

 B2



2/3
 n2

 n1



1/3
…(8.6)
Clear water flow


Q2
y2  

2/3
 40D m B 22 
3/7
...(8.7)
First apply the regime equation on the reduced width of 126,61 m. In this case q = 850/126,61 =
6,714 m³/s.m leading to a mean flow depth, y of 3,915 m. From Table 8.5, ymax can be determined as
follows: ymax = 1,25 x 3,915 = 4,893 m. This reflects a scour depth, ds = 4,893 – 2,98 = 1,913 m
Table 8.5: Factors to convert mean flow depth (y) to maximum channel depth
Description
Multiplying factor
Straight reach of channel
1,25(*)
Moderate bend
1,50
Severe bend
1,75
Right-angled abrupt turn
2,00
Note:
* Neill recommends that this factor be increased to 1,50 in cases where dune movement
takes place on the riverbed.
Secondly the contraction equations are used to determine the scour depth after it has been established
if the flow will be sediment laden or not.
V* can be determined using Equation 8.8.
V* =
gDS =
9,81(2,98)(0,002) = 0,242 m/s
…(8.8)
and the term, V*D50/ν = 483 >> 13, thus in turbulent flow region (see Figure 8.8).
8-94
Bridges and major culverts
The critical shear velocity is:
V*C
 0,12
VSS
…(8.9)
The settling velocity, Vss can be obtained from Figure 8.9 for the representative particle, D50, and the
relative density of 2,65, it follows:
Vss = 0,24 m/s, and V*c = 0,029 m/s
The velocity at the boundary between sediment movement and no sediment movement (the ‘critical’
velocity), Vc, is determined from the logarithmic relationship:
Vc  5,75V*c log
12R
ks
From Equation 8.10: Vc  5,75V*c log
…(8.10)

 0,937  
12R
   0,625 m/s
 5,75 0,029log12


ks
0,002



Figure 8.8: Modified Lui Diagram showing the relationships for incipient sediment movement
8-95
Bridges and major culverts
Figure 8.9: Settling velocity as a function of the sediment size
(Shape factor not taken into consideration) (8.13)
Figure 8.10: Long constriction in sediment-laden flow: definition of terms
8-96
Bridges and major culverts
The average approach flow velocity of 1,299 m/s > ‘critical’ velocity of 0,625 m/s, thus sediment will
be entrained and Equation 8.11 together with Figure 8.10 can be used to estimate contraction scour.
y2  Qt 


y 1  Q c 
6/7
y 2  850 


y1  542,6 
 B1

 B2



2/3
 n2

 n1



1/3
…(8.11)
6/7
 1,469 (widths and n-values are equal for these sections)
y2 = (1,469)(2,98) = 4,378 m
Assuming a level bed with a total depth of 4,378 m, the velocity in the contraction can be determined:
850
v2 
 1,63 m/s
4,378126,61  51,5
Note that in this case the downstream area is 521,5 m², calculated as follows (4,378 x (126,61 –
5(1,5))). This is larger than the upstream main channel area of 258,73 m² (Table 8.3), and thus the
flow is expanding. Equation 8.12 is used to determine the contraction scour depth.
 v 2  v12
d s  y 2  y1   1  K  2
 2g

 and with K = 1 for a sudden transition


 1,63 2  1,299 2
d s  4,378  2,98  1  1,0
29,81

ds = 1,468 m
…(8.12)




This scour depth (1,468 m) is less than that obtained with the regime theory (1,913 m).
(iii)
Local scour at piers and abutments
For piers in alluvial cohesionless materials:
Use Equations 8.13 and 8.14 to compute local scour in two different ways for alluvial channels
(cohesionless material). Obtain the factors needed for Equation 8.13 from Table 8.6 and Table 8.7.
Obtain the factors needed for Equation 8.14 from Table 8.6 to Table 8.8 and K4 in cases where
armouring is applicable. Compare answers obtained from Equations 8.13 and 8.14 and select a
conservative answer using good engineering judgement.
8-97
Bridges and major culverts
Table 8.6: Correction factor K1, for pier nose shape
Length/Width
Shape of pier in plan #
K1
ratio (L/b)
Circular
1,0
1,0
2,0
0,91
3,0
0,76
Lenticular
4,0
0,67-0,73
7,0
0,41
Parabolic nose
0,8
Triangular 60º
0,75
Triangular 90º
1,25
2,0
0,91
Elliptic
3,0
0,83
Ogival
4,0
0,86-0,92
2,0
1,11
Rectangular
4,0
1,11 (HEC 18) - 1,40 (F&C)
6,0
1,11
Note:
#
Table 8.6 is based on the list by Faraday and Charlton (1983), which is more
complete than the list in HEC 18 documentation
Table 8.7: Correction factor K2, for angle of attack of the flow
Angle (skew angle
L/b = 4
L/b = 8
L/b = 12
of flow)
0
1,0
1,0
1,0
15
1,5
2,0
2,5
30
2,0
2,75
3,5
45
2,3
3,3
4,3
90
2,5
3,9
5,0
Note: In the case of L/b larger than 12, the ratio’s for L/b = 12 should be used.
Table 8.8: Correction factor K3, for bed conditions
Bed condition
Dune Height (m)
K3
Clear-water scour
Not applicable
1,1
Plane bed and anti-dune flow
Not applicable
1,1
Small dunes
0,6 m – 3 m
1,1
Medium dunes
3m–9m
1,1 – 1,2
Large dunes
≥9m
1,3
From Equation 8.13, with depth y0 in the bridge section as determined from regime:
0,25
d s  1,8y 0,75
 y0
0 b
where:
ds
y0
b
=
=
=
…(8.13)
local scour depth at pier (m)
depth upstream of pier (m)
pier width (m)
d s  1,8 (3,915 0,75 )(1,5 0,25 )  3,915
d s  1,629 m
Note that the scour level is (3,915 + 1,629) = 5,544 m below the design flood level.
8-98
Bridges and major culverts
Alternatively Equation 8.14, for the longest piers close to the minimum river invert could be used to
calculate the local scour depth at the pier.
0,35
ys
y 
…(8.14)
 2,0 K 1 K 2 K 3 K 4  1  Fr10,43
b
 b
with
b
= 1,5 m
= 2,98 m (normal flow depth upstream of the bridge, Table 8.3)
y1
= 0,429 based on main channel data directly upstream of the pier
Fr1
= 1,0 for round nose
K1
K2
= 1,0 for zero skew angle
= 1,1 for small dunes
K3
= 1,0 for uniform sediment (no armouring), see Drainage Manual for details of
K4
calculating K4 correction factor, then
ys
 2,98 
 2,0 1,0  1,0  1,1 1,0  

b
 1,5 
ys = 2,915 m
0,35
0,429 0,43  1,943
Note that the scour level is (2,98 + 2,915) = 5,895 m below the design flood level associated with
the normal flow depth and a fixed bed level.
For abutments in alluvial cohesionless materials:
Apply factors in Table 8.9 to the general short-term average scour depth obtained from Equation 8.13.
From Table 8.9 the factor for flow that impinges at right angles on bank = 2,25; hence the scour at the
abutments can be determined as shown below:
d s (abutments )  2,25 3,915  2,98   2,10 m
(iv)
Total scour
Total scour is the sum of the long and short-term general scour, contraction scour and local scour.
Table 8.9 reflects a summary of all the calculated scour depths.
Table 8.9: Summary of the calculated scour depths for Worked Example 8.2
Scour type
Calculated scour depth, ds (m)
Short term general scour
No scour
Regime equation
1,913
Contraction scour
Contraction equation
1,468
Piers
2,915
Local scour
Abutments
2,102
Piers
4,828
Total expected scour
Abutments
4,013
8-99
Bridges and major culverts
Review of the contraction or short-term scour using different analyses procedures
The potential general scour at the bridge has been determined in (i) using Equations 8.5. A more
correct approach is to estimate contraction scour separately for the main channel and over banks, as is
done in HEC-RAS, where the over bank flows may then reflect clear water scour. The scour depth in
the channel calculated in the approach used in HEC-RAS is less than 3,1 m. With the regime theory
reflecting a scour depth of 1,91 m and the HEC-RAS result of 3,1 m, the contraction scour calculation
of 1,468 m using Equation 8.12 is too conservative and hence discarded.
Based on the summary in Table 8.9 the total scour can be determined as follows.
Total scour at piers in main channel
Total scour level at piers, below design flood level (not accounting for backwater)
= 1,913 + 2,915 = 4,828 m
Total scour at abutments
With the right abutment on the edge of the main channel, the scour would be the sum of main channel
contraction scour plus abutment scour, thus:
Total scour at abutments = 1,913+ 2,1 = 4,013 m below design flood level
The scour for the left bank abutment would be less.
Verify the scour depth with the method based on the principle of applied stream power
For total scour at piers in alluvial rivers, check the answer against values obtained by means of
Equation 8.15 that is based on the principle of applied stream power.
Equation 8.15 reflected the following relationship:
C(Yt )(vss k s )1/3
q g
F
…(8.15)
With F = 0,8; ks = 0,002 m ; vss = 0,24 m/s; q = 542,6/126,61 = 4,29 m³/s.m and C calculated from
the Chezy relationship for total section, C = 67,5; it follows that:
Yt = 2,03 m below design flood level, which is substantially less than obtained above.
The designer will experience these conflicting results, which reflect amongst other the complexities
involved in the mathematical description of scour estimates and the shortcoming in the assumption
that the material is cohesionless.
Considering the risk of failure of the structure due to scour and the potential consequences, these cases
require further evaluation by experienced persons.
The problem is also evaluated using HEC-RAS, and the data files are contained as Example 2 in the
supporting data files.
8-100
Bridges and major culverts
9
STORMWATER ANALYSES AND DESIGN
9.1
Example 9.1 – Pipe flow
Problem description Example 9.1
Water flows from a submerged catch pit at a kerb inlet through a 20 m concrete drain pipe where it
releases into a river stream. The inside diameter of the pipe is 0,3 m. The pipe has a slope of 0,5 % and
the depth of the water in the catch pit above the top of the pipe is 0,2 m (i.e. available head).
Calculate the discharge rate for this set-up.
Solution Example 9.1
To solve this problem the conservation of energy principle will be used i.e. Equation 9.1. The entrance
(point 1) and exit (point 2), are open to atmosphere and thus p1/γ = p2/γ = 0 if the stream line is
selected along the top of the water surface.
v12 p 1
v 22 p 2

 z1 

 z 2  h f1  2  h ι 1  2
2g γ
2g
γ
...(9.1)
The velocity in the catch pit ( v1 ) is negligible (large catch pit area in comparison with pipe area). If
the datum line is selected through the invert of the pipe outlet (point 2) z2 will be zero and z1 can be
calculated as follows:
z 1  (0,2)  20 0,005   0,3
The first term is the height above the pipe inlet and the second term the length of the pipe multiplied
by the slope of the pipe to obtain the vertical height difference between inlet and outlet.
The last two terms in the energy equation are the loss terms. The friction loss can be calculated using
the Chezy equation (Equation 9.2) with the C-value determined by Equation 9.3. The absolute
roughness value of the pipe was estimated as ks = 0,0004 m.
h f 1- 2 
v2L
C2R
…(9.2)
 D
 12  
 12R 
4
 or C  5,75 g log    for circular pipes
C  5,75 g log

ks 
 ks 




…(9.3)
  0,3  
 12

4 
C  5,75 9,81 log 
 60,37
 0,0004 




h f1- 2 
v 22 20 
 0,07317v 22
60,37 2  0,3 
 4 
9-101
Stormwater analyses and design
A secondary inlet loss will occur at the entrance. From Table 9.1, an inlet coefficient of k = 0,5 will
be used for a blunt entrance.
Table 9.1: Transition losses in pipe flows
Description
Sketch
k-value
Inlets
Protruding
0,9
kv 2
h1 
2g
Oblique
0,7
Blunt
0,5
Well-rounded
0,2
Sudden
1,0
Cone 45° < θ < 180°
1,0
θ = 30°
0,7
θ = 15°
0,2
Sudden
0,5
Cone
0,25
θ = 90°
0,4
θ = 45°
0,3
Sudden
1,0
( v = average velocity in
conduit)
Diverging sections
2
k v 1  v 2 
h1 
2g
Converging sections
h1 
kv 2
2g
Bends
kv 22
h1 
2g
Outlets
kv 2
h1  1
2g

A 
1  1 
A2 

2
The diameter does not change and the velocity where the water enters the pipe can be assumed to be
equal to v 2 .
h1 
kv 22 0,5 v 22

 0,02548 v 22
2g
29,81
The energy equation is simplified as follows:
02  0  0,3  v 22  0  0  0,07317 v 2  0,02548 v 2
2
2
29,81
29,81

 

v 2 = 1,416 m/s
  0,3  2 
3
Q  v 2 A 2  1,416   π
   0,1 m /s
  2  


This pipe can discharge 100 l/s if it is allowed to dam at the entrance up to 500 mm above the pipe
inlet level.
9-102
Stormwater analyses and design
9.2
Example 9.2 – Introduction to using EPASWMM
The EPA Storm Water Management Model (SWMM) is a dynamic rainfall-runoff simulation model
that computes runoff quantity and quality from primarily urban areas. The runoff component of
SWMM operates on a collection of subcatchment areas that receive precipitation and generate runoff
and pollutant loads. The routing portion of SWMM transports this runoff through a system of pipes,
channels, storage/treatment devices, pumps and regulators. SWMM tracks the quantity and quality of
runoff generated within each subcatchment and the flow rate, flow depth, and quality of water in each
pipe and channel during a simulation period comprised of multiple time steps.
SWMM was first developed in 1971 and since then has undergone several major upgrades. It
continues to be widely used throughout the world for planning, analysis, and design related to storm
water runoff, combined sewers, sanitary sewers, and other drainage systems in urban areas and has
also been used for modelling non-urban areas. The most current implementation of the model is
version 5.0 which was released in 2005. It has modernized both the model’s structure and its user
interface, making SWMM easier to use and more accessible to a new generation of hydrologists,
engineers, and water resources management specialists.
All the practical exercises after this first tutorial are developed for the same catchment area and each
one builds in some degree on the results of a previous example. Therefore, it is recommended to begin
with Exercise 1 and work sequentially through up to Exercise 6, while hopefully building the required
input data files and running them with SWMM for each exercise. These files, as well as the backdrop
image files that are needed to complete the exercises, are available on the flash drive/DVD.
Goal: This first tutorial provides an introduction to using EPA SWMM, Version 5,
for modeling the quantity of storm water runoff produced from an urban area. The
topics to be covered include:
Project Setup
Constructing a SWMM Model
Saving and Opening Projects
Setting the Properties of SWMM Objects
Running a Single Event Analysis
Viewing Simulation Results
In the exercises the decimal separator will be the decimal comma (,) whilst in the EPA SWMM
program the decimal point (.) is used. The EPA SWMM program is constantly upgraded and the
screen layouts on newer versions may differ from what is shown in this example.
PROJECT SETUP
To begin this tutorial, start the EPA SWMM program by double clicking the EPA SWMM icon on the
desktop. The main window should appear as shown in Figure 9.1.
9-103
Stormwater analyses and design
Figure 9.1: SWMM 5 main window
In this tutorial a drainage system serving a 0,48 ha residential area will be modelled. The system
layout is shown below in Figure 9.2 and consists of subcatchment areas S1 through S3, storm sewer
conduits C1 through C4, and conduit junctions J1 through J4. The system discharges to a stream at the
point labelled Out1. The first steps are to create the objects shown in this diagram on SWMM's Study
Area Map and setting the various properties of these objects. The water quantity response to a 75 mm,
6-hour rainfall event, as well as a continuous, multi-year record will then be simulated.
Figure 9.2: System layout
9-104
Stormwater analyses and design
Our first task is to create a new project in EPA SWMM and make sure that certain default options are
selected. Using these defaults will simplify the data entry tasks later on. The first step in developing a
SWMM application is to start a new project.
1. Go to File menu on the main window and select New.
2. Select Project >> Defaults to open the Project Defaults dialog.
3. On the ID Labels page, set the ID Prefixes as follows (leave the others blank) and shown in
Figure 9.3:
Rain Gages:
Gage
Subcatchments:
S
Junctions:
J
Outfalls:
Out
Conduits:
C
ID Increment:
1
Figure 9.3: Project Defaults: ID labels
This will make EPA SWMM automatically label new objects with consecutive numbers
following the designated prefix.
4. On the Subcatchments page of the dialog set the following default values (as shown in
Figure 9.4):
Area:
1,619
Width:
120
% Slope:
0,5
% Imperv:
50
N-Imperv:
0,01
N-Perv:
0,10
Dstore-Imperv:
1,3
Dstore-Perv:
1,3
%Zero-Imperv:
25,0
9-105
Stormwater analyses and design
Figure 9.4: Project Defaults: Subcatchments
Infiltration Model <click
to edit>, as
shown in Figure 9.5.
Method:
Green-Ampt
- Suction Head:
90
- Conductivity:
12,5
- Initial Deficit:
0,26
Figure 9.5: Infiltration Editor
5. On the Nodes/Links page set the following default values (Figure 9.6):
Node Invert:
0
Node Max. Depth:
1,2
Node Ponded Area:
0
Conduit Length:
120
Conduit Geometry: <click
to edit >, as shown in Figure 9.7.
- Shape:
Circular
- Max. Depth:
0,3
- Barrels
1
Conduit Roughness:
0,01
Flow Units:
LPS
Routing Model:
Kinematic Wave
Force Main Equation: Hazen-Williams
9-106
Stormwater analyses and design
Figure 9.6: Project Defaults: Nodes/Links
Figure 9.7: Cross-Section Editor
6. Select Save as defaults for all new projects and click OK to accept these choices and close the
dialog.
Setting Map Options
Next we will set some map display options so that ID labels and symbols will be displayed as we add
objects to the study area map, and links will have direction arrows.
1. Select Tools >> Map Display Options to bring up the Map Options dialog (see Figure 9.8).
9-107
Stormwater analyses and design
Figure 9.8: Map Options: Subcatchments
2. Select the Subcatchments page, set the Fill Style to Diagonal and the Symbol Size to 5 (as
shown in Figure 9.8).
3. Then select the Nodes page and set the Node Size to 5 (see Figure 9.9).
Figure 9.9: Map Options: Nodes
4. Select the Annotation page and check off the boxes that will display ID labels for
Subcatchments, Nodes, and Links. Leave the others un-checked as shown in Figure 9.10.
9-108
Stormwater analyses and design
Figure 9.10: Map Options: Annotation
5. Finally, select the Flow Arrows page; select the Filled Arrow style, and set the Arrow size
to 7 (see Figure 9.11).
Figure 9.11: Map Options: Flow Arrows
6. Click the OK button to accept these choices and close the dialog.
Before placing objects on the map we should set its dimensions.
1. Select View | Dimensions … to bring up the Map Dimensions dialog.
2. You can leave the dimensions at their default values for this example. Set the Map Units to
Meters by selection this option and click on the OK button.
Finally, look in the status bar at the bottom of the main window and check that the Auto-Length
feature is Off. If it is on, then click the down arrow button and select "Auto-Length: Off" from the popup menu that appears.
9-109
Stormwater analyses and design
CONSTRUCTING A SWMM MODEL
Drawing the Drainage Area Subcatchments
We are now ready to begin adding components to the Study Area Map to create the model layout as
shown in Figure 9.12. We will start with the subcatchments.
Figure 9.12: Model layout
1. Begin by clicking the
button on the Object Toolbar. (If the toolbar is not visible then
select View | Toolbars | Object). Notice how the mouse cursor changes shape to a pencil.
2. Move the mouse to the map location where one of the corners of subcatchment S1 lies and
left-click the mouse.
3. Do the same for the next three corners and then right-click the mouse (or hit the Enter key) to
close up the rectangle that represents subcatchment S1. You can press the Esc key if instead
you wanted to cancel your partially drawn subcatchment and start over again. Don't worry if
the shape or position of the object isn't quite right. We will go back later and show how to fix
this.
4. Repeat this process for subcatchments S2 and S3. Note.
Observe how sequential ID labels are generated automatically as we add objects to the map. The
model should look similar to the one shown in Figure 9.13.
9-110
Stormwater analyses and design
Figure 9.13: Model with the three subcatchments
Drawing the Drainage System Nodes
Next we will add in the junction nodes and the outfall node that comprise part of the drainage network.
1. To begin adding junctions, click the
button on the Object Toolbar.
2. Move the mouse to the position of junction J1 (as shown in Figure 9.12) and left-click it. Do
the same for junctions J2 through J4.
3. To add the outfall node, click the
button on the Object Toolbar, move the mouse to the
outfall's location on the map, and left-click. Note how the outfall was automatically given the
name Out1.
The model should look similar to the one shown in Figure 9.14.
9-111
Stormwater analyses and design
Figure 9.14: Model with added junctions and outlet
Drawing the Drainage System Links
Now we will add the storm sewer conduits that connect our drainage system nodes to one another.
(You must have created a link's end nodes as described in the previous topic before you can create the
link.) We will begin with conduit C1 which connects junction J1 to J2.
1. Click the
button on the Object Toolbar. The mouse cursor changes shape to a crosshair.
2. Click the mouse on junction J1. Note how the mouse cursor changes shape to a pencil.
3. Move the mouse over to junction J2 (note how an outline of the conduit is drawn as you move
the mouse) and left-click to create the conduit. You could have cancelled the operation by
either right-clicking or by hitting the Esc key.
Repeat this procedure for conduits C2 through C4. The model should look similar to the one shown in
Figure 9.15.
9-112
Stormwater analyses and design
Figure 9.15: Model with added links
Adding a Rain Gage
To complete the construction of our study area schematic a rain gage need to be added.
1. Click the Rain Gage button
on the Object Toolbar.
2. Move the mouse over the Study Area Map to where the gage should be located and left-click
the mouse.
Note in Figure 9.15 that the subcatchments are not yet linked to a specific junction. This will be done
later in the exercise.
Re-Positioning Objects
At this point we have completed drawing the example study area. Your system should look like the
one shown in Figure 9.16. If the rain gage, subcatchments or nodes are out of position you can move
them around by:
1. Clicking the
button to place the map in Object Selection mode;
2. clicking on the object to be moved;
3. dragging the object with the left mouse button held down to its new position.
9-113
Stormwater analyses and design
Figure 9.16: Model layout
To re-shape a subcatchment's outline:
1. With the map in Object Selection mode, click on the subcatchment's centroid (indicated by a
solid square within the subcatchment) to select it.
2. Then click the
button on the Map Toolbar to put the map into Vertex Selection mode.
3. Select a vertex point on the subcatchment outline by clicking on it (note how the selected
vertex is indicated by a filled solid square).
4. Drag the vertex to its new position with the left mouse button held down.
5. If need be, vertices can be added to or deleted from the outline by right-clicking the mouse and
selecting the appropriate option from the popup menu that appears.
6. When finished, click the
button to return to Object Selection mode.
This same procedure can also be used to re-shape a link.
Saving and opening the project
Having completed the initial design of our example project it is a good idea to give it a title and save
our work to a file at this point. To do this:
1. Select the Title/Notes category from the Data Browser and click the
9.17).
9-114
button (see Figure
Stormwater analyses and design
Figure 9.17: Title/Notes Editor
2.
In the Project Title/Notes dialog that appears, enter "Practical Exercise E5" as the title of
our project and click the OK button to close the dialog.
3.
From the File menu select the Save As option.
4.
In the Save As dialog that appears (Figure 9.18), select a folder and file name under
which to save this project. We suggest naming the file E5.inp. (An extension of .inp will
be added to the file name if one is not supplied.)
5.
Click Save to save the project to file.
The project data is saved to the file in a readable text format. You can view what the file looks like by
selecting Project | Details from the main menu. To open our project at some later time, we would
select the Open command from the File menu.
9-115
Stormwater analyses and design
Figure 9.18: Save As dialog box
SETTING THE PROPERTIES OF SWMM OBJECTS
Setting Properties
As visual objects are added to our project, SWMM assigns them a default set of properties. To change
the value of a specific property for an object we must select the object into the Property Editor
(shown in Figure 9.19). There are several different ways to do this. If the Property Editor is already
visible then you can simply click on the object or select it from the Data page of the Browser. If the
Editor is not visible then you can make it appear by one of the following actions:
Double-click the object on the map.
Right-click on the object and select Properties from the pop-up menu that appears.
Select the object from the Data page of the Browser window and then click the Browser's
button.
Whenever the Property Editor has the focus you can press the F1 key to obtain a more detailed
description of the properties listed.
9-116
Stormwater analyses and design
Figure 9.19: Property Editor
Setting Subcatchment Properties
Two key properties of our subcatchments that need to be set are the rain gage that supplies rainfall
data to the subcatchment and the node of the drainage system that receives runoff from the
subcatchment. Since all of our subcatchments utilize the same rain gage, Gage1, we can use a shortcut
method to set this property for all subcatchments at once:
1. From the main menu select Edit | Select All.
2. Then select Edit | Group Edit to make a Group Editor dialog appear.
3. Select Subcatchments as the class of object to edit, Rain Gage as the property to edit, and
type in Gage1 as the new value (as shown in Figure 9.20).
Figure 9.20: Group Editor dialog
4. Click OK to change the rain gage of all subcatchments to Gage1. A confirmation dialog will
appear noting that 3 subcatchments have changed (Figure 9.21). Select No when asked to
continue editing.
9-117
Stormwater analyses and design
Figure 9.21: Confirmation dialog
To set the outlet node of our subcatchments we have to proceed one by one, since these vary by
subcatchment:
1. Double click on subcatchment S1 or select it from the Data Browser and click the Browser's
button to bring up the Property Editor.
2. Type J1 in the Outlet field and press Enter. Note how a dotted line is drawn between the
subcatchment and the node (Figure 9.22).
Figure 9.22: Linking subcatchment and junction
3. Click on subcatchment S2 and enter J2 as its Outlet.
4. Click on subcatchment S3 and enter J3 as its Outlet.
Finally, we wish to represent area S3 as being less developed than the others. Select S3 into the
Property Editor and set its % Imperviousness to 25 (Figure 9.23).
9-118
Stormwater analyses and design
Figure 9.23: Setting %Imperviousness
Setting Node/Link Properties
The junctions and outfall of our drainage system need to have invert elevations assigned to them. As
we did with the subcatchments, select each junction individually into the Property Editor and set its
Invert Elevation to the value shown in Table 9.2.
Table 9.2: Node properties
Node
Invert (m)
J1
J2
J3
J4
Out1
1129,3
1127,4
1128,3
1126,8
1125,9
Only one of the conduits in our example system has a non-default property value. This is conduit C4,
the outlet pipe, whose diameter should be 0,45 m. instead of 0,3 m. To change its diameter (maximum
depth), select conduit C4 into the Property Editor and set the Max. Depth value to 0,45.
Setting Rain Gage Properties
In order to provide a source of rainfall input to our project we need to set the rain gage properties.
Select Gage1 into the Property Editor and set the following properties (see Figure 9.24):
Rain Format:
Rain Interval:
Data Source:
Series Name:
INTENSITY
1:00
TIMESERIES
TS1
9-119
Stormwater analyses and design
Figure 9.24: Rain Gage property editor
As mentioned earlier, a simulation of the response of the study area to a 75 mm, 6-hour design storm is
required. A time series named TS1 will contain the hourly rainfall intensities that make up this storm.
Thus a time series object is created and populate with data. To do this:
1. From the Data Browser select the Time Series category of objects.
2. Click the
button on the Browser which will bring up a Time Series Editor form.
3. Enter TS1 in the Time Series Name field.
4. Enter the values into the Time and Value columns of the data entry grid (leave the Date
column blank) as shown in Figure 9.25.
Figure 9.25: Time Series Editor
9-120
Stormwater analyses and design
5. You can click the View button on the dialog to see a graph of the time series values (Figure
9.26). Click Close to return to the Time Series Editor.
Figure 9.26: Time Series Viewer
6. Click the OK button to accept the new time series.
RUNNING A SINGLE EVENT ANALYSIS
Before analysing the performance of our example drainage system we need to set some options that
determine how the analysis will be carried out. To do this:
1. From the Data Browser, select the Options category and click the
button.
2. On the General page of the Simulation Options dialog that appears, select Kinematic Wave
as the flow routing method. The Infiltration model should already be set to Green-Ampt. The
Allow Ponding option should be unchecked (see Figure 9.27).
9-121
Stormwater analyses and design
Figure 9.27: Simulation options – General
3. On the Dates page of the dialog, set the End Analysis time to 12:00:00 (Figure 9.28) and the
Dates and Times as indicated on Figure 9.28.
Figure 9.28: Simulation options – Dates
4. On the Time Steps page, set the Routing time step to 60 sec (Figure 9.29).
9-122
Stormwater analyses and design
Figure 9.29: Simulation options – Time Steps
5. Click OK to close the Simulation Options dialog.
We are now ready to run the simulation. To do so, select Project | Run Simulation (or click the
button). After the run was completed the Run Status will be indicated as shown in Figure 9.30.
Figure 9.30: Run Status
9-123
Stormwater analyses and design
VIEWING SIMULATION RESULTS
Viewing Analysis Results
If there was a problem in running the simulation, a Status Report will appear describing what errors
occurred.
Upon successfully completing a run, there are numerous ways in which to view the results of the
simulation. A few will be illustrated:
o
o
o
o
Viewing the Status Report
Viewing results on the map
Viewing a time series plot
Viewing a profile plot
Viewing the Status Report
The Status Report contains useful summary information about the results of a simulation run. To
view the report, select Report | Status (shown in Figure 9.31)
Figure 9.31: Status report
For the system we just analysed the report indicates the following:
1. The quality of the simulation is quite good, with negligible mass balance continuity errors for
both runoff and routing (-0.23% and -0.02%, respectively, if all data were entered correctly).
2. Of the 75 mm of rain that fell on the study area, 43,75 mm infiltrated into the ground and
essentially the remainder became runoff.
9-124
Stormwater analyses and design
3. The Node Flooding Summary table indicates there was internal flooding in the system at
node J2.
4. The Conduit Surcharge Summary table shows that Conduit C2, just downstream of node J2,
was at full capacity and therefore appears to be slightly undersized.
Viewing Results on the Map
Simulation results (as well as some design parameters, such as subcatchment area, node invert
elevation, link maximum depth) can be viewed in colour-coded fashion on the study area map. To
view a particular variable in this fashion:
1. Select the Map page of the Browser panel.
2. Select the variables to view for Subcatchments, Nodes, and Links from the dropdown combo
boxes in the Themes panel. Try for instance Runoff, Depth and Flow respectively as shown in
Figure 9.32.
Figure 9.32: Themes panel
3. The colour coding used for a particular variable is displayed with a legend on the study area
map. To toggle the display of a legend, select View | Legends (see Figure 9.33).
Figure 9.33: Legends
4. To move a legend to another location, drag it with the left mouse button held down.
5. To change the colour coding and the breakpoint values for different colours, select View |
Legends | Modify and then the pertinent class of object (or if the legend is already visible,
simply right-click on it). Attempt to set the breakpoint values as indicated in Figure 9.33.
6. To view numerical values for the variables being displayed on the map, select Tools | Map
Display Options and then select the Annotation page of the Map Options dialog. Use the
check boxes for Rain Gages, Subcatchments, Nodes, and Links to specify what kind of
annotation to add.
7. The Date / Time of Day / Elapsed Time controls on the Time Period panel Map Browser
can be used to move through the simulation results in time. Set the Time of Day to 3:00:00 to
obtain the view as depicted in Figure 9.34.
9-125
Stormwater analyses and design
Figure 9.34: Viewing results (using simulation time)
8. You can use the controls in the Animator panel of the Map Browser to animate the map
display through time. For example, pressing the button will run the animation forward in
time.
Viewing a Time Series Plot
To generate a time series plot of a simulation result:
1.
Select Report | Graph | Time Series or simply click
on the Standard Toolbar.
2.
A Time Series Plot dialog will appear. It is used to select the objects and variables to be
plotted.
For this example, the Time Series Plot dialog can be used to graph the flows in conduits C1 and C2 as
follows (shown in Figure 9.35):
9-126
Stormwater analyses and design
Figure 9.35: Time Series Plot
1.
Select Links as the Object Category.
2.
Select Flow as the Variable to plot.
3.
Click on conduit C1 (either on the map or in the Data Browser) and then click
dialog to add it to the list of links plotted. Do the same for conduit C2.
4.
Press OK to create the plot as shown in Figure 9.36.
in the
Figure 9.36: Graph – Link Flow
After a plot is created you can:
o customize its appearance by selecting Report | Customize or right clicking on the plot (see
Figure 9.37),
9-127
Stormwater analyses and design
o
copy it to the clipboard and paste it into another application by selecting Edit | Copy To or
clicking
o
on the Standard Toolbar
print it by selecting File | Print or File | Print Preview (use File | Page Setup first to set
margins, orientation, etc.).
Figure 9.37: Graph Options
Viewing a Profile Plot
SWMM can generate profile plots showing how water surface depth varies across a path of connected
nodes and links. Create such a plot for the conduits connecting junction J1 to the outfall Out1 of our
example drainage system. To do this:
1. Select Report | Graph | Profile or simply click
on the Standard Toolbar.
2. Either enter J1 in the Start Node field of the Profile Plot dialog that appears or select it on the
map or from the Data Browser and click the
button next to the field.
3. Do the same for node Out1 in the End Node field of the dialog.
4. Click the Find Path button. An ordered list of the links which form a connected path between
the specified Start and End nodes will be displayed in the Links in Profile box see Figure
9.38. You can edit the entries in this box if need be.
9-128
Stormwater analyses and design
Figure 9.38: Profile plot
5. Click the OK button to create the plot (Figure 9.39), showing the water surface profile as it
exists at the simulation time currently selected in the Map Browser.
Figure 9.39: Profile – Node J1 – Out1
As you move through time using the Map Browser or with the Animator control, the water depth
profile on the plot will be updated. Observe how node J2 becomes flooded between hours 2 and 3 of
the storm event as shown in Figure 9.40.
9-129
Stormwater analyses and design
Figure 9.40: Flooding shown at junction J2
The appearance of a profile plot can be customized or it can be copied or printed using the same
procedures as for a time series plot.
Running a Dynamic Wave Analysis
In the analysis just run we chose to use the Kinematic Wave method of routing flows through our
drainage system. This is an efficient but simplified approach that cannot deal with such phenomena as
backwater effects, pressurized flow, flow reversal, and non-dendritic layouts. SWMM also includes a
Dynamic Wave routing procedure that can represent these conditions. This procedure, however,
requires more computation time, due to the need for smaller time steps to maintain numerical stability.
Most of the effects mentioned above would not apply to our example. However we had one conduit,
C2, that flowed full and caused its upstream junction to flood. It could be that this pipe is actually
being pressurized and could therefore convey more flow than was computed using Kinematic Wave
routing. We would now like to see what would happen if we apply Dynamic Wave routing instead.
To run the analysis with Dynamic Wave routing:
1. From the Data Browser, select the Options category and click the
button.
2. On the General page of the Simulation Options dialog that appears, select Dynamic Wave as
the flow routing method (see Figure 9.41).
9-130
Stormwater analyses and design
Figure 9.41: Simulation options
3. Click OK to close the form and select Project | Run Simulation (or click the
run the analysis.
button) to re-
If you look at the Status Report for this run you will see that there is no longer any flooding and that
the peak flow carried by conduit C2 has been increased from 95,17 l/s to 112,56 l/s (the conduit now
flows pressurized).
A profile can be drawn again which will indicate the pressurized flow conditions experienced in link
C2, see Figure 9.42.
We have only touched the surface of SWMM's capabilities. Some additional features of the program
that you will find useful include:
o
o
o
o
o
o
o
o
o
o
Water quality analysis;
running a continuous simulation;
performing a frequency analysis;
utilizing additional types of drainage elements, such as storage units, flow dividers, pumps,
and regulators, to model more complex types of systems;
using control rules to simulate real-time operation of pumps and regulators ;
employing different types of externally-imposed inflows at drainage system nodes, such as
direct time series inflows, dry weather inflows, and rainfall-derived inflow/infiltration;
modelling groundwater interflow between aquifers beneath subcatchment areas and drainage
system nodes;
modelling snow fall accumulation and melting within subcatchments;
adding calibration data to a project so that simulated results can be compared with measured
values;
utilizing a background street, site plan, or topo map to assist in laying out a system's drainage
elements and to help relate simulated results to real-world locations.
9-131
Stormwater analyses and design
Figure 9.42: Pressurized flow conditions in link C2
You can find more information on these and other features in the SWMM User's Manual. Once you
have reached this stage of the exercise you should be in a position to answer the following questions
based on the model that has been set-up at this point.
1. What is the maximum depth at junction J2 and when does this occur?
2. What is the determined system runoff coefficient for this exercise? Hint: see Status Report
3. What is the maximum flow at the system outlet?
4. What is the peak runoff from catchment S2 and when does it occur?
5. What is the head difference between junctions J1 and J2 at 02:45?
6. What is the velocity and Froude number in link C4 at 04:00? What would be the type of flow
at this time step?
7. What capacity is still available in link C1?
8. Draw the flow versus time graph for link C1.
9. What happens to the flow routing continuity if the Routing time step is set to 5 seconds instead
of 60 seconds?
9-132
Stormwater analyses and design
10
ASSESSMENT OF HYDRAULIC CAPACITY OF EXISTING DRAINAGE
STRUCTURES
10.1
Example 10.1 – Level pool routing
Problem description Example 10.1
You have to determine the attenuation and translation that results from the routing of a given inflow
hydrograph through a dam, see Figure 10.1 (The methodology is the same as for a culvert, using an
outflow equation from Table 7.1 or the continuity of energy relationship). The following is known:
Outflow stage relationship of the spillway of the dam is given by:
Q  C d LH 1,5
where:
Q
Cd
L
H
=
=
=
=
discharge (m3/s)
discharge coefficient
length of the spillway (m)
total energy head (measured above the spillway level) (m)
In this case the outflow can be determined by the following relationship: Q  110 H 1,5
Area-volume relationship of the storage volume is given as indicated below:
Surface area at the spill level = 7,5 km2
Surface area at a level above spill level = 7,5 + 1,5H km2
H = reflects the difference between the free surface level and the spill level, i.e. total energy (m)
Figure 10.1: Section through the spillway of the dam
The inflow hydrograph is given in Figure 10.2.
10-133
Assessment of existing drainage structures
Figure 10.2: Inflow hydrograph
Solution Example 10.1
It is known that the storage relationship is:
H
H
O
O
S   AdH  10 6  (7,5 1,5H)dH
S  10 6 (7,5 H  0,75 H 2  k)
It is known that S = 0, when H = 0 and hence the integration constant, k = 0.
Assume that the time step, Δt = 2 hours = 7200 seconds; then it follows that in the auxiliary function:
N
S O
 :
Δt 2
I1  I 2
 O1 and by substituting the known values, it follows:
2
A distance away from the spill section where the velocity approaches zero in the dam the difference
between the water level and the spillway level reflects the total energy, i.e. h = H
10 6
N
(7,5 H  0,75 H 2 )  55 H1,5
7 200
N 2  N1 
N  1041,7H  104 ,17 H 2  55 H 1, 5
N  104,17H(10  H  0,53 H )
The relationship for N and H to be used in the auxiliary function is shown in Table 10.1 (and
graphically in Figure 10.3).
10-134
Assessment of existing drainage structures
Table 10.1: Relationship of N versus O, for different H-values
H
O
N
0,2
9,8
217,4
0,4
27,8
447,3
0,6
51,1
688,1
0,8
78,7
939,4
1,0
110,0
1200,9
1,2
144,6
1472,3
1,4
182,2
1753,7
1,6
222,6
2044,7
1,8
265,6
2345,4
2,0
311,1
2655,6
Figure 10.3: Graphical presentation of the auxiliary function
If the inflow and outflow hydrographs are plotted (Figure 10.4) it will be observed that:


the intersect of the hydrographs coincides with the maximum storage; and
the maximum outflow rate will be associated with the time of the intersect.
Figure 10.4: The inflow and calculated outflow hydrographs
Summary of the results:
Attenuation = 360-180 = 180 m3/s
Translation = 24-12 = 12 h
10-135
Assessment of existing drainage structures
10.2
Example 10.2 – Level pool routing trough a culvert (inlet controlled)
Problem description Example 10.2
You have to determine the attenuation and translation that results from the routing of a given inflow
hydrograph through an existing culvert, Figure 10.5. The culvert has a square inlet with dimensions of
3,6 m high and 3m wide. The level of the shoulder break point (SBP) is 5 m as measured from the
culvert’s invert.
The methodology for applying level pool routing is the same for a culvert as being described from 1st
principles in Example 10.1 with the exception of using the outflow characteristics as given in Table
10.5. In this example, the Routing Utility given on the accompanying flash drive/DVD is used to
estimate the effect of upstream storages to calculate the attenuation and translation for an existing
culvert structure.
Figure 10.5: Existing culvert
The following catchment parameters upstream of the culvert are known and are given in Table 10.2.
10-136
Assessment of existing drainage structures
Table 10.2: Catchment parameters upstream of the culvert
Longest water Course - 6,65 km
Catchment Area - 9,07 km2
Longitudinal profile for longest water course in catchment
Calculation of the time of concentration for flow in a defined watercourse. (This calculation is by
default done by the Routing Utility and is also given in Table 10.3.)
In a defined watercourse, channel flow occurs. The recommended empirical formula for calculating
the time of concentration in natural channels was developed by the US Soil Conservation Service.
ΤC
 0,87L2
 
 1 000 S av
Where:



0,385
…(10.1)
TC
L
=
=
Sav
=
time of concentration (hours)
hydraulic length of the catchment, measured along the
flow path from the catchment boundary to the point
where the flood needs to be determined (km)
average slope (m/m)
The user may calculate the average slope as defined in Figure 10.6.
10-137
Assessment of existing drainage structures
Figure 10.6: Slope definition for a defined water course
S av 
H 0,85L  H 0,10L
1 0000,75L
Where:
Sav
H0,10L
H0,85L
L
…(10.2)
=
=
=
=
average slope of the catchment (m/m) (see Figure 10.6)
elevation height at 10% of the length of the watercourse (m)
elevation height at 85% of the length of the watercourse (m)
length of the watercourse (km)
The catchment parameters required to determine the average slope for the catchment from Table 10.2
is given in Table 10.3.
Table 10.3: Catchment characteristics with respect to the defined water course
Catchment parameter
Value
Longest Water Course (km)
6,65
Start Elevation (m)
1439
End elevation (m)
1537
10% elevation (m/m)
1443
85% elevation (m/m)
1494
Average slope (m/m)
0,0147
Area (km2)
9,07
Time of Concentration, Tc (hr)
1,45
The area-height relationship for the upstream side of the culvert is given in Table 10.4. These values
can be entered in the blue cells in the Routing Utility in the table titled “Area/Volume Relationship
Upstream of Culvert”. From this relationship, the Routing Utility will automatically calculate the
corresponding volume-height relationship (Table 10.4, Figure 10.7).
10-138
Assessment of existing drainage structures
Table 10.4: Area-height relationship for the upstream side of the culvert
Elevation
(Contour
intervals) (m)
Depth measured
from culvert
Invert (m)
Area (m2)
1401
1402
1403
1404
1405
1406
1407
0
1
2
3
4
5
6
0
1300
27100
47000
85100
127800
139080
16
450000
14
400000
350000
12
Height (m)
Area vs. Height Relationship
Area vs. Volume Relationship
8
250000
200000
6
Volume (m3)
300000
10
150000
4
100000
2
50000
0
0
20000
40000
60000
80000
Area (m2)
100000
120000
0
140000
Figure 10.7: Area-Height and Area-Volume relationship for the upstream side of the culvert
The discharge capacity of culverts operating as inlet controlled systems and varying upstream water
levels, are reflected in Table 10.5. The outlet characteristics can be defined for a rectangular culvert
by the equations as given below in column 2 for the different ratios of H1/D
10-139
Assessment of existing drainage structures
Table 10.5: The capacity of culverts
ROUND CULVERTS
RECTANGULAR CULVERTS
D = inside diameter (m)
D = height (inside) (m)
B = width (inside) (m)
For:
For :
0 < H1/D < 0,8
S 
 0,48 0 
gD
 0,4 
Q
D
2
0,05
0 < H1/D ≤ 1,2
 H1 
D
 
1,9
2
2
Q  C B BH1
gH1
3
3
Where: CB = 1,0 for rounded inlets (r > 0,1B)
CB = 0,9 for square inlets
And for: 0,8 < H1/D ≤ 1,2 *
S 
 0,44  0 
gD
 0,4 
Q
D
2
0,05
 H1 
D
 
And for: H1/D > 1,2
Q  C h BD 2gH 1  C h D 
1,5
(S0 = slope of culvert bed with
effect on capacity)
Note:
slight
Where: Ch = 0,8 for rounded inlets
Ch = 0,6 for square inlets
* For H1/D > 1,2, the orifice formulae applies
D

Q  C D A 2 g  H 1   with CD ≈ 0,6
2

The estimated peak flow rate for the catchment was anticipated to be 76 m3/s for a return period of
Q2T. By assuming a triangular distribution of inflow, the inflow hydrograph is given in Figure 10.8.
10-140
Assessment of existing drainage structures
80
70
Inflow (m³/s)
Flow rate (m3/s)
60
50
40
30
20
10
0
0
50
100
150
Time (min)
200
250
Figure 10.8: Inflow hydrograph
Solution Example 10.2
Step 1: Open the Routing Utility by double clicking on the icon.
Step 2: Accept the user agreement.
Step 3: Enter the site specific catchment and culvert parameters as given in the problem statement
above in the allocate blue cells in the Routing Utility:











Top width (## Times the Time of Concentration) = 0 ;
Maximum inflow (Design Flow rate for normal routing or Q2T for the review of existing
culverts) = 76 m3/s;
Number of Culverts = 1 unit;
Culvert Height = 3,6 m;
Culvert Width = 3,0 m;
Culvert Shape Coefficient - CB = 0,9;
Culvert Shape Coefficient - CH = 0,6;
Maximum allowable damming depth measured from invert of culvert = 5 m;
Longest Water Course 6,65 km;
Average Slope 0,0147 m/m; and
Area-Height relationship as given in Table 10.4.
10-141
Assessment of existing drainage structures
After entering these parameters in the Variable and Area/Volume Relationship Upstream of
Culvert tables in the Routing Utility, the screen captures should look like that given in Table 10.6
and Table 10.7.
Table 10.6: Print screen of entered catchment and culvert parameters
Only fill in values where the cells are blue shaded
Variable
Top width (## Times the Time of Concentration)
Maximum outflow
Volume of Inflow
Volume of Outflow
Routing volume difference
Maximum flow depth
Volume of Storage at Maximum flow depth
Maximum inflow (Design Flow rate for normal routing or Q2T for the review of
existing culverts)
% reduction in peak (Attenuation)
Total Time H1/D > 1,2
Standing water that may cause piping
Number of Culverts
Culvert Height
Culvert Width
Culvert Shape Coefficient - CB
Culvert Shape Coefficient - Ch
Maximum allowable damming depth measured from invert of culvert
H/D maximum Ratio
Longest Water Course
Average Slope
Calculated Tc
Time duration of Outflow (dV/dt≈0)
10-142
Value Units
0
45,18
m3/s
594389
m3
594389
m3
0,0%
4,64
m
185794
m3
76,00
40,3%
102
1,70
1,00
3,60
3,00
0,9
0,6
5,0
1,29
6,65
0,0147
1,45
436
7,26
m3/s
min
hours
units
m
m
m
km
m/m
hours
min
hours
Assessment of existing drainage structures
Table 10.7: Print screen of entered Area-Height parameters
Area/Volume Relationship
Upstream of Culvert
Elevation (Contour intervals)
Depth measured from
Area
Delta
(m)
culvert Invert (m)
(m2)
Volume (m³)
1401
0
0
0
1402
1
1300
650
1403
2
27100
14200
1404
3
47000
37050
1405
4
85100
66050
1406
5
127800
106450
1407
6
139080
133440
1408
7
69540
1409
8
0
1410
9
0
1411
10
0
1412
11
0
1413
12
0
1414
13
0
1415
14
0
1416
15
0
Volume
(m3)
0
650
14850
51900
117950
224400
357840
427380
427380
427380
427380
427380
427380
427380
427380
427380
Step 4: View the auxiliary function.
The auxiliary function used to estimate the outflow from the culvert can be viewed under the
Auxiliary Function tab (Figure 10.9). Notice the vertical increase for outflows exceeding
63 m3/s. This was due to the Area-Height relationship that was not completed for all 16
available increments. However, this does not have any influence on the outcome of the results
since the maximum damming depth is only 4,64 m and that corresponds to an outflow of
45,18 m3/s which is lower than the allowable damming depth of 5 m to the SBP.
10-143
Assessment of existing drainage structures
120
100
Outflow(m3/s)
80
60
40
Auxiliary Function
20
0
0.0
2000.0
4000.0
6000.0
8000.0
10000.0
Auxiliary Function (m3/s)
12000.0
14000.0
16000.0
Figure 10.9: Graphical presentation of the auxiliary function
Step 5: Interpret the inflow and outflow hydrographs.
Depicted on the inflow (blue line) and outflow (red line) hydrographs (Figure 10.10) are also
the change in volume with time (dV/dt) as well as the duration for which the upstream energy
head (H1) exceeds a ratio of 1,2D. These values are reflected by the dashed purple line and
green solid line respectively.
If the inflow and outflow hydrographs are plotted (Figure 10.10) it will be observed that:


the intersect of the hydrographs coincides with the maximum storage; and
the maximum outflow rate will be associated with the time of the intersect.
10-144
Assessment of existing drainage structures
80
0.80
70
Inflow (m³/s)
0.60
Outflow (m³/s)
Total Time H/D>1.2
dV/dt (m³)
0.40
50
0.20
40
0.00
30
-0.20
20
Change in Volume (m3/s)
Flow rate (m3/s)
60
-0.40
10
-0.60
0
0
50
100
150
200
Time (min)
250
300
350
400
Figure 10.10: Inflow and calculated outflow hydrographs
Step 6: The results are summarized under the Summary of Results tab and can be printed by clicking
on the Print Summary Sheet button in the upper right corner of the screen (Figure 10.11).
Included on the summary sheet is a table that depicts the outcome of the assessment for
existing culvert structures. In this case the culvert has not met the criteria as described in
Chapter 10 and thus Fails the hydraulic criteria for existing culverts.
Attenuation = 76 - 45,18 = 30,82 m3/s
Translation = 154 - 87= 67 min
10-145
Assessment of existing drainage structures
Routing Utility for the Investigation of Existing Hydraulic Structures
Variable
Maximum outflow
Maximum inflow (Design Flow rate for normal routing or Q2T for the review of
exisitng culverts)
Total Time H1/D>1.2
Number of Culverts
Culvert Height
Culvert Width
Maximum allowable damming depth measured from invert of culvert
Calculated Time of Concentraction (Tc)
Time duration of Outflow (dV/dt≈0)
Value
Units
45.18
m /s
76.00
102.19
1.00
3.60
3.00
5.00
1.45
7.26
m /s
min
units
m
m
m
hours
hours
3
3
Print
Summary
Sheet
Investigation of existing culvert structures
(Refer to Figure 10.1 SANRAL DRAINAGE MANUAL)
3
Review of maximum temporal storage
VT1 (m )
185794
Review of the duration of excessive energy (upstream inundation)
Ts (min)
102.19
Overall culvert structure outcome:
3
0,5 Vstorm (m ) Pass/Fail
297199
Fail
0,5 Tc (min)
86.90
Pass/Fail
Fail
0
0
Culvert Structure Fail
Inflow and Outflow Hydrographs
80
0.80
70
Inflow (m³/s)
Outflow (m³/s)
Total Time H/D>1.20.60
dV/dt (m³)
60
Flow rate (m3 /s)
0.20
40
0.00
30
-0.20
Change in Volume (m3/s)
0.40
50
20
-0.40
10
-0.60
0
0
100
200
300
Time (min)
400
500
Developed by:
Disclaimed: This program was developed for the convenience of its users. Although every reasonable effort has been made to ensure that the program is accurate and reliable the program developers,
Sinotech CC and/or Prof SJ van Vuuren accept no liability of any kind for any results, interpretation thereof or any use made of the results obtained with these programs. All users of this program do
so entirely at their own risk
Figure 10.11: Summary of the results
Step 7: Re-evaluating the system with an upgraded system of 2 culverts of the same dimensions, it can
be perceived that the maximum outflow is increased from 45,18 m3/s to 60,52 m3/s for the
same inflow characteristics. However, upstream damming is significantly reduced from
4,64 m to 3,51 m. Now the structure meets the hydraulic criteria as given in Chapter 10 and
thus Pass the hydraulic criteria for existing culverts (Figure 10.12).
10-146
Assessment of existing drainage structures
Routing Utility for the Investigation of Existing Hydraulic Structures
Variable
Maximum outflow
Maximum inflow (Design Flow rate for normal routing or Q2T for the review of
exisitng culverts)
Total Time H1/D>1.2
Number of Culverts
Culvert Height
Culvert Width
Maximum allowable damming depth measured from invert of culvert
Calculated Time of Concentraction (Tc)
Time duration of Outflow (dV/dt≈0)
Value
Units
60.52
m /s
76.00
0.00
2.00
3.60
3.00
5.00
1.45
5.16
m /s
min
units
m
m
m
hours
hours
3
3
Print
Summary
Sheet
Investigation of existing culvert structures
(Refer to Figure 10.1 SANRAL DRAINAGE MANUAL)
3
Review of maximum temporal storage
VT1 (m )
85527
Review of the duration of excessive energy (upstream inundation)
Ts (min)
0.00
Overall culvert structure outcome:
3
0,5 Vstorm (m ) Pass/Fail
297199
Pass
0,5 Tc (min)
86.90
Pass/Fail
Pass
1
1
Culvert Structure Pass
0.50
70
Inflow (m³/s)
Outflow (m³/s)
0.40
Total Time H/D>1.2
dV/dt (m³)
60
0.30
50
0.20
40
0.10
30
0.00
20
-0.10
10
-0.20
Change in Volume (m3/s)
Flow rate (m3 /s)
Inflow and Outflow Hydrographs
80
-0.30
0
0
100
200
300
Time (min)
400
500
Developed by:
Disclaimed: This program was developed for the convenience of its users. Although every reasonable effort has been made to ensure that the program is accurate and reliable the program developers,
Sinotech CC and/or Prof SJ van Vuuren accept no liability of any kind for any results, interpretation thereof or any use made of the results obtained with these programs. All users of this program do
so entirely at their own risk
Figure 10.12: Summary of the results for re-assessed culvert with 2 units of the same dimensions
10-147
Assessment of existing drainage structures
11
FREE SURFACE FLOW DETERMINATION
HEC-RAS is constantly being upgraded and the screen layouts on newer versions may differ
from what is shown in this chapter.
11.1
Basic flood line determination (HEC-RAS)
Goal: This is an exercise to perform a basic flow analysis on a single river reach. The water surface
profile should be determined for this river section in order to obtain the flood line levels at a specific
site. The specific site is earmarked for the development of a shopping complex and is situated along the
Tsitsa River in the Eastern Cape. The 1:20, 1:50 and 1:100 year flood line levels should be determined.
STARTING A NEW PROJECT
To begin this exercise, start the HEC-RAS program by double clicking the HEC-RAS icon on the
desktop. The main window should appear as shown in Figure 11.1.
Figure 11.1: HEC-RAS main window
The first step in developing a HEC-RAS application is to start a new project. Go to File menu on the
main window and select New Project. The New Project window should appear as shown in Figure
11.2. Set the drive and directory you would like to work in. Enter the project title and file name as
shown in Figure 11.2. Once you have entered the information, press the OK button to accepted the
title and file name and create the new project.
Figure 11.2: New Project window
Once back at the HEC-RAS Main window select from the menu bar Options, and set the units that
you would like to work in to be metric units as well as be the default setting for all new projects (see
Figure 11.3 and Figure 11.4).
11-148
Free surface flow determination
In the right hand corner of the main screen it will now indicate SI units.
Figure 11.3: Options menu
Figure 11.4: Unit systems
ENTERING GEOMETRIC DATA
First a steady state flow model will be developed:
The next step is to enter the Geometric Data. This is accomplished by selecting Geometric Data from
the Edit menu on the HEC-RAS Main window (Figure 11.1) or clicking the short cut button on the
menu bar
. Once this option is selected, the geometric data window will be shown (see Figure 5).
This screen can be maximized by clicking on the maximize button
in the right hand corner of the
window.
Figure 11.5: Geometric Data window
11-149
Free surface flow determination
Drawing the schematic of the river system
A plan view of the river section with cross sections is shown below in Figure 11.6.
Figure 11.6: Plan view of river section
The first step is to draw the river system schematically by performing the following steps:
 Although it is only a schematic drawing one would still like to draw it more or less to scale.
To assist with this HEC-RAS has an option to import a background picture.

Click on the Add/Edit background picture button
on the menu bar. The program will
show the Background Pictures on Schematic window (Figure 11.7).
11-150
Free surface flow determination
Figure 11.7: Background Pictures on Schematic window

Click on the Add button and select the background picture (Exercise 1 – Background
picture.jpg)

HEC-RAS will indicate that the picture extents past the current schematic boundaries and ask
you if you would want to increase the schematic extents (Figure 11.8). Select Yes.
Figure 11.8: Increasing the schematic extents

Once the picture has been selected click on the Close button (Figure 11.7).

Use the Schematic view selector box to drag the extents of the inserted picture over the entire
screen (Figure 11.9).

Now the river section can be drawn over the background picture. Click the River Reach
button on the geometric data window.

Move the mouse pointer over the drawing area and place the pointer at the location in which
you would like to start drawing the reach.
11-151
Free surface flow determination
Schematic view
selector box
Figure 11.9: Viewing the background picture
 Press the left mouse button once to start drawing the reach. Move the mouse pointer and
continue to press the left mouse button to add additional points to the line segment. To end
the drawing of the reach, double click the left mouse button and the last point on the reach will
be placed at the current mouse pointer location (right click will remove the last point drawn).
All reaches must be drawn from the upstream to downstream (in the positive flow direction)
i.e. start at cross section 12 down to cross section 1 (Decreasing numeric values).

Once the reach is drawn, the interface will prompt you to enter an identifier for the River
name and the Reach name. The River identifier can be up to 32 characters, while the reach
name is limited to 12 characters. In this exercise the river will be called, Tsitsa and the reach
Lower reach (see Figure 10).
Figure 11.10: River and reach names
Once you have finished the drawing of the river system, there are several options available for
editing the schematic. The options include changing the name, adding points to a reach,
removing points from a reach, deleting a reach, and deleting a junction. The editing features
are located under the Edit menu on the Geometric Data window.
11-152
Free surface flow determination

Since the schematic of the river has now been drawn there is no more need for the background
picture. To switch off the background picture click on the Add/Edit background picture
button
on the menu bar. Deselect the picture as shown in Figure 11.11.
Figure 11.11: Deselecting the background picture

When you first draw the schematic there will be no tic marks representing the cross sections as
shown in Figure 11.12. The tic marks only show up after you have entered cross sections.
11-153
Free surface flow determination
Figure 11.12: Geometric Data window with Tsitsa river schematic
Entering cross section data
The next step is to enter the cross section data. This is accomplished by clicking the cross
section button on the Geometric window (Figure 11.12). Once this button is clicked, the
Cross Section Data editor will appear as shown in Figure 11.13.
11-154
Free surface flow determination
Figure 11.13: Cross section Data Editor
To enter cross section data follow these steps:

Select a River and a Reach to work with. In this exercise there is only one River (Tsitsa) and
one Reach (Lower reach).

Go to the Options menu and select Add a new Cross Section. An input box will appear to
prompt you to enter a river station identifier for the new cross section (see Figure 11.14).
Figure 11.14: Add a new river station
The identifier does not have to be the actual river station, but it must be a numerical value.
The numeric value describes where the cross section is located in reference to all other cross
sections within the reach. Cross sections are located from upstream (highest river station) to
downstream (lowest river station). For this cross section enter a value of 12.

For this cross section, enter all the data as shown in Figure 11.15.
11-155
Free surface flow determination
Figure 11.15: Cross Section Data Editor with data

Enter the:
Description: Upstream boundary of this river section
Downstream reach lengths: LOB = 100, Channel = 95 and ROB = 90
Manning n-values: LOB = 0,05, Channel = 0,035 and ROB = 0,05
Station and elevation details:
Nr
Station
Elevation
1
100
100,3
2
103
97,3
3
125
96,1
4
133
94,4
5
135
94,3
6
138
95,6
7
148
96,0
8
154
99,5
Main channel stations: Left bank = 125 and Right bank = 138
Cont\Exp coefficients: Contraction = 0,1 and Expansion = 0,3

Once all the data is entered press the Apply Data button. This button is used to instruct the
program to accept the entered data into memory. This button does not save the data to the
hard disk. This is done by clicking on Save Geometry Data under the File menu on the
Geometric Data window (which will be explained later).

Plot the cross section to visually inspect the data. This is accomplished by pressing the Plot
Cross Section option under the Plot menu on the Cross Section Data Editor or by clicking on
the Expand XS editor to include a XS plot
that shown in Figure 11.16 below.
11-156
. The cross section should look similar to
Free surface flow determination
Figure 11.16: Cross section plot for river station 12
Note the manning roughness values at the top of the cross section and the specified bank
stations (red dots) (Figure 11.16).
In practice the steps listed above would be repeated for every cross section that is entered. In order to
reduce the amount of data entry for this exercise, the current cross section will be copied and adjusted
to represent other cross sections within the river system.
Two options of completing cross section data entry:
Method 1: # Novice users: Enter the rest of the 11 cross sections one by one as detailed in the
steps above. Data for each cross section is provided in the following 11 figures.
Method 2: # Expert users: Skip the next two pages.
11-157
Free surface flow determination
METHOD 1
Figure 11.17: Cross section 11 data
Figure 11.18: Cross section 10 data
Figure 11.19: Cross section 9 data
Figure 11.20: Cross section 8 data
Figure 11.21: Cross section 7 data
Figure 11.22: Cross section 6 data
11-158
Free surface flow determination
Figure 11.23: Cross section 5 data
Figure 11.24: Cross section 4 data
Figure 11.25: Cross section 3 data
Figure 11.26: Cross section 2 data
Figure 11.27: Cross section 1 data
11-159
Free surface flow determination
If you have completed entering the cross section data as shown in Figure 11.17 to Figure 11.27 skip
the next two pages.
METHOD 2
# Expert users: Follow the following steps to copy the current cross sections and adjust to look
similar to Figure 11.17 to Figure 11.27.

Go to the Options menu on the cross Section Data Editor and select Copy Current Cross
Section. An input box will appear to prompt you to select a river reach, and then enter a river
station for the new cross section, see Figure 11.28. For this exercise, keep the river and reach
as Tsitsa River and Lower reach, then enter a new river station of 11.
Figure 11.28: Copying and existing cross section
Press the OK button and the new cross section will appear in the editor.

Change the cross section description to “Tsitsa River 11”.

Adjust all the elevations of the cross sections by –0,2 meter. This is accomplished by
selecting the Adjust Elevations feature from the Options menu on the Cross Section Data
Editor.

Adjust the cross section stationing to reduce the overbanks by 10%.

This is accomplished by selecting the Adjust Stations feature from the Options menu on the
Cross Section Data Editor, then select Multiply by a Factor. When the input box appears for
this option, three data entry fields will be available to adjust the stationing of the left
overbank, channel, and the right overbank separately. Enter values of 0,9 for the right and left
overbanks, but leave the main channel field blank. This will reduce the stationing of both
overbanks by 10%, but leave the main channel unchanged.

Downstream reach lengths change to LOB = 48, Channel = 42 and ROB = 40 for this cross
section.

Press the Apply Data button (The data should be similar to that shown in Figure 11.17). Plot
the cross section to visually inspect it (see Figure 11.29).
11-160
Free surface flow determination
Figure 11.29: Cross section plot (cross section 11)
These seven steps above should be repeated to enter all the data for Tsitsa River (Lower Reach). The
necessary adjustments are listed in Table 11.1. Perform the cross section duplications in order that
they are listed in the table. Make sure to change the description of each cross section, and also press
the Apply Data button after making the adjustments for each cross section.
Table 11.1: Cross section adjustments for duplicating sections
Cross section
Description
River
station
Adjusted
elevation
Adjusted stationing
Downstream reach lengths
Left
O.B.
Channel
Right
O.B.
Left
O.B.
Channel
Right
O.B.
Tsitsa River 11
11
-0,20
0,9
-
0,9
48
42
40
Tsitsa River 10
10
-0,10
1,2
1,0
1,1
95
90
85
Tsitsa River 9
9
-0,10
-
1,1
-
100
102
105
Tsitsa River 8
8
-0,05
-
1,3
-
100
110
120
Tsitsa River 7
7
-0,10
1,5
-
-
120
120
125
Tsitsa River 6
6
-0,15
-
2,0
2,0
80
82
85
Cross section at
site
5
-0,05
2,0
-
-
80
80
80
Tsitsa River 4
4
-0,05
0,5
1,0
1,0
180
180
180
Tsitsa River 3
3
-0,12
-
-
0,5
115
105
100
Tsitsa River 2
2
-0,18
0,5
0,5
-
155
155
150
Downstream
boundary of river
section
1
-0,10
0,8
-
-
0
0
0
11-161
Free surface flow determination
Table 11.1 is simply a quick way to generate varying cross sections for this exercise. The method
however is quite useful when working with a man-made structure such as a channel, which has similar
cross sections.
# Novice & Expert users continue
This completes all the cross section data for the Tsitsa River (Lower reach) save the data file before
continuing. Saving the data to a file is achieved by exiting the Cross Section Data editor window and
selecting the Save Geometry Data As option from the File menu on the Geometric Data window.
After selecting this option you will be prompted to enter a Title for the geometric data (Figure 30).
Enter “Natural Tsitsa River” for this exercise, and then press the OK button. A file name is
automatically assigned to the geometry data based on what you entered for the project file name i.e.
Exercise1.g01.
Figure 11.30: Save Geometry Data As

Return to the Cross Section Data editor window and from the Plot menu select Plot Profile...
to view the longitudinal profile of the entered cross sections (see Figure 11.31).
Figure 11.31: Longitudinal profile plot
11-162
Free surface flow determination
When returning to the Geometric Data window the user will notice that the Tsitsa River now also
shows the schematic layout with the position of the entered cross sections, see Figure 11.32.
Figure 11.32: Schematic layout of entered system
We have completed the required geometric data and can now continue and enter the Steady Flow
Data.
ENTERING STEADY FLOW DATA
The next step in developing the required data to perform steady flow water surface profile calculations
is to enter the steady flow data. To bring up the steady flow data editor, select Steady Flow Data
from the Edit menu on the HEC-RAS main window or click on the Steady Flow Data button
the menu bar. The steady Flow Data editor should appear as shown in Figure 11.33.
11-163
on
Free surface flow determination
Figure 11.33: Steady Flow Data window

The first set of required data to enter is the number of profiles to be calculated. For this
exercise enter “3" as shown in Figure 34 (and click on the Apply button). The next step is to
enter the flow data. Flow data are entered from upstream to downstream for each reach. At
least one flow rate must be entered for every reach in the river system. Once a flow value is
entered at the upstream end of a reach, it is assumed that the flow remains constant until
another flow value is encountered within the reach. Additional flow values can be entered at
any cross section location within a reach. In this exercise there is only 1 reach and thus it will
only be required to enter 1 set of flow data. In this exercise, flow data will be entered at the
upstream end of the reach i.e. at cross section 12.

Profile labels will automatically default to “PF1" and “PF2" etc. These labels can be changed
to whatever is descriptive of the flow. In this exercise these should be changed to 1:20 yr,
1:50 yr and 1:100 yr. Under the Options menu go to Edit Profile Names and change the
profile names. Click on the OK button to accept the names.

Enter the 1:20, 1:50 and 1:100 year flood peak values of 35, 80 and 150 m³/s respectively (see
Figure 34).
11-164
Free surface flow determination
Figure 11.34: Steady flow data

The next step is to enter any required boundary conditions. To enter boundary conditions,
press the Reach Boundary Conditions button at the top of the Steady Flow Data editor (see
Figure 11.34). The boundary conditions editor will appear as shown in Figure 11.35.
Figure 11.35: Steady Flow Boundary Conditions

Boundary conditions are necessary to establish the starting water surface at the boundaries of
the river system. A starting water surface is necessary in order for the program to begin
calculations. In a subcritical flow regime, boundary conditions are only required at the
downstream end of the river system.
If a mixed flow regime calculation is going to be performed, then boundary conditions must
be entered at all open ends of the river system.
11-165
Free surface flow determination
The boundary conditions editor contains a table listing of every river and reach. Each reach
has an upstream and a downstream boundary condition. Connections to junctions are
considered internal boundary conditions. Internal boundary conditions are automatically
listed in the table, based on how the river system is connected in the geometric data editor.
The user is only required to enter the necessary external boundary conditions.
In this exercise it is assumed that the flow is subcritical throughout the river system (Verify if
this is correct!!!). Therefore, it is only necessary to enter a boundary condition at the
downstream end of the Tsitsa River, Lower reach. Boundary conditions are entered by first
selecting the cell in which you wish to enter a boundary condition. Then the type of boundary
condition is selected from the four available types listed above the table see Figure 11.35
(Known Water Surface, Critical Depth, Normal Depth or a Rating Curve).
In this exercise it is assumed that there are no control points in the river further
downstream and that cross section 1 is far enough downstream and can be assumed to
flow at normal flow depth.

Click in the cell in the Table (Figure 11.35) under the Downstream column and then click on
the Normal Depth button. In other words the program will start at this downstream
boundary, calculate the normal flow depth and work systematically upstream in the river
section.
A pop up box will appear (see Figure 11.36) requesting you to enter an average slope at the
downstream end of the river reach. Enter a value of 0,001 (m/m) then click on the OK button.
Figure 11.36: Pop-up box (enter the average downstream slope)
This completes all of the necessary boundary condition data (see Figure 11.37).

Click the OK button on the Boundary Conditions window to accept the data and return to the
Steady Flow Data screen.
11-166
Free surface flow determination
Figure 11.37: Accepted boundary condition data

The last step is to save the data to a file. To save the data, select the Save Flow Data As
option from the File menu on the Steady Flow Data Editor. A pop-up box will prompt you to
enter a description/title of the flow data (Figure 38). For this exercise enter: Calculated flood
peaks. A file name is automatically assigned to the steady flow data based on what you
entered for the project file name i.e. Assignment1.f01.
Figure 11.38: Save Flow Data As
Once the data has been saved, you can close the Steady Flow Data Editor.
PERFORMING THE HYDRAULIC CALCULATIONS
Now that all of the data has been entered, we can calculate the steady water surface profiles. To
perform the simulations, go to the HEC-RAS main window and select Steady Flow Analysis from the
Run menu or click on the Steady Flow Analysis button
on the menu bar. The Steady Flow
Analysis window should appear as shown in Figure 11.39, except yours will not have any plan title or
Short ID yet.
11-167
Free surface flow determination
Figure 11.39: Steady Flow Analysis Simulation Window

The first step is to put together a Plan. The Plan defines which geometry and flow data are to
be used, as well as providing a title and short identifier for the run. To establish a plan, select
New Plan from the File menu on the Steady Flow Analysis window. Enter the plan title as
First run and then press the OK button (Figure 11.40).
Figure 11.40: Creating new plan

You will be prompted to enter a short identifier. Enter a title of Run1 in the Short ID box
(Figure 11.41) and click on the OK button.
Figure 11.41: Plan identifier

The next step is to select the desired flow regime for which the model will perform
calculations. For this example we will be performing Subcritical flow calculations only since
only a downstream boundary condition was specified. Make sure Subcritical is the selected
flow regime.
11-168
Free surface flow determination

Additional job control features are available from the Options menu bar. Select Critical
Depth Output Option… from this menu. A pop-up window will appear in which the user
can select the Critical Always Calculated option (Figure 11.42). The program will then
always calculate the critical flow depth for every flow rate. Click on the OK button.
Figure 11.42: Critical depth calculation option

Once you have defined a plan and set all the desired job control information, the plan
information should be saved. Saving the plan information is accomplished by selecting Save
Plan from the File menu of the Steady Flow Analysis window.
Now that everything has been saved and set, the steady flow computations can be performed by
pressing the Compute button at the bottom of the Steady Flow Simulation window (Figure 11.39).
Once the computations have been completed, the computation window can be closed, as well as the
Steady Flow Simulation window.
VIEWING RESULTS
Once the model has finished all of the computations successfully, you can begin viewing the results.
Several output options are available from the View menu bar on the HEC-RAS main window. These
options include:
Cross section plots
Profile plots
General profile plot
Rating curves
X-Y-Z perspective plots
Detailed tabular output at a specific
cross section (cross section table)
Limited tabular output at many cross
sections (profile table)
Cross section plots
Begin by plotting a cross section. Select Cross Sections from the View menu on the HEC-RAS main
window. Any cross section can be plotted by selecting the appropriate river, reach and river station
(see Figure 11.43). Several plotting features are available from the Options menu bar on the cross
section plot window. These options include: zoom in; zoom out; selecting which plans, profiles,
variables to plot; and control over lines, labels, symbols, scaling etc.
11-169
Free surface flow determination
Figure 11.43: Cross section (all three profiles)
Select different cross sections to plot and practice using some of the features available under the
options menu bar.
Profile plot
The second plot, which is of value, is the water surface profile. Select Water Surface Profiles from
the View menu.
This should give you a profile plot as shown in Figure 11.44.
Try and obtain the profile plot to look exactly like Figure 11.44 selecting various options under the
Options menu (grid, labels, line types, text, profiles etc.).
11-170
Free surface flow determination
Figure 11.44: Water Surface Profile (for entire reach)
General profile plots
The third plot option, which is of value, is the General Profile Plot. Select General Profile Plot from
the View menu. This should give you a profile plot as shown in Figure 11.45.
From the Standard Plots menu various other useful plots can also be made such as Froude numbers
(on left bank, main channel and right bank), see Figure 11.46.
11-171
Free surface flow determination
Figure 11.45: General profile plot (velocities)
Figure 11.46: General profile plot (Froude numbers)
11-172
Free surface flow determination
The data used to generate the plots can also be viewed in Table format by clicking on the Table tab
next to the Plot tab. The generated plot or data can be copied to the clipboard by simply going to the
File menu (for that specific tab), see Figure 11.47 and Figure 11.48.
Figure 11.47: General profile plot (Copying the plot to the clipboard)
Figure 11.48: General profile plot (Writing data to a file (csv type))
This copying of pictures/graphs/data can be done throughout HEC-RAS.
Rating curve
Select Rating Curves from the View menu plot a computed rating curve. A rating curve based on the
computed water surface profiles will appear as shown in Figure 11.49. You can look at the computed
rating curve for any location (cross section) by selecting the appropriate river, reach and river station.
11-173
Free surface flow determination
Figure 11.49: Rating Curve (cross section 5)
HEC-RAS basically plots a curve through the three flows used in the calculation i.e. 35 m³/s, 80 m³/s
and 150 m³/s. The more flows used in the calculation the more accurate rating curve will be obtained.
X-Y-Z Perspective Plot
Select X-Y-Z Perspective Plots from the View menu to plot a 3D view of the river section (Figure
11.50). Set the Rotation Angle to –70 and the Asimuth Angle to 19 to obtain the same view as shown
in Figure 11.50. This type of view gives a clear view of the widening of the river at cross section 5
and 6.
11-174
Free surface flow determination
Figure 11.50: X-Y-Z Perspective Plot
Tabular output
Detailed tabular output
Now look at some tabular output. Go to the View menu on the HEC-RAS main window. There are
two types of tables available, a detailed output table and a profile summary table. Select Detailed
Output Tables to get the first table to appear. The table should be similar to the one shown in Figure
11.51 (notice the warning at the bottom of the table for river station number 3). This table shows
detailed hydraulic information at a single cross section. Other cross sections can be viewed by
selecting the appropriate reach and river from the table.
11-175
Free surface flow determination
Figure 11.51: Detailed table output
Summary Errors, Warnings, and Notes
The HEC-RAS software has a system of Errors, Warnings, and Notes that are passed from the
computation programs to the user interface. During the computations, the computation programs will
set flags for at a particular node (nodes are cross sections, bridges, culverts, or multiple openings)
whenever it is necessary. These message flags are written to the standard output file, along with the
computed results for that node. When the user interface reads the computed results from the output
file, if any errors, warnings, or notes exist, they are interpreted and displayed in various locations from
the interface.
The user can request a summary of all the errors, warnings, and notes that occurred during the
computations. This is accomplished by selecting Summary Errors, Warnings, and Notes from the
View menu on the main HEC-RAS window or clicking the short cut button
.
Once this is selected, a window will pop up displaying all of the messages. The user can select a
specific River and Reach, as well as which Profile and Plan to view. The user has the options of
expanding the window; printing the messages; or sending them to the windows clipboard.
Besides the summary window, messages will automatically appear on the cross section specific tables.
When a cross section or hydraulic structure is being displayed, any errors, warnings, or notes for that
location and profile will show up in the Errors, Warnings, and Notes message box at the bottom of the
table. An example of this table is shown in Figure 11.51.
11-176
Free surface flow determination
In general, the errors, warnings, and notes messages should be self-explanatory. The three categories
of messages are the following:
ERRORS: Error messages are only sent when there are problems that prevent the program from being
able to complete the run.
WARNINGS: Warning messages provide information to the user that may or may not require action
on the user’s part. In general, whenever a warning is set at a location, the user should review the
hydraulic results at that location to ensure that the results are reasonable. If the hydraulic results are
found to be reasonable, then the message can be ignored. However, in many instances, a warning level
message may require the user to take some action that will cause the message to disappear on future
runs. Many of the warning messages are caused by either inadequate or bad data. Some common
problems that cause warning messages to occur are the following:
Cross sections spaced to far apart. This can cause several warning messages to be set.
Cross sections starting and ending stations not high enough. If a computed water surface is higher
than either end point of the cross section, a warning message will appear.
Bad Starting Water Surface Elevation. If the user specifies a boundary condition that is not possible
for the specified flow regime, the program will take action and set an appropriate warning message.
Bad Cross Section Data. This can cause several problems, but most often the program will not be
able to balance the energy equation and will default to critical depth.
NOTES: Note level messages are set to provide information to the user about how the program is
performing the computations.
Profile Summary Table
Go to the View menu on the HEC-RAS main window. There are two types of tables available, a
detailed output table and a profile summary table. Select Profile Summary Table. This table shows a
limited number of hydraulic variables for several cross sections in the selected river reach (see Figure
11.52).
Figure 11.52: Profile Summary Table (Standard Table)
There are several types of profile tables listed under the Std. Tables menu (see Figure 11.53) of the
profile table window. Each one of these tables shows typical detail relevant to the specific structure.
11-177
Free surface flow determination
Figure 11.53: Std. Tables menu
A special feature of the profile summary tables is the ability for users to define their own output tables.
User defined output tables are available by selecting Define Table… from the Options menu of the
profile table. When this option is selected, a window will appear, as shown in Figure 11.54. At the
top of the window is a table for the user selected variable headings (Table Column Headings), the
units, and the number of decimal places to be displayed for each variable. Below this table is a list
containing all of the available variables that can be included in your user-defined table. The variables
are listed in alphabetical order. Below the list of variables is a message box that is used to display the
definition of the selected variable.
Figure 11.54: Define a table
11-178
Free surface flow determination
To get a definition of a particular variable, simply click the left mouse button once while the mouse
pointer is over the desired variable. The description of the variable will show up at the bottom of the
window. To add variables to the column headings, simply double click the left mouse button while the
mouse pointer is over the desired variable. The variable will be placed in the active field of the table
column headings. To select a specific column to place a variable in, click the left mouse button once
while the mouse pointer is over the desired table column field. To delete a variable from the table
headings, double click the left mouse button while the mouse pointer is over the variable that you want
to delete. The number of decimal places for each variable can be changed by simply typing in a new
value.
User defined tables are limited to 15 variables. Once you have selected all of the variables that you
want, press the OK button at the bottom of the window. The profile table will automatically be
updated to display the new table
Once you have the table displayed in the profile table window, you can save the table headings for
future use. To save a table heading, select Save Table from the Options menu on the profile table
window. When this option is selected, a pop up window will appear, prompting you to enter a name
for the table. Once you enter the name, press the OK button at the bottom of the pop up window. The
table name will then be added to a list of tables included under the User Tables menu on the profile
table window.
Create a user defined table as detailed above with the following columns:
 Q Total (Total flow rate)
 W.S. Elev (Water surface elevation)
 Crit W.S. (Critical water surface elevation)
 Vel Chnl (Velocity in the main channel)
 Froude # Chl (Froude number in the main channel)
Save the table (Exercise 1 – Table) and view the summary table thereof with 1:50 and 1:100 year
profiles (selected from the Options menu) (Figure 11.55).
11-179
Free surface flow determination
Figure 11.55: User defined table
At the end of this exercise the following objectives should have been met:

Be able to set-up a HEC-RAS project

Know how to enter geometric data

Understand the setting of boundaries and controls

Know how to enter steady flow data

Know how to analyse a river system

Know how to extract information
11-180
Free surface flow determination
Questions
1. What is the normal flow depth for the 1:50 year flood at cross section 1?
2. Define the flow type in the river.
3. What is the kinetic energy component at cross section 11 for the 1:50 year flood?
4. What is the kinetic energy component at cross section 5 (the proposed site) for the 1:50 year
flood?
5. Why is there a difference between the kinetic energy component at cross section 5 and 11?
6. What are the flood levels (1:20, 1:50 and 1:100) at the proposed site (cross section 5)?
7. What will the water level be at cross section 5 if the flood peak is 100 m³/s?
8. What is the energy weighting coefficient (alpha) for cross section 5 for the 1:50 year flood?
9. How wide is the river flowing at cross section 5 during the 1:100 year flood?
10. What is the hydraulic depth in the main channel during the 1:100 year flood at cross section 5?
11. How would you know if cross section 5 or 6 was functioning as a control point in the river
section?
12. Are you in a position to draw in the 1:20, 1:50 and 1:100 year flood lines for the proposed
site?
11-181
Free surface flow determination
11.2
Setting-up a HEC-RAS model (river section, bridge and weir) and performing
unsteady flow analysis
Goal: This is an exercise to perform an unsteady flow analysis on a river system. The
river system contains a bridge structure and an inline weir.
STARTING A NEW PROJECT
To begin this exercise, start the HEC-RAS program by double clicking the HEC-RAS icon on the
desktop. The main window should appear as shown in Figure 11.56.
Figure 11.56: HEC-RAS main window
The first step in developing a HEC-RAS application is to start a new project. Go to File menu on the
main window and select New Project. The New Project window should appear as shown in Figure
11.57. Set the drive and directory you would like to work in. Enter the project title and file name as
typically shown in Figure 11.57. Once you have entered the information, press the OK button to
accepted the title and file name and create the new project.
Figure 11.57: New Project window
Once back at the HEC-RAS Main window select from the menu bar Options, and set the units that
you would like to work in to be metric units as well as be the default setting for all new projects
(assignments). In the right hand corner of the main screen it will now indicate SI units.
11-182
Free surface flow determination
ENTERING GEOMETRIC DATA
The next step is to enter the Geometric Data. This is accomplished by selecting Geometric Data from
the Edit menu on the HEC-RAS Main window (Figure 11.56) or clicking the short cut button on the
menu bar
11.58).
. Once this option is selected, the geometric data window will be shown (see Figure
Figure 11.58: Geometric Data window
Drawing the schematic of the river system
A plan view of the river section with cross sections is shown below in Figure 11.59.
11-183
Free surface flow determination
Figure 11.59: Plan view of river section
The first step is to draw the river system schematically by performing the following steps:

Click the River Reach button on the geometric data window.

Move the mouse pointer over the drawing area and place the pointer at the location in which
you would like to start drawing the reach.

Press the left mouse button once to start drawing the reach. Move the mouse pointer and
continue to press the left mouse button to add additional points to the line segment. To end
the drawing of the reach, double click the left mouse button and the last point on the reach will
be placed at the current mouse pointer location (right click will remove the last point drawn).
All reaches must be drawn from the upstream to downstream (in the positive flow direction)
i.e. start at cross section 100 down to cross section 70, 65 down to cross section 40 and from
cross section 8 to 3 (see Figure 11.60).

Once a reach is drawn, the interface will prompt you to enter an identifier for the River name
and the Reach name. The River identifier can be up to 32 characters, while the reach name is
limited to 12 characters. In this exercise the rivers will be called, Riet and Blesbok and the
reaches Upper and Lower reach (see Figure 11.60).
11-184
Free surface flow determination

Once you enter the identifiers for Blesbok River or for the lower reach of the Riet River, you
will be prompted to enter an identifier for the junction, in this case Sahara. Junctions in HECRAS are locations where two or more reaches join together or split apart.

When you first draw the schematic there will be no tic marks representing the cross sections.
The tic marks only show up after you have entered cross sections.
Figure 11.60: Geometric Data window (schematic)
Entering cross section data
The next step is to enter the cross section data. This is accomplished by clicking the cross
section button on the Geometric window (Figure 11.60). Once this button is clicked, the
Cross Section Data editor will appear as shown in Figure 11.61.
11-185
Free surface flow determination
Figure 11.61: Cross section Data Editor
To enter cross section data follow these steps:
 Select a River and a Reach to work with (from the drop down lists).

Go to the Options menu and select Add a new Cross Section. An input box will appear to
prompt you to enter a river station identifier for the new cross section (see Figure 11.62).
Figure 11.62: Add a new river station
The identifier does not have to be the actual river station, but it must be a numerical value.
The numeric value describes where the cross section is located in reference to all other cross
sections within the reach. Cross sections are located from upstream (highest river station) to
downstream (lowest river station). For this cross section enter a value of 100.

For this cross section, enter all the data as shown in Figure 11.63.
11-186
Free surface flow determination
Figure 11.63: Cross Section Data Editor with data

Enter the:
Description: Upstream River Station
Downstream reach lengths: LOB = 25, Channel = 28 and ROB = 30,5
Manning n-values: LOB = 0,035, Channel = 0,025 and ROB = 0,035
Station and elevation details:
Nr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Station
0,00
3,05
4,57
8,53
9,75
10,67
12,19
15,24
18,29
19,81
21,34
22,56
24,08
25,30
26,21
Elevation
26,82
25,60
24,69
23,77
22,25
21,03
20,42
19,51
19,45
20,73
22,25
24,23
24,38
25,91
28,04
Main channel stations: Left bank = 8,53 and Right bank = 22,56
Cont\Exp coefficients: Contraction = 0,1 and Expansion = 0,3
11-187
Free surface flow determination

Once all the data is entered press the Apply Data button. This button is used to instruct the
program to accept the entered data into memory. This button does not save the data to the
hard disk (click on Exit on the Cross Section Data editor window). This is done by clicking
on Save Geometry Data under the File menu on the Geometric Data window. After
selecting this option you will be prompted to enter a Title for the geometric data (Figure
11.64). Enter “Base Geometry” for this exercise, and then press the OK button. A file name
is automatically assigned to the geometry data based on what you entered for the project file
name i.e. Exercise2.g01.
Figure 11.64: Save Geometry Data As

Instead of retyping all the cross section data, an Excel spreadsheet containing all the stations
and elevation data is provided. To quickly enter all the cross sectional data follow the
following 6 steps
o
Step 1: Select a River and a Reach to work with (from the drop down lists).
o
Step 2: Go to the Options menu and select Add a new Cross Section. An input box
will appear to prompt you to enter a river station identifier for the new cross section
(see Figure 11.62).
o
Step 3: Set the Horizontal Variation in n Values under the Options menu to true
(ticked) see Figure 11.65.
Figure 11.65: Horizontal Variation in n Values (Options menu)
11-188
Free surface flow determination
o
Step 4: Go to the Excel spreadsheet (Exercise 2 - Cross sections.xls) and copy the
Station, Elevation and n-value data for the specific cross section/river station (see
Figure 11.66).
Figure 11.66: Copying cross section data from Excel
o
o
Step 5: Return to HEC-RAS, and select same number (or more) number of rows in the
Cross Section Data editor window (see Figure 11.67). From the Edit menu click on
Paste, to insert the data in the table.
Step 6: Enter the rest of the other characteristic data:
Description: “”
Downstream reach lengths: LOB = 22,9, Channel = 29,0 and ROB = 33,5
Main channel stations: Left bank = 8,32 and Right bank = 22,56
Cont\Exp coefficients: Contraction = 0,1 and Expansion = 0,3
All the other characteristic data is provided in Table 11.2.
The spreadsheet printout of all the cross section data is attached in Appendix A for
reference.
11-189
Free surface flow determination
Figure 11.67: Pasting the cross section data from Excel into the Cross Section Data Editor table
Figure 11.68: Completed Cross Sectional Data (Cross section 95)
11-190
Free surface flow determination
Riet
Lower
Lower
Upper
Reach
Blesbok
Riet
River
Table 11.2: Cross section data
River
Main channel
station
bank stations
LOB
ROB
100
8,53
22,56
95
8,32
22,56
90
8,14
22,56
85
7,92
22,56
80
7,71
22,56
75
7,53
22,56
70
7,32
22,56
65
8,78
31,64
60
8,53
31,64
55
8,32
31,64
50
8,08
31,64
45
7,86
31,64
40
7,62
31,64
8
13,17
20,18
7
13,23
20,30
6
13,26
20,42
5
13,32
20,54
4
13,35
20,67
3
13,41
20,82
Downstream reach length
LOB
25,0
22,9
25,9
23,8
25,6
24,4
0,0
25,0
25,9
27,4
24,4
25,9
0,0
22,9
24,4
21,3
25,9
24,8
0,0
Channel
28,0
29,0
29,0
28,0
27,4
29,0
0,0
29,0
30,5
30,5
27,4
29,0
0,0
24,4
26,8
24,4
29,0
25,9
0,0
ROB
30,5
33,5
30,5
31,4
30,5
33,5
0,0
33,5
36,6
30,5
30,5
32,0
0,0
27,4
29,9
27,4
30,5
29,9
0,0
For the last cross section of the river system (cross section 40) you can enter the
following description: Downstream River Station

Remember to save the Geometry data at regular intervals in case of a power failure or human
error. To assist with this you could also go to the main HEC-RAS screen and set the Backup
saving function at a short interval (Options menu, Program Setup, Set Time for Automatic
Backup… and enter 5 minutes). Make sure the Automatically Backup Data is selected (see
Figure 11.69).
Figure 11.69: Automatically Backup Data
Entering junction data
The next step is to enter the junction data. This is accomplished by clicking the
Junction button on the Geometric window (Figure 11.58). Once this button is
clicked, the Junction Data editor will appear as shown in Figure 11.70.
11-191
Free surface flow determination
Figure 11.70: Junction Data Editor

There is only one junction in the river system. For this junction add the following description:
Division of Upper Reach and Lower Reach at Confluence with Blesbok River (see Figure
11.70)

Reach lengths across the junction are entered in the junction editor, rather than in the cross
section data. This allows for the lengths across very complicated confluences (i.e. flow splits)
to be accommodated. This is the reason why the reach lengths in the cross section data for the
last cross section of each reach was left blank or set to zero. Enter the junction lengths of 24,4
m and 21,3 m for the Riet River – Upper reach and Blesbok River – Lower reach respectively
(see Figure 11.70).

In this exercise the energy equation will be used to compute the water surface profiles through
the junction for steady flow computations i.e. select the Energy option. If the momentum
equation was selected, then an angle can be entered for one or more of the reaches flowing
into or out of a junction. The momentum equation is set up to account for the angle of the
flow entering the junction.

For Unsteady flow computations the Force Equal WS Elevations option is selected.

Once you have entered all the data for the junction, click on the Apply button and close the
window by pressing the OK button.

Remember to save the Geometry data by clicking on Save Geometry Data from the File
menu.

Once all the data has been successfully entered your system should look like the schematic
layout shown in Figure 11.60.
11-192
Free surface flow determination
ENTERING AND EDITING UNSTEADY FLOW DATA
Once all of the geometric data are entered, the modeler can then enter the unsteady flow data that
is required. To bring up the unsteady flow data editor, select Unsteady Flow Data from the Edit
menu on the HEC-RAS main window or clicking the short cut button on the menu bar
Unsteady Flow data editor should appear as shown in Figure 11.71, for this exercise.
. The
Figure 11.71: Unsteady Flow Data Editor
The user is required to enter boundary conditions at all of the external boundaries of the system, as
well as any desired internal locations, and set the initial flow conditions at the beginning of the
simulation.
Boundary conditions are entered by first selecting the Boundary Conditions tab from the
Unsteady Flow Data editor. River, Reach, and River Station locations of the external bounds of
the system will automatically be shown in the table. Boundary conditions are entered by first
selecting a cell in the table for a particular location, then selecting the boundary condition type that
is desired at that location. Not all boundary condition types are available for use at all locations.
The program will automatically gray-out the boundary condition types that are not relevant when
the user highlights a particular location in the table.
11-193
Free surface flow determination
Users can also add locations for entering other internal boundary conditions. To add additional
boundary condition location, select the desired River, Reach, and River Station from the drop
down lists and press the Add a Boundary Condition Location button. In this exercise this is
however not required.
Boundary Conditions
There are several different types of boundary conditions available to the user. The following
is a short discussion of each type:
 Flow Hydrograph (this is the type that you can enter for this exercise)
A flow hydrograph can be used as either an upstream boundary or downstream boundary
condition, but is most commonly used as an upstream boundary condition. When the flow
hydrograph button is pressed, the window shown in Figure 11.72 will appear. As shown, the
user can either read the data from a HEC-DSS (HEC Data Storage System) file, or can enter
the hydrograph ordinates into a table (Since River station 8 was selected as shown in Figure
11.71 the flow hydrograph detail for this stations is first required).
Figure 11.72: Flow Hydrograph (River station 8 – Blesbok River)
 The user also has the option of entering a flow hydrograph directly into a table, as shown in
Figure 11.72. The first step is to select a Data time interval from the drop down list.
Currently the program only supports regular interval time series data.
11-194
Free surface flow determination
A list of allowable time intervals is shown in the drop down window of the data interval list
box. For this exercise select 15 Minute.
 To enter data into the table, the user is required to select either Use Simulation Time or Fixed
Start Time. For this exercise select Use Simulation Time.
 Instead of entering the data points of the flow hydrographs one-by-one by hand open the Excel
spreadsheet entitled: Exercise 2 - Flow hydrographs.xls. Copy the flow rate values for the
Blesbok River flow hydrograph (only the flow rates). Return to the HEC-RAS Flow
Hydrograph data editor, select at least 25 rows in the hydrograph table and press Ctrl V on
the keyboard to paste the copied data (see Figure 11.73).
Figure 11.73: Flow Hydrograph (River station 8 – Blesbok River)
 An option listed at the bottom of the flow hydrograph boundary condition is to make this
boundary a Critical Boundary Condition. When you select this option, the program will
monitor the inflow hydrograph to see if a change in flow rate from one time step to the next is
exceeded.
If the change in flow rate does exceed the user entered maximum, the program will
automatically cut the time step in half until the change in flow rate does not exceed the user
specified max.
11-195
Free surface flow determination
 The other options at the bottom of this editor are Min Flow and Multiplier. Both of these
options apply to user entered hydrographs or hydrographs read from HEC-DSS. The “Min
Flow” option allows the user to specify a minimum flow to be used in the hydrograph. This
option is very useful when too low of a flow is causing stability problems.
 The flow hydrograph for this exercise can be plotted by clicking on the Plot Data button (see
Figure 11.74).
Figure 11.74: Flow hydrograph (Plot of River station 8 flow hydrograph)
The maximum peak flow value is 31,0 m³/s (time 2:30)
 Similarly a flow hydrograph can be entered for River station 100, which is the upstream
boundary of the Riet River – Upper reach.
 The completed Flow Hydrograph editor screen and plot screen is shown in Figure 11.75 and
Figure 11.76 respectively. The maximum peak flow value is 84,0 m³/s (time 2:00).
The spreadsheet (Exercise 2 - Flow hydrographs.xls) containing the flow hydrographs is
provided on the supporting flash drive/DVD.
11-196
Free surface flow determination
Figure 11.75: Flow Hydrograph (River station 100 – Riet River)
Figure 11.76: Flow hydrograph (Plot of River station 100 flow hydrograph)
11-197
Free surface flow determination
 Normal Depth (this is the type that you can enter for this exercise)
The Normal Depth option can only be used as a downstream boundary condition for an openended reach. This option uses Manning’s equation to estimate a stage for each computed
flow. Select River station 40’s cell on the Unsteady Flow Data editor window. Click the
Normal Depth button. A pop-up window will prompt you to enter the downstream friction
slope, which should be used to calculate the flow depth at this downstream boundary for each
flow (in the time series arriving at this river station), see Figure 11.77. Enter a slope of
0,001 m/m.
Figure 11.77: Normal flow depth boundary (River station 40)
Other boundary types not used in this example:
Stage Hydrograph
A stage hydrograph can be used as either an upstream or downstream boundary condition.
The editor for a stage hydrograph is similar to the flow hydrograph editor. The user has the
choice of either attaching a HEC-DSS file and path name or entering the data directly into a
table.
11-198
Free surface flow determination
Rating Curve
The rating curve option can be used as a downstream boundary condition. The user can either
read the rating curve from HEC-DSS or enter it by hand into the editor. The downstream
rating curve is a single valued relationship, and does not reflect a loop in the rating, which
may occur during an event.
Elevation Controlled Gate
This option allows the user to control the opening and closing of gates based on the elevation
of the water surface upstream of the structure. A gate begins to open when a user specified
elevation is exceeded. The gate opens at a rate specified by the user.
Initial Conditions
 In addition to the boundary conditions, the user must establish the initial conditions of the
system at the beginning of the unsteady flow simulation. Initial conditions consist of flow and
stage information at each of the cross sections, as well as elevations for any storage areas
defined in the system. Initial conditions are established from within the Unsteady Flow Data
editor by selecting the Initial Conditions tab. After the Initial Conditions tab is selected, the
Unsteady Flow editor will appear as shown in Figure 11.78.
Figure 11.78: Unsteady Flow Data (Initial Conditions)
 As shown in Figure 11.78, the user has two options for establishing the initial conditions of
the system. The first option is to enter flow data for each reach and have the program perform
a steady flow backwater run to compute the corresponding stages at each cross section.
11-199
Free surface flow determination
This option also requires the user to enter a starting elevation for any storage areas that are
part of the system. This is the most common method for establishing initial conditions. Flow
data can be changed at any cross section, but at a minimum the user must enter a flow at the
upper end of each reach.
The second option is to read in a file of stages and flows that were written from a previous run,
which is called a “Restart file”. The first option is used in this exercise.
Enter the initial flows as indicated in Figure 11.78, 0,5 m³/s, 1,0 m³/s and 1,5 m³/s for cross
sections 8, 100 and 65 respectively.
Saving the Unsteady Flow Data
 The last step in developing the unsteady flow data is to save the information to a file. To save
the data, select the Save Unsteady Flow Data As from the File menu on the Unsteady Flow
Data editor. A pop-up window will appear prompting you to enter a title for the data as
shown in Figure 11.79. Enter “Base Unsteady Flow” for this exercise, and then press the OK
button. A file name is automatically assigned to the Unsteady Flow Data based on what you
entered for the project file name i.e. Exercise1.u01.
Figure 11.79: Saving Unsteady Flow Data
Other unsteady Flow Data Options
Several options are available from the Unsteady Flow Data editor to assist users in entering
and viewing data. These features can be found under the Options menu at the top of the
window. The following options are available:
Delete Boundary Condition
This option allows the user to delete a boundary condition from the table. To use this option,
first select the row to be deleted with the mouse pointer. Then select Delete Boundary
Condition from the options menu. The row will be deleted and all rows below it will move
up one. Only user inserted boundary conditions can be deleted from the table. If the boundary
condition is an open end of the system, the system will not allow that boundary to be deleted.
There must always be some type of boundary condition at all the open ends of the system.
Internal RS Initial Stages
This option allows the user to specify starting water surface elevations for any internal cross
section within the system. A common application of this would be to specify the starting pool
elevation for the first cross section upstream of a dam (modeled with the inline weir/spillway
11-200
Free surface flow determination
option). The user specifies locations and water surface elevations, which are then used to
establish the initial conditions for the system at the beginning of a run.
Observed Data In DSS
This option allows the user to attach observed data pathnames from a HEC-DSS file to
specific river stations within the model.
When an observed data path name is attached to a specific river station location, the user can
get a plot of the observed flow or stage hydrograph on the same plot as the computed flow and
stage hydrographs. Additionally, the observed data will show up on profile and cross section
plots. To use this option, the user selects Observed Data In DSS from the Options menu of
the Unsteady Flow Data editor.
Minimum Flow and Flow Ratio Table
This option brings up a global editor that will show all the locations in which flow
hydrographs have been attached as boundary conditions. The editor allows the user to enter a
minimum flow or a flow factor for each flow hydrograph boundary condition.
UNSTEADY FLOW ANALYSIS
Performing Unsteady Flow Calculations
Once all of the geometry and unsteady flow data have been entered, the user can begin
performing the unsteady flow calculations. To run the simulation, go to the HEC-RAS main
window and select Unsteady Flow Analysis from the Run menu or click on the Unsteady
on the menu bar. The Unsteady Flow Analysis window will
Flow Analysis button
appear as shown in Figure 11.80.
11-201
Free surface flow determination
Figure 11.80: Unsteady Flow Analysis
 The first step is to put together a Plan. The Plan defines which geometry and flow data are to
be used, as well as providing a title and short identifier for the run.
To establish a plan, select New Plan from the File menu on the Unsteady Flow Analysis
window. Enter the plan title as Base analysis and then press the OK button (Figure 11.81).
Figure 11.81: Creating new plan
 You will be prompted to enter a short identifier. Enter a title of Base in the Short ID box
(Figure 11.82) and click on the OK button.
11-202
Free surface flow determination
Figure 11.82: Plan identifier
 Selecting Programs to Run
There are three components used in performing an unsteady flow analysis within HEC-RAS.
These components are: a geometric data pre-processor; the unsteady flow simulator; and an
output post-processor (see Figure 11.80).
o
Geometric Pre-Processor
The pre-processor is used to process the geometric data into a series of hydraulic
properties tables, rating curves, and family of rating curves. This is done in order to
speed up the unsteady flow calculations. Instead of calculating hydraulic variables for
each cross-section, during each iteration, the program interpolates the hydraulic variables
from the tables. The pre-processor must be executed at least once, but then only needs to
be re-executed if something in the geometric data has changed.
o
Unsteady Flow Simulation
The unsteady flow computations within HEC-RAS are performed by a modified version
of the UNET (Unsteady NETwork model) program, developed by Dr. Robert Barkau
(Barkau, 1992) and modified by HEC. The unsteady flow simulation is actually a threestep process. First, a program called RDSS (Read DSS data) runs.
This software reads data from a HEC-DSS file and then converts all of the boundary
condition time series data into the user specified computation interval. Next, the UNET
program runs. This software reads the hydraulic properties table computed by the preprocessor, as well as the boundary conditions and flow data from the interface and the
RDSS program.
The program then performs the unsteady flow calculations. The final step is a program
called TABLE. This software takes the results from the UNET unsteady flow run and
writes them to a HEC-DSS file.
o
Post-Processor
The post-processor is used to compute detailed hydraulic information for a set of user
specified time lines during the unsteady flow simulation periods. In general, the unsteady
flow computations only compute stage and flow at all of the computation nodes, as well
as stage and flow hydrographs at user specified locations. If the post-processor is not run,
then the user will only be able to view the stage and flow hydrographs and no other
output from HEC-RAS. By running the post-processor, the user will have all of the
available plots and tables for unsteady flow that HEC-RAS normally produces for steady
flow.
 Simulation time window
The user is required to enter a time window that defines the start and end of the simulation
period. The time window requires a starting date and time and an ending date and time.
11-203
Free surface flow determination
In this exercise the flow hydrograph shown in Figure 11.73 and Figure 11.75 starts at 0:00
and has data until 06:00 and this is used in the simulation time window. The date can be
anything since the option to Use Simulation Time on the Flow Hydrograph window was
selected (see Figure 11.73 and Figure 11.75). Enter the Starting date as 01JAN2013 and the
Ending date as 01JAN2013. Enter the Starting time as 0000 and the Ending time as 0600.
 Computational settings
The computational Settings area contains the Computational Interval, Hydrograph Output
Interval, Detailed Output Interval, the name and path of the output DSS file, and whether or
not the program is run in a mixed flow regime. The computation interval is probably one of
the most important parameters entered into the model. It should be small enough to accurately
describe the rise and fall of the hydrographs being routed but not small to take forever to
compute.
For this exercise set the Computational Interval at 5 minutes (from the drop down list). Set
the Hydrograph Output Interval to 15 minutes and the Detailed Output Interval also at
15 minutes.
The DSS Output filename is the file that contains all the calculated data in a format that can
be read by HEC-RAS and used in displaying all the results (tables and graphs). The default
will be …..\Exercise2.dss and does not have to be changed for this exercise.
The completed Unsteady Flow Analysis screen is shown in Figure 11.83.
Figure 11.83: Unsteady Flow Analysis (completed)
Click on the Compute button to run the Unsteady Flow Analysis.
11-204
Free surface flow determination
VIEWING THE RESULTS
Once the model has finished all of the computations successfully, you can begin viewing the
results. Several output options are available from the View menu bar on the HEC-RAS main
window. These options include:
a) Cross section plots
b) Profile plots
c) General profile plot
d) Rating curves
e) X-Y-Z perspective plots
f) Detailed tabular output at a specific cross section (cross section table)
g) Limited tabular output at many cross sections (profile table)
 Begin by plotting a cross section. Select Cross Sections from the View menu bar on the HECRAS main window. Any cross section can be plotted by selecting the appropriate river, reach
and river station (See Figure 11.84). Several plotting features are available from the Options
menu bar on the cross section plot window. These options include: zoom in; zoom out;
selecting which plans, profiles, variables to plot; and control over lines, labels, symbols,
scaling etc.
Figure 11.84: Cross section (Riet River: Upper reach – River station 100)
 Select different cross sections to plot and practice using some of the features available under
the options menu bar. First try and view the change in water level at this cross section. Click
, on the Cross Section window. An Animation Control window will
on the Play button,
appear (see Figure 11.85). Click on the Expand button, , to see the entire control.
11-205
Free surface flow determination
Figure 11.85: Animation Control
Set the Zero Delay horizontal scroll bar as indicated (in Figure 11.85) and click on the play
button,
, to view the changing water surface levels and energy grade lines at this cross
section. Click the Stop button, , to stop the animation.
 Try and make a movie clip by viewing the change in flow levels with time (Figure 11.84), this
can be done by clicking on the Record button (red dot Figure 11.84) to start recording and
clicking it again will stop recording. You will be prompted as shown in Figure 11.86,
whether or not you would like to record a movie (AVI). Click on the Yes button, remember
the program starts recording as soon as you click on the Yes button.
Figure 11.86: Confirming that a movie clip should be recorded
Click on the Play button,
, to start playing the animation as explained earlier. Once the
animation ends click on the Record button (red dot Figure 11.84) again to stop recording.
The recorded screen captures will be shown as indicated in Figure 11.87. You now have the
option of saving the screens after performing some editorial work to an AVI file by clicking
on the Write AVI button.
11-206
Free surface flow determination
Figure 11.87: Recorded screens
 Next plot a water surface profile. Select Water Surface Profiles from the View menu bar.
This should give you a profile plot as shown in Figure 11.88.
Figure 11.88: Water Surface Profile (for Riet River: Upper reach)
11-207
Free surface flow determination
 Also have a look at a General Profile Plot and the X-Y-Z Perspective Plot (Figure 11.89).
Also look at some tabular output. Go to the View menu bar on the HEC-RAS main window.
There are two types of tables available, a detailed output table and a profile summary table.
Select Detailed Output Tables to get the first table to appear. This table shows detailed
hydraulic information at the cross section. Other cross sections can be viewed by selecting the
appropriate reach and river from the table. A table with all the errors, warnings and comments
can also be viewed, by selecting Summary, Err Warn, Notes... from the View menu on the
HEC-RAS main window.
Figure 11.89: X-Y-Z Perspective plot
You will now be in a position to answer some of the questions at the back of this exercise
(Questions 1 to 5).
BRIDGES
In the next section a bridge structure will be added downstream of the confluence of the two rivers.
HEC-RAS computes energy losses caused by structures such as bridges and culverts in three parts.
One part consists of losses that occur in the reach immediately downstream from the structure where
an expansion of flow takes place. The second part is the losses at the structure itself, which can be
modeled with several different methods. The third part consists of losses that occur in the reach
immediately upstream of the structure where the flow is contracting to get through the opening.
Cross section locations
The bridge routine utilizes four user defined cross sections in the computation of energy losses due to
the structure.
11-208
Free surface flow determination
Cross section 1 is located sufficiently downstream from the structure so that the flow is not affected
by the structure (i.e. the flow has fully expanded)
Cross section 2 is located immediately downstream from the bridge (i.e. within a short distance).
This cross section should represent the natural ground just outside the bridge.
Cross section 3 should be located just upstream of the bridge. The distance between cross section 3
and the bridge should be relatively short. This distance should only reflect the length required for the
abrupt acceleration and contraction of the flow that occurs in the immediate area of the opening.
Cross section 4 is an upstream cross section where the flow lines are approximately parallel and the
cross section is fully effective.
Entering bridge data
 To enter bridge data the user presses the Bridge/Culvert button on the Geometric data
window (Figure 11.60). Once the Bridge/culvert button is pressed, the Bridge/Culvert Data
Editor will appear as shown in Figure 11.90.
11-209
Free surface flow determination
Figure 11.90: Bridge/Culvert Data window
To add a bridge to the model, take the following steps:
 Select the river and reach that you would like to place the bridge in (from the drop down lists)
i.e. Riet river and Lower reach.
 From the Options menu, select Add a Bridge and/or Culvert from the list. An input box
will appear prompting you to enter a river station identifier for the new bridge.
Enter 52 as shown in Figure 11.91.
Figure 11.91: Bridge river station (Riet River: Lower reach)
 Enter the Description of the bridge: Stephnie bridge (see Figure 11.92)
11-210
Free surface flow determination
Figure 11.92: Upstream and downstream view of cross sections at bridge
 Enter all of the required data for the new bridge. This includes:
a. Bridge deck
b. Sloping abutments (optional)
c. Piers (optional)
d. Bridge modeling approach information
 From the Bridge/Culvert Data Editor select the Deck/Roadway icon to activate the
Deck/Roadway Data Editor as shown in Figure 11.93.
 The first input at the top of the editor is the distance from the upstream side of the bridge deck
to the cross section immediately upstream from the bridge (i.e. river station 55). This distance
is 5 m.
 The bridge deck itself will have a width of 7,5 m. The weir flow coefficient selected for this
analysis is 1,44.
 The bridge deck will be 0,9 m high and will have a slope across it of 0,05 m (for road
drainage).
11-211
Free surface flow determination
Figure 11.93: Bridge/Deck and Roadway data editor window
 At every station position the high chord and low chord of the bridge should be entered as
shown in Figure 11.93 to provide a bridge shape as shown in Figure 11.94.
 The US and DS Embankment SS (upstream and downstream embankment side slope) values
should be entered as 2 (horizontal to 1 vertical). These values are used for the graphical
representation on the profile plot.
 At the bottom of the Deck/Roadway Data Editor, there are three additional fields of data
entry. The first is the Max Allowable Submergence. This input ratio of downstream water
depth to upstream energy, as measured above the minimum weir elevation. When the ratio is
exceeded, the program will no longer consider the bridge deck to act as a weir and will switch
the computation mode to energy (standard step) method. For this exercise the default value of
0,95 (95%) should be selected.

The second field at the bottom of the editor is the Min Weir Flow Elevation. This is the
elevation that determines when weir flow will start to occur over the bridge. If this field is left
blank (as in this exercise), the program will default to use the lowest high cord value on the
upstream side of the bridge. The last field at the bottom of the editor is the selection of the
Weir Crest Shape. This selection will determine the reduction of the weir flow coefficient
due to submergence. For this exercise, a Broad Crested weir shape should be selected.

Click the OK button
11-212
Free surface flow determination
Figure 11.94: Bridge data (View of bridge)
 This bridge has three piers that should be entered. From the Bridge/Culvert Data Editor
select the Pier icon to activate the Pier Data Editor as shown in Figure 11.95. The three piers
are entered by specifying the Centerline station at the upstream side as well as the
downstream side. The first pier is positioned at 15 m. It has a width of 0,5 m and it starts at a
level below the ground profile and ends at a level inside the bridge defined cords i.e. 20 and
23 m.
 Click on the Add button to add a pier (Pier #2). The second pier is at centerline 20 m, has a
width of 0,5 m and starts at elevation 19 m and ends at elevation 23 m.
 Click on the Add button to add a pier (Pier #3). The third pier is at centerline 25 m, has a
width of 0,5 m and starts at elevation 19 m and ends at elevation 23 m.
 Click on the OK button to return to the Bridge Culvert Data editor to view the specified piers
(see Figure 11.96).
11-213
Free surface flow determination
Figure 11.95: Pier Data Editor
Figure 11.96: Bridge data (View of bridge with piers)
11-214
Free surface flow determination

Another cross section within a short distance downstream of the bridge is also required. This
cross section should represent the natural ground where the flow is not affected by the by the
structure (fully expanded). Return to the Geometric Data Editor by exiting the Bridge
Culvert Data window (Exit under the File menu). Click on the Cross Section button,
,
on the Geometric window (Figure 11.60). Go to cross section 55, just upstream of the new
bridge (Riet River: Lower reach). Under the Options menu, click on Copy current cross
section. Enter the new River station name, 51, as shown in Figure 11.97.
Figure 11.97: New cross section (River station 51)
This will position the new cross section downstream of the newly added bridge (which is at
cross section 52). The reach lengths should also be corrected. This new cross section is 8 m
downstream of the bridge, thus the distance from River station 55 to the bridge is 5 m, the
width of the bridge is 7,5 m and this cross section is a further 8 m downstream of the bridge.
The total distance from River station 55 to River station 51 is 20,5 m. Go to River station 55
and change all the reach lengths to 20,5 m. Click on the Apply button to accept the changes.
Now go to the newly created River station 51 and change the reach lengths (by subtracting the
20,5 m from the previous lengths) to:
Downstream reach lengths: LOB = 6,9 Channel = 10,0 and ROB = 10,0
The total reach lengths between River station 55 and River station 50 will thus still remain the
same.

The average slope between River stations 55 and 50 is 0,000656 m/m. The newly added River
station 51 currently has the same elevations as River station 55 (since it is a copy of RS 55).
To adjust the elevation of this River station (RS 51) with a value of the distance multiplied
with the average slope i.e. 20,5 m x 0,000656 = ± 13 mm click on Adjust Elevations under
the Options menu. Enter an adjustment of -0,013 m (as shown in Figure 11.98) and click on
the OK button.
Figure 11.98: Adjusting the elevation (River station 51)

The new River station 51 will then have the values as shown in Figure 11.99.
11-215
Free surface flow determination
Figure 11.99: River station 51 data

Before we continue we need to save the Geometric data. This is done by clicking on Save
Geometry Data As under the File menu on the Geometric Data window. After selecting this
option you will be prompted to enter a Title for the geometric data (Figure 11.100). Enter
“Base Geometry + bridge” for this exercise, and then press the OK button. A file name is
automatically assigned to the geometry data based on what you entered for the project file
name i.e. Exercise2.g02.
Figure 11.100: Save Geometry Data As

The next step is to enter the ineffective flow areas. Any ineffective flow areas that exist due to
the bridge should be entered. At a bridge ineffective flow areas normally occur just upstream
and downstream of the road embankment, away from the bridge opening. It was for this
reason that River station 51 was added just downstream of the bridge.

At River station 55 we need to enter the ineffective flow area by selecting Ineffective Flow
Areas from the Options menu under the Cross Section Data Editor window. An initial
estimate of the stationing of the ineffective flow areas, a ratio of 1:1 of distance from the
bridge to the cross section was used (as an example). In this exercise the upstream cross
section is 5 m upstream of the bridge. Therefore, the left and right ineffective flow areas
should be set at 5 m left and right of the bridge opening. This however indicates that no
ineffective flow area has to be specified since this will already be within the natural profile.
11-216
Free surface flow determination
As an example the ineffective flow areas for this exercise were specified at 1 m left and right
of the bridge opening at the upstream river station (RS 55), see Figure 11.101. The bridge
opening starts at station 12,5 m and ends at 27,5 m. These will both be permanent ineffective
areas up to the level of the bridge deck.
Figure 11.101: Ineffective flow areas for river station 55

No ineffective flow areas were specified for the newly created downstream river station 51.
The ineffective flow areas could also be set by clicking on the Bounding XS’s 55 button on
the Bridge Culvert Data Editor screen (see Figure 11.96).

The entered bridge should now look similar to that shown in Figure 11.102.
Figure 11.102: Bridge data (View of bridge with piers and ineffective flow areas)
11-217
Free surface flow determination

The contraction and expansion coefficients are used by the program to determine the transition
energy losses between two adjacent cross sections. Typical bridge contraction and expansion
coefficients are 0,3 and 0,5 respectively. Select Contraction\Expansion Coefficients (Steady
Flow) from the Tables menu on the Geometric Data Editor window and change the
contraction and expansion coefficients as indicated in Figure 11.103. These coefficients could
also be changed by clicking on the Cross Section Data editor and changing the cross sections
coefficients individually there. Please note these coefficients shown in Figure 11.103 are for
the Steady Flow analysis only. Similarly coefficients can be entered for an Unsteady Flow
Analysis by selecting Contraction\Expansion Coefficients (Unsteady Flow) from the
Tables menu on the Geometric Data Editor window.
Figure 11.103: Contraction and Expansion coefficients

Bridge Modeling Approach
The bridge routines allow the modeler to analyse the bridge flows by using different methods
with the same geometry. The different methods are: low flow, high flow and combination
flow.
From the Geometric Data Editor, select the Bridge/Culvert icon and then the Bridge
Modeling Approach button. This will activate the Bridge Modeling Approach Editor as
shown in Figure 11.104.

For this exercise select the energy, momentum and Yarnell equations.
The Energy equation method considers the bridge as just being part of the natural channel and
requires Manning’s “n” values for the friction losses through the bridge and coefficients of
contraction and expansion.
The Momentum Balance method performs a momentum balance through the bridge area and
requires the selection of drag coefficient, Cd. Set the drag coefficient to 2,0 (Square nose
piers).
Yarnell Class A flows exists when the water surface through the bridge is completely
subcritical (i.e. above the critical depth). The flow regime without the bridge was subcritical
and thus Yarnell should also be selected. Enter the Yarnell pier coefficient K as 1,25 (Square
nose and tail).
11-218
Free surface flow determination
Select the Highest Energy Answer option. The program will show the results for the answer
for the method with the greatest energy loss as the final solution.
For high flows Energy Only (Standard Step) should be selected.
Figure 11.104: Bridge Modeling Approach Editor

Go to the Hydraulic Table Parameters Editor by clicking on the HTab Param icon

Set the Head Water Maximum Elevation value to 24,5 m (see Figure 11.105) and click on
the OK button.
.
Figure 11.105: Bridge Modeling Approach Editor

Before we continue we need to save the Geometric data. This is done by clicking on Save
Geometry Data under the File menu on the Geometric Data window.
11-219
Free surface flow determination
UNSTEADY FLOW ANALYSIS WITH BRIDGE
Performing Unsteady Flow Calculations with the Bridge
Once all of the geometry and unsteady flow data have been entered, the user can begin
performing the unsteady flow calculations. To run the simulation, go to the HEC-RAS main
window and select Unsteady Flow Analysis from the Run menu or click on the Unsteady
Flow Analysis button
on the menu bar. The Unsteady Flow Analysis window will
appear as shown in Figure 11.106.
Figure 11.106: Unsteady Flow Analysis
 The first step is to put together a new Plan. The Plan defines which geometry and flow data
are to be used, as well as providing a title and short identifier for the run.
To establish a plan, select New Plan from the File menu on the Unsteady Flow Analysis
window. Enter the plan title as Base analysis + bridge and then press the OK button (Figure
11.107).
11-220
Free surface flow determination
Figure 11.107: Creating new plan
 You will be prompted to enter a short identifier. Enter a title of Bridge in the Short ID box
(Figure 11.108) and click on the OK button.
Figure 11.108: Plan identifier
 Select the correct Geometry file and Unsteady flow file from the drop down list.
 Selecting Programs to Run
There are three components used in performing an unsteady flow analysis within HEC-RAS.
These components are: a geometric data pre-processor; the unsteady flow simulator; and an
output post-processor (see Figure 11.106).
 Simulation time window
The user is required to enter a time window that defines the start and end of the simulation
period. The time window requires a starting date and time and an ending date and time.
In this exercise the flow hydrograph shown in Figure 11.73 and Figure 11.75 starts at 0:00
and has data until 06:00 and this is used in the simulation time window. The date can be
anything since the option to Use Simulation Time on the Flow Hydrograph window was
selected (see Figure 11.73 and Figure 11.75). Enter the Starting date as 01JAN2013 and the
Ending date as 01JAN2013. Enter the Starting time as 0000 and the Ending time as 0600.
 Computational settings
The computational Settings area contains the Computational Interval, Hydrograph Output
Interval, Detailed Output Interval, the name and path of the output DSS file, and whether or
not the program is run in a mixed flow regime. The computation interval is probably one of
the most important parameters entered into the model. This should be small enough to
accurately describe the rise and fall of the hydrographs being routed but not small to take
forever to compute.
11-221
Free surface flow determination
For this exercise set the Computational Interval at 5 minutes (from the drop down list). Set
the Hydrograph Output Interval to 15 minutes and the Detailed Output Interval also at 15
minutes.
The DSS Output filename is the file that contains all the calculated data in a format that can
be read by HEC-RAS and used in displaying all the results (tables and graphs). The default
will be …..\Exercise2.dss and does not have to be changed for this exercise.
The completed Unsteady Flow Analysis screen is shown in Figure 11.109.
Figure 11.109: Unsteady Flow Analysis (completed)

Click on the Compute button to run the Unsteady Flow Analysis.
11-222
Free surface flow determination
VIEWING THE RESULTS
Once the model has finished all of the computations successfully, you can begin viewing the
results. Several output options area available from the View menu bar on the HEC-RAS main
window. These options include:
a) Cross section plots
b) Profile plots
c) General profile plot
d) Rating curves
e) X-Y-Z perspective plots
f) Detailed tabular output at a specific cross section (cross section table)
g) Limited tabular output at many cross sections (profile table)
 Begin by plotting a cross section. Select Cross Sections from the View menu bar on the
HEC-RAS main window. Any cross section can be plotted by selecting the appropriate river,
reach and river station (See Figure 11.110). Several plotting features are available from the
Options menu bar on the cross section plot window. These options include: zoom in; zoom
out; selecting which plans, profiles, variables to plot; and control over lines, labels, symbols,
scaling etc.
Figure 11.110: Cross section view (Riet River: Lower reach – River station 52 (upstream of
bridge)
 Next plot a water surface profile. Select Water Surface Profiles from the View menu bar.
Click on the Play button,
, to view the Animation Control window (see Figure 11.111).
Click on the Expand button, , to see the entire control.
11-223
Free surface flow determination
Figure 11.111: Animation Control
 Set the Zero Delay horizontal scroll bar as indicated (in Figure 11.111) and click on the play
button, , to view the changing water surface levels and energy grade lines of the river reach
profile plot. This should give you a profile plot as shown in Figure 11.112 for the maximum
water surface.
Figure 11.112: Water Surface Profile (for Riet River: Lower reach- Maximum WS)
 Also have a look at a General Profile Plot and the X-Y-Z Perspective Plot (Figure 11.113).
Also look at some tabular output. Go to the View menu bar on the HEC-RAS main window.
There are two types of tables available, a detailed output table and a profile summary table.
Select Detailed Output Tables to get the first table to appear. This table shows detailed
hydraulic information at the bridge. Other cross sections can be viewed by selecting the
appropriate reach and river from the table. A table with all the errors, warnings and comments
can also be viewed, by selecting Summary, Err Warn, Notes... from the View menu on the
HEC-RAS main window.
11-224
Free surface flow determination
Figure 11.113: X-Y-Z Perspective plot (Riet river: Lower reach, selected stations)
You will now be in a position to answer some more of the questions at the end of this
exercise (Questions 6 to 10).
ADDING AN INLINE STRUCTURE (WEIR)
In the next section an inline weir will be added in the Blesbok River – Lower reach.
Entering weir data
 To enter inline weir data click on the Inline structure button on the Geometric data window
(Figure 11.58). Once the Inline structure button is pressed, the Inline structure Data Editor
will appear as shown in Figure 11.114.
To add the inline weir in the model, take the following steps:
 Select the river and reach that you would like to place the weir in (from the drop down lists)
i.e. Blesbok River and Lower reach.
 From the Options menu, select Add an Inline structure from the list. An input box will
appear prompting you to enter a river station identifier for the inline structure.
Enter 6.5 as shown in Figure 11.115.
11-225
Free surface flow determination
Figure 11.114: Inline weir Data window
Figure 11.115: Inline weir river station (Blesbok River: Lower reach)
 Enter the Description of the inline structure: Maya weir (see Figure 11.116).
 Enter all of the required data for the new bridge. This includes:
a. Weir/Embankment details
b. Gate detail
 From the Inline Structure Data editor select the Weir/Embankment icon to activate the
Inline Structure Weir Station Elevation Editor as shown in Figure 11.117.
11-226
Free surface flow determination
Figure 11.116: View of the cross section at the weir (RS 6.5)
Figure 11.117: Inline weir (Inline Structure Weir Station Elevation Editor)
 The first input at the top of the editor is the distance from the upstream cross section and the
deck (i.e. river station 7). This distance is 10 m.
11-227
Free surface flow determination
 The deck itself will have a width of 5 m.
 The weir flow coefficient selected for this analysis is 1,44.
 At every station position enter station and elevation of the top of the weir embankment shown
in Figure 11.117 to provide the weir as shown in Figure 11.118.
 The US and DS Embankment SS (upstream and downstream embankment side slope) values
should be entered as 1 (1 horizontal to 1 vertical). These values are used for the graphical
representation on the profile plot.

The last field at the bottom of the editor is the selection of the Weir Crest Shape. This
selection will determine the reduction of the weir flow coefficient due to submergence. For
this exercise, a Broad Crested weir shape should be selected.

Click the OK button.
Figure 11.118: Inline weir (Viewing the weir)
 Enter the Pilot flow of 50 l/s i.e. 0,05 m³/s (Pilot discharge for leakage or to keep the
downstream channel wet at low flows) (see Figure 11.118).
11-228
Free surface flow determination
Gated Spillway Data
In addition to uncontrolled overflow weirs, the user can add gated spillways (this is optional).
To add gated spillways to the structure, press the Gate button on the Inline Structure Data
editor. Once this button is pressed, the gated editor will appear as shown in Figure 11.119
(except yours will be blank until you have entered some data).
Figure 11.119: Gated Spillway Editor
The Gated Spillway editor is similar to the Culvert editor in concept. The user enters the
physical description of the gates, as well as the required coefficients, in the Gated Spillway
editor. The functionality of the gates is defined as part of the Unsteady Flow data. The
following is a list of the data contained on this editor:
 Gate Group - The Gate Group is automatically assigned to "Gate #1" the first time you open
the editor. The user can enter up to 10 different Gate Groups at each particular river crossing,
and each gate group can have up to 25 identical gate openings. If all of the gate openings are
exactly the same, then only one gate group needs to be entered. If the user has gate openings
that are different in shape, size, elevation, or have different coefficients, then additional Gate
Groups must be added for each Gate type.
 Height - This field is used to enter the maximum possible height that the gate can be opened
in meters (Enter 1,2 m).
 Width - This field is used for entering the width of the gate in meters (Enter 1,2 m).
11-229
Free surface flow determination
 Invert - This field is used for entering the elevation of the gate invert (sill elevation of the
spillway inside of the gate) in meters. (Enter 20 m).
 Gate Type - This field is used for selecting the type of gate. A number of different gate types
are available. Select from the drop down list Sluice.
 Sluice Discharge Coefficient - This field is used for entering the coefficient of discharge for
the gate opening. This coefficient ranges from 0,5 to 0,7 for sluice gates. For this sluice gate
enter 0,6.
 Orifice Coefficient - This field is used to enter an orifice coefficient, which will be used for
the gate opening when the gate becomes more than 80 percent submerged. Between 67 percent
and 80 percent submerged, the program uses a transition between the fully submerged orifice
equation and the free flow equations. When the flow is less than 67 percent submerged, the
program uses the free flow gate equations. Enter an Orifice Coefficient of 0,8.
 Head Reference – This field is used to select the reference point for which the upstream
energy head will be computed from. The default is the gate sill (invert), which is normally
used when the flow through the gate goes out into a channel. If the gate causes the flow to jet
out freely into the atmosphere, then the head reference should be selected as the centerline
elevation of the gate opening. If the gate crest is an ogee spillway crest, then the center of the
gate opening should be used. Ogee spillway crests are normally designed to follow the shape
of water jetting freely into the atmosphere. For this exercise select from the drop down list Sill
(invert).
 Weir Shape - This parameter allows the user to select between a Broad Crested, Sharp
Crested shape weir and an Ogee shaped weir. Select Broad Crested.
 Weir Coefficient - This field is used for entering a weir coefficient that will be used for the
gate opening. This coefficient will only be used when the gate is opened to an elevation
higher than the upstream water surface elevation. When this occurs, the flow through the gate
is calculated as weir flow. Enter the Weir Coefficient of 1,67.
 Centerline Stations - This table is used for entering the centerline stationing of the identical
gate openings. The user should enter a different centerline stationing for each gate opening
that is part of the current gate group. All gate openings within the same gate group are exactly
identical in every way, except their centerline stationing. As a user adds new centerline
stationing values, the number of identical gates in the group is automatically incremented and
displayed in the field labelled "# Openings". Enter the Centerline Station as 16,25 m.
 Once all of the data for the gates has been entered (as shown in Figure 11.119), the user needs
to press the OK button for the data to be accepted. If the user presses the OK button, this does
not mean that the data is saved to the hard disk; it is only stored in memory and accepted as
being good data. This data is part of the geometry data, and is stored in the geometric data file.
The data can be stored to the hard disk by selecting from the File menu of the Geometric
Data window Save Geometry Data As.

After selecting this option you will be prompted to enter a Title for the geometric data (Figure
11.120). Enter “Base Geometry + bridge + weir” for this exercise, and then press the OK
button. A file name is automatically assigned to the geometry data based on what you entered
for the project file name i.e. Exercise2.g03.
11-230
Free surface flow determination
Figure 11.120: Save Geometry Data As
Figure 11.121: Inline weir (Viewing the weir + gate)
 The newly added weir will be shown on the Geometric Data editor window as shown in
Figure 11.122.
11-231
Free surface flow determination
Figure 11.122: Layout of river system (Bridge + weir)
Entering the gate opening characteristics
Once all of the geometric data are entered, the modeller can then enter the unsteady flow data that
is required for the gate. To bring up the unsteady flow data editor, select Unsteady Flow Data
from the Edit menu on the HEC-RAS main window or clicking the short cut button on the menu
bar . The Unsteady Flow data editor should appear as shown in Figure 11.123, for this
exercise.
11-232
Free surface flow determination
Figure 11.123: Unsteady Flow Data Editor
The boundary conditions at all the external boundaries of the system have already been entered.
The internal control at the weir will now also be entered.
 If the River station 6.5 IS is not in the list of Boundary Conditions click on the Add RS button
and add this internal boundary.
 Click in the Boundary Condition column next to the River station 6.5 IS. HEC-RAS allows
the user to select the type of boundary required from the available buttons: T.S. Gate Opening,
Elev Controlled Gates, Navigation Dams or Rules.
 For this exercise the gates will be controlled, opening and closing by means of the water
surface elevation. With the Boundary Condition Type block highlighted click on the Elev
Controlled Gates button. This will show the Elevation Controlled Gates data editor as
shown in Figure 11.124.
11-233
Free surface flow determination
Figure 11.124: Elevation Controlled Gates data editor

This option allows the user to control the opening and closing of gates based on the elevation
of the water surface upstream of the structure. A gate begins to open when a user specified
elevation is exceeded in this case 23,5 m (see Figure 11.125). The gate will begin to close
again when the water surface elevation reaches 22,5 m.

The gate opens at a rate specified by the user (0,1 m/min).

The closing of the gate is at a user specified rate (also 0,1 m/min.).

The user must also enter a maximum and minimum gate opening. For this exercise the
Maximum Gate Opening is set at 1,1 m and the Minimum Gate Opening is set at 0 m.

The Initial gate opening is closed and thus this value must be entered as 0. Figure 11.125
shows the completed data for this gate.
Figure 11.125: Elevation Controlled Gates data editor
11-234
Free surface flow determination
Saving the Unsteady Flow Data
 The last step in developing the unsteady flow data is to save the information to a file. To save
the data, select the Save Unsteady Flow Data As from the File menu on the Unsteady Flow
Data editor. A pop-up window will appear prompting you to enter a title for the data as shown
in Figure 11.126. Enter “Base Unsteady Flow + gates” for this exercise, and then press the
OK button. A file name is automatically assigned to the Unsteady Flow Data based on what
you entered for the project file name i.e. Exercise2.u02.
Figure 11.126: Saving Unsteady Flow Data
The completed Unsteady Flow Data screen should now include the additional boundary at the
inline structure (RS 6.5) as shown in Figure 11.127.
Figure 11.127: Unsteady Flow Data
 Initial conditions. There is no need to add any initial flow conditions at the new internal
control since the flow entered at River station 8 will also flow over the weir at the start of the
analysis.
11-235
Free surface flow determination
UNSTEADY FLOW ANALYSIS WITH INLINE STRUCTURE AND BRIDGE
Performing Unsteady Flow Calculations with the Inline Structure and the Bridge
Once all of the geometry and unsteady flow data have been entered, the user can begin
performing the unsteady flow calculations. To run the simulation, go to the HEC-RAS main
window and select Unsteady Flow Analysis from the Run menu or click on the Unsteady
Flow Analysis button
on the menu bar. The Unsteady Flow Analysis window will
appear as shown in Figure 11.128.
Figure 11.128: Unsteady Flow Analysis
 The first step is to put together a new Plan. The Plan defines which geometry and flow data
are to be used, as well as providing a title and short identifier for the run.
To establish a plan, select New Plan from the File menu on the Unsteady Flow Analysis
window. Enter the plan title as Base analysis + bridge + weir and then press the OK button
(Figure 11.129).
11-236
Free surface flow determination
Figure 11.129: Creating new plan
 You will be prompted to enter a short identifier. Enter a title of Base+b+w in the Short ID
box and click on the OK button.
 Select the correct Geometry file and Unsteady flow file from the drop down list i.e. Base
Geometry + bridge + weir and Base Unsteady Flow + gates respectively.
 Selecting Programs to Run
There are three components used in performing an unsteady flow analysis within HEC-RAS.
These components are: a geometric data pre-processor; the unsteady flow simulator; and an
output post-processor (see Figure 11.128).
 Simulation time window
The user is required to enter a time window that defines the start and end of the simulation
period. The time window requires a starting date and time and an ending date and time.
In this exercise the flow hydrograph shown in Figure 11.73 and Figure 11.75 starts at 0:00
and has data until 06:00 and this is used in the simulation time window. The date can be
anything since the option to Use Simulation Time on the Flow Hydrograph window was
selected (see Figures 18 and 20). Enter the Starting date as 01JAN2013 and the Ending date
as 01JAN2013. Enter the Starting time as 0000 and the Ending time as 0600.
 Computational settings
The computational Settings area contains the Computational Interval, Hydrograph Output
Interval, Detailed Output Interval, the name and path of the output DSS file, and whether or
not the program is run in a mixed flow regime. The computation interval is probably one of
the most important parameters entered into the model. This should be small enough to
accurately describe the rise and fall of the hydrographs being routed but not small to take
forever to compute.
In this exercise the newly added gates close within 1 minute and thus a smaller
Computational Interval of 1 minute (from the drop down list) should be selected. Set the
Hydrograph Output Interval to 1 minute and the Detailed Output Interval also at 1 minute.
The DSS Output filename is the file that contains all the calculated data in a format that can
be read by HEC-RAS and used in displaying all the results (tables and graphs). The default
will be …..\Exercise2.dss and does not have to be changed for this exercise.
 Also select the Mixed Flow Regime option since mixed flow might occur at the flow over the
weir. The completed Unsteady Flow Analysis screen is shown in Figure 11.130.
11-237
Free surface flow determination
Figure 11.130: Unsteady Flow Analysis (completed)
Click on the Compute button to run the Unsteady Flow Analysis.
VIEWING THE RESULTS
Once the model has finished all of the computations successfully, you can begin viewing the
results. Several output options are available from the View menu bar on the HEC-RAS main
window. These options include:
a)
b)
c)
d)
e)
f)
g)
Cross section plots
Profile plots
General profile plot
Rating curves
X-Y-Z perspective plots
Detailed tabular output at a specific cross section (cross section table)
Limited tabular output at many cross sections (profile table)
 Begin by plotting a cross section. Select Cross Sections from the View menu bar on the HECRAS main window. Any cross section can be plotted by selecting the appropriate river, reach
and river station (See Figure 11.131 and Figure 11.132). Several plotting features are
available from the Options menu bar on the cross section plot window. These options include:
zoom in; zoom out; selecting which plans, profiles, variables to plot; and control over lines,
labels, symbols, scaling etc.
11-238
Free surface flow determination
Figure 11.131: Cross section view (Blesbok river: Lower reach – River station 6.5 (Inline
structure) at maximum water surface (gates open)
Figure 11.132: Cross section view (Blesbok river: Lower reach – River station 6.5 (Inline
structure) at time step when gates just closed completely
 Next plot a water surface profile. Select Water Surface Profiles from the View menu bar.
Click on the Play button,
, to view the Animation Control window (see Figure 11.133).
Click on the Expand button, , to see the entire control.
11-239
Free surface flow determination
Figure 11.133: Animation Control
 Set the Zero Delay horizontal scroll bar as indicated (in Figure 11.133) and click on the play
button, , to view the changing water surface levels and energy grade lines of the river reach
profile plot. This should give you a profile plot as shown in Figure 11.134 for the maximum
water surface.
Figure 11.134: Water Surface Profile (for Blesbok river: Lower reach- Maximum Water surface
and gate open)
 Also have a look at the tabular output at the inline structure (RS 6.5). Go to the View menu
bar on the HEC-RAS main window and select Detailed Output Tables. From the Type menu
select Inline structures. This table shows detailed hydraulic information at the inline
structure. Other cross sections or structures can be viewed by selecting the appropriate reach
and river from the table and select the type of data to view.
11-240
Free surface flow determination
Figure 11.135: Detailed Tabular Output (Blesbok river: Lower reach, Inline structure)
At the end of this exercise the following objectives should have been met:

Be able to a river system containing more than one river reach

Know how to enter unsteady flow data and defining and entering the boundary controls

Be able to analyse the river system (unsteady flow)

Know how to define a bridge structure and a weir

Know how to set the boundaries for unsteady flow with opening and closing gates

Know how to obtain results from an unsteady flow analysis
Questions
1. Define the flow type in the river.
2. Does the flow at any of the cross section flow onto the banks of the river system?
3. At what time does the maximum flow at cross section 40 occur and what is the peak flow?
What is the normal flow depth during this peak flow?
11-241
Free surface flow determination
4. What will be the effect on the obtained water level at cross section 3 during maximum flow, if
the Junction was analysed using Momentum instead of energy with the Blesbok river joining
at an angle of 45°.
5. Describe the reason for the differences in the Rating curves (Flow rate versus Water Surface
Elevation) for cross section 40 and cross section 100.
6. What effect does the bridge have on the maximum water surface level at cross section 70?
7. What is the maximum damming upstream of the bridge?
8. Is the bridge function as a control?
9. What will happen if the flow hydrographs of the Upper reach of the Riet river is increased
with 100%?
10. What increase in flow velocity is experienced due to the bridge compared to the before
scenario?
11. What is the maximum flow through the gate at the inline structure and at what time step does
this occur?
12. What effect does the added inline structure have on the flow conditions at the bridge (flow
depth, velocity etc.)?
13. What will be the effect if the Computational Interval, Hydrograph Output Interval and
Detailed Output Interval are also set to 15 minutes and the rate of opening and closing of the
gates are set to 1,2 m/min.
11-242
Free surface flow determination
12
SUB-SURFACE DRAINAGE
12.1
Example 12.1 - Herringbone drainage system
Problem description Example 12.1:
Calculate the maximum infiltration rate (mm/day), which may be discharged via the depicted subsurface herringbone system to a main drainage pipe. The diameter of the central pipe is 150 mm and
its slope 1:500. The diameter of the laterals is 100 mm and their slopes 1: 100. The Manning n-value
for the pipes is 0,011s/m1/3. Figure 12.1 reflects the layout.
Figure 12.1: Layout of the herringbone drainage system
Solution Example 12.1:
For each lateral, flowing 70% full:
q 
26,92 x 10 d S 0,7
6
8/3
nA
S
A  S (L  )
2
L 
S 
1/2
0
Refer to Figure 12.2
152 152  21,21m
L
 10,61m
2
(Valid in this example since laterals are placed at 45º and dimensions
are equal 15 m x 15 m)

10,61 

A  10,61  (21,21) 

2 

 281,3 m 2

q 
26,92 x 10 0,1 0,01  0,7  1312 mm/day
6
8/3
1/2
0,011281,3
12-243
Sub-surface drainage
Figure 12.2: General view of a herringbone drainage system
Flow rate, Q, for 14 laterals:
Q
= (1,312)(281,3)(14)
Q
= 5167 m³/day
Hence
Q
≈ 0,06 m³/s
Capacity of main pipe: (Manning Formula)


2/3
π
 0,15 
0,15 2 

4
4 

Q 
0,011
 1 


 500 
1/2
Q = 0,00805 m³/s
But this << 0,06 m³/s !
Q ≈ 695 m³/day
 q max 
695
281,314 
qmax = 177 mm/day (<< 1312 mm/day)
12-244
Sub-surface drainage
APPENDICES
A-245
Appendices
APPENDIX 3A
STATISTICAL ANALYSIS
A-246
Appendices
Single station direct statistical analysis
The following frequency distributions are discussed for untransformed and log10-transformed data:
 Untransformed data
Normal, Extreme Value Type 1 and General Extreme Value
 Log10-transformed data
Log-Normal, Log-Gumbel and Log-Pearson Type III
Step 1: Determine the mean, standard deviation and skewness coefficient of the raw data and the log10
transformed data as follows:
x
Mean
x
Standard deviation
 x x

s
 N 1

cV 
Coefficient of variation
=
x
=
N
s
=
=
g
cV
=
=

…(3A.1)
 
2
0,5


…(3A.2)


3

  x  x 
N

g  

s3
 N  1N  2  

Skewness coefficient
where:
x
N
s
…(3A.3)
…(3A.4)
x
observed value (or of the logarithm of the observed value for the log
distributions)
mean of observed values (or of the logarithm of the observed value for the
log distributions)
the total number of observations
the standard deviation of the observed values (or of the logarithm of the
observed values)
skewness coefficient
coefficient of variation
Step 2: The peak value for the desired return period and assumed distribution function can be derived
for each of the frequency distributions as follows:

Normal distribution
The normal distribution is applicable where the observed values represent the effects of a large
number of independent processes. The distribution is symmetrical about the mean and is
therefore only suitable for data where the skewness coefficient (g) is equal to, or close to zero.
The spread about the mean is a function of the coefficient of variation. For high coefficient of
variation values, the bottom tail may extend below zero and may result in negative flows
being generated when the distribution is applied to untransformed data.
The standarized normal distribution has a cumulative distribution function:
G y   
y

1
2
2
e 0,5y dy
…(3A.5)
where y is the standarized variable and is related to x by:
y
x  x
…(3A.6)
s
A-247
Appendices
The value of y for a given value of G(y) cannot be solved directly from Equation 3A.4, and
hence published tables have to be used. Based on the return period, read from Table 3A.1b
the value of G(y) and obtain y from Table 3A.1a.
Q T  x  sy

…(3A.7)
Extreme Value Type 1 (EV1/MM) distribution
From Table 3A.4 (g = 1,14) read the value of WT for the required return period. Calculate QT
directly using:
Q T  x  s0,780W T  0,450 

…(3A.8)
General Extreme Value (GEV/MM) distribution
For the known value of the skewness coefficient (g) read off the value WT from Table 3A.4
and the values of k, E(y) and var(y) from Table 3A.2 by using linear interpolation.
For EV2 distribution:
QT  x 
s2
1  E(y)  kWT 
var(y)
…(3A.9)
For EV3 distribution:
QT  x 

s2
- 1  E(y)  kWT 
var(y)
…(3A.10)
Log-normal (LN/MM) distribution
For this distribution, the logarithms of the data are assumed to be normally distributed. Based
on the skewness coefficient (g), obtain the value WT for the required return period from
Table 3A.3.

Q T  antilog log(x)  s log WT
where:
slog
=
log x  =
…(3A.11)
the standard deviation of the logarithms of the observed values as shown in
equation 3A.11
s log
and




 logx   logx 

N 1


2




0,5
…(3A.12)
the logarithm of the mean of the observed values
Confidence bands
The confidence, with which the values of the magnitude-return period relationships are
estimated, depends on the number of observations contained in the data set. The greater the
number of observations, the greater the degree of assurance, and subsequently the narrower
the confidence band.
A-248
Appendices
The displacement of the two-sided 95% confidence band about the estimated value can be
read from Table 3A.3 where N is the number of observations. The 95% confidence limits are:


Q T(95%)  antilog log(x)  s log WT  Wα 
…(3A.13)
where:
=
Wα

displacement of the confidence band (column 5 in Table 3A.3)
Log-Gumbel (Log-Extreme Value Type 1) (LEV1/MM) distribution
From Table 3A.4 (g = 1,14) read the value of WT for the required return period. Calculate QT
directly using:


Q T  antilog log(x)  s log 0,780WT  0,450

…(3A.14)
Log-Pearson Type III (LP3/MM) distribution
From Table 3A.3 determine the value of WT for the known skewness coefficient (g) of the
log-transformed data by linear interpolation.

Q T  antilog log(x)  s log WT

…(3A.15)
Based on an example from Flood Risk Reduction Measures by WJR Alexander the incorporation of
the influence of historical information, missing data and outliers is required to determine the
confidence of the results. It is thus required to calculate the historically weighted mean ( x h ), standard
deviation ( s h ) and skewness coefficient ( g h ).
WT   x b   x a 
YT  WT LW 
0,5
 WT   d 2b   d a2  


 YT  WT LW   1 
 YT  WTLWWT  d 3b   d 3a 
xh 
…(3A.16)
sh
…(3A.17)



3
s

gh  
 YT  LWWT  1YT  WTLW  2


…(3A.18)
where:
YT
=
WT
=
NA
=
NB
=
NC
=
LW
=
ZR
=
and where:
total time span (= NA + NB + NC)
weight applied to data = (YT – NA) / NB
floods equal to or above the high threshold
floods between high and low thresholds
missing data
low outliers including zero flows
zero flows
=
is the value of a peak equal to or above the high threshold
xa
=
is the value of a peak below the high threshold
xb
da and db =
are deviations of xa + xb from x h
All values being the logarithms of the data.
A-249
Appendices
These historically weighted values of the mean, standard deviation and the skewness coefficient are
then used in the equations for the LN/MM, LP3/MM, EV1/MM and GEV/MM distribution in the
usual way (3.1).
For a detailed description of the adjustment required when:

low outliers are removed from the data;

gauged zero flows exist; or

how to handle missing data;
see Flood Risk Reduction Measures by WJR Alexander.
Evaluating Example 3.2 for the Tsitsa River, utilizing Equations 3A.1 to 3A.15 (if the missing data is
not included in the statistical analysis) will provide the following results:
Table 3A.5a: Summary of parameters - Example 3.2
(missing data excluded)
Variable Untransformed data Transformed data
484,550
2,5463
x
YT
40
40
NC
0
0
s
390,677
0,366
g
1,344
-0,1462
cV
0,8063
0,1437
Table 3A.5b: Summary of results – Example 3.2 (missing data excluded)
Return period
N/MM
EV1/MM GEV/MM LN/MM LEV1/MM LP3/MM
2
485
421
414
352
307
358
5
813
766
758
714
645
719
10
985
994
991
1035
1057
1022
20
1127
1214
1221
1401
1696
1359
50
1287
1497
1527
1980
3126
1850
100
1394
1710
1764
2507
4953
2286
The next set of results is based on the historically weighted mean ( x h ), standard deviation ( s h ) and
skewness coefficient ( g h ) (Table 3A.6a and b) which incorporates the missing data.
Table 3A.6a: Summary of parameters - Example 3.2
(missing data included)
Variable Untransformed data Transformed data
476,912
2,542
xh
YT
NC
sh
gh
cV
53
13
378,305
53
13
0,362
1,304
-0,157
0,793
0,142
Table 3A.6b: Summary of results - Example 3.2 (missing data included)
A-250
Appendices
Return period
2
5
10
20
50
100
N/MM
477
795
962
1099
1254
1357
EV1/MM
416
749
971
1183
1457
1664
GEV/MM
418
726
934
1137
1407
1615
LN/MM
348
702
1012
1367
1924
2429
LEV1/MM
304
635
1034
1651
3022
4764
LP3/MM
355
706
999
1323
1790
2202
Step 3: Graphical representation of historical data
Arrange the observed data in descending order of magnitude and assign to each value a rank
number starting from one. Determine the plotting position (return period) for each value using
the Weibull formula. The general equation is given below and the values for the constants a
and b are provided in Table 3A.7.
Τ
nl  a
m-b
… (3A.19)
where:
T
nl
m
a
b
=
=
=
=
=
return period in years
length of record in years
number, in descending order, of the ranked annual peak floods
constant (see Table 3A.7)
constant (see Table 3A.7)
If the horizontal axis has a probability classification, the probability (P) is calculated as:

1

… (3A.20)
Some of the commonly used plotting positions recommended for use in hydrological analyses
are given in Table 3A.7. If several distributions are plotted on a single graph, then the general
purpose Cunane plotting position should be used.
Table 3A.7: Commonly used plotting positions
Type
Plotting position
Distribution
Weibull (1939)
a=1&b=0
Normal, Pearson 3
Blom (1958)
a = 0,25 & b = 0,375 Normal
Gringorten (1963)
a = 0,12 & b = 0,44
Exponential, EV1 & GEV
Cunane (1978) average of
a = 0,2 & b = 0,4
General purpose
above two
Beard (1962)
a = 0,4 & b = 0,3
Pearson 3
Greenwood (1979)
a = 0 & b = 0,35
Wakeby, GEV
Plot the values against their estimated return periods on log-probability paper; draw the best
fitting straight line through the plotted points and extrapolate to determine the estimated
maximum value for the required return period. Alternatively utilize software such as Utility
Programs for Drainage or HEC-SSP included on the supporting flash drive/DVD.
A-251
Appendices
Table 3A.1: Properties of the standardized normal distribution
Table 3A.1a
Table 3A.1b
Standardized normal distribution
Standardized normal distribution
T
G(y)%
WT
y
G(y)%
y
G(y)%
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
1,40
1,45
1,50
1,55
1,60
1,65
1,70
1,75
1,80
1,85
1,90
1,95
2,00
2,05
2,10
2,15
2,20
2,25
2,30
2,35
2,40
2,45
2,50
2,55
2,60
2,65
2,70
2,75
2,80
2,85
2,90
2,95
3,00
3,05
3,10
3,15
3,20
3,25
3,30
3,35
3,40
3,45
3,50
3,55
3,60
3,65
3,70
3,75
50,00
51,99
53,98
55,96
57,93
59,87
61,79
63,68
65,54
67,36
69,14
70,88
72,57
74,22
75,81
77,34
78,81
80,24
81,59
82,89
84,13
85,31
86,43
87,49
88,49
89,44
90,32
91,15
91,26
92,65
93,32
93,94
94,52
95,05
95,54
95,99
96,41
96,78
97,13
97,44
97,72
97,98
98,21
98,43
98,61
98,78
98,93
99,06
99,18
99,29
99,38
99,46
99,53
99,60
99,65
99,70
99,74
99,78
99,81
99,84
99,86
99,88
99,90
99,92
99,93
99,94
99,95
99,96
99,97
99,97
99,98
99,98
99,98
99,99
99,99
99,99
-0,00
-0,05
-0,10
-0,15
-0,20
-0,25
-0,30
-0,35
-0,40
-0,45
-0,50
-0,55
-0,60
-0,65
-0,70
-0,75
-0,80
-0,85
-0,90
-0,95
-1,00
-1,05
-1,10
-1,15
-1,20
-1,25
-1,30
-1,35
-1,40
-1,45
-1,50
-1,55
-1,60
-1,65
-1,70
-1,75
-1,80
-1,85
-1,90
-1,95
-2,00
-2,05
-2,10
-2,15
-2,20
-2,25
-2,30
-2,35
-2,40
-2,45
-2,50
-2,55
-2,60
-2,65
-2,70
-2,75
-2,80
-2,85
-2,90
-2,95
-3,00
-3,05
-3,10
-3,15
-3,20
-3,25
-3,30
-3,35
-3,40
--3,45
--3,50
--3,55
--3,60
--3,65
--3,70
--3,75
50,00
48,01
46,02
44,04
42,07
40,13
38,21
36,32
34,46
32,64
30,86
29,12
27,43
25,78
24,19
22,66
21,19
19,76
18,41
17,11
15,87
14,69
13,57
12,51
11,51
10,56
9,68
8,85
8,08
7,35
6,68
6,06
5,48
4,95
4,46
4,01
3,59
3,22
2,87
2,56
2,28
2,02
1,79
1,57
1,39
1,22
1,07
0,94
0,82
0,71
0,62
0,54
0,47
0,40
0,35
0,30
0,26
0,22
0,19
0,16
0,14
0,16
0,10
0,08
0,07
0,06
0,05
0,04
0,03
0,03
0,02
0,02
0,02
0,01
0,01
0,01
A-252
1000
500
200
100
50
20
10
5
2
5
10
20
50
100
200
500
1000
5000
10000
0,1
0,2
0,5
1,0
2,0
5,0
10,0
20,0
50,0
80,0
90,0
95,0
98,0
99,0
99,5
99,8
99,9
99,98
99,99
-3,09
-2,88
-2,58
-2,33
-2,05
-1,64
-1,28
-0,84
0,00
0,84
1,28
1,64
2,05
2,33
2,58
2,88
3,09
3,55
3,72
Appendices
Table 3A.2: Parameters of the standardized general extreme value distribution
Standardized general extreme value distribution
g
k
E(y)
var(y)
-2,000
-1,900
-1,800
-1,700
-1,600
-1,500
-1,400
-1,300
-1,200
-1,100
-1,000
-0,900
-0,800
-0,700
-0,600
-0,500
-0,400
-0,300
-0,200
-0,100
0,000
0,100
0,200
0,300
0,400
0,500
0,600
0,700
0,800
0,900
1,000
1,100
1,200
1,300
1,400
1,500
1,600
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
2,500
2,600
2,700
2,800
2,900
3,000
3,100
3,200
3,300
3,400
3,500
3,600
3,700
3,800
3,900
4,000
4,100
4,200
4,300
4,400
4,500
4,600
4,700
4,800
4,900
5,000
1,406
1,321
1,240
1,163
1,089
1,018
0,950
0,885
0,824
0,765
0,708
0,655
0,604
0,555
0,509
0,465
0,424
0,384
0,346
0,311
0,277
0,245
0,215
0,187
0,160
0,134
0,110
0,088
0,067
0,047
0,028
0,010
-0,006
-0,022
-0,037
-0,050
-0,063
-0,075
-0,086
-0,097
-0,107
-0,116
-0,125
-0,133
-0,140
-0,148
-0,154
-0,160
-0,166
-0,172
-0,177
-0,182
-0,187
-0,191
-0,195
-0,199
-0,203
-0,207
-0,210
-0,213
-0,217
-0,220
-0,223
-0,225
-0,228
-0,231
-0,233
-0,236
-0,238
-0,240
-0,242
-1,247
-1,182
-1,127
-1,080
-1,041
-1,008
-0,980
-0,957
-0,938
-0,922
-0,910
-0,901
-0,894
-0,889
-0,887
-0,886
-0,886
-0,888
-0,892
-0,896
-0,901
-0,907
-0,914
-0,922
-0,930
-0,938
-0,947
-0,956
-0,966
-0,975
-0,985
-0,994
1,004
1,013
1,023
1,032
1,041
1,049
1,058
1,066
1,074
1,082
1,089
1,097
1,104
1,110
1,116
1,123
1,128
1,134
1,139
1,145
1,150
1,154
1,159
1,163
1,168
1,172
1,176
1,180
1,183
1,187
1,191
1,194
1,197
1,201
1,204
1,207
1,210
1,213
1,215
3,204
2,505
1,984
1,590
1,287
1,052
0,868
0,721
0,602
0,507
0,428
0,362
0,307
0,261
0,222
0,188
0,159
0,134
0,112
0,094
0,077
0,063
0,050
0,039
0,030
0,022
0,016
0,010
0,006
0,003
0,001
0,000
0,000
0,001
0,002
0,005
0,008
0,011
0,016
0,021
0,026
0,032
0,038
0,044
0,051
0,058
0,065
0,072
0,080
0,087
0,094
0,102
0,110
0,117
0,125
0,132
0,140
0,148
0,155
0,163
0,170
0,178
0,186
0,193
0,201
0,208
0,215
0,223
0,230
0,237
0,244
A-253
Appendices
Table 3A.3a: Values of the standardized variate WT for the normal and exponential
distributions
Return
period
(years)
Nonexceedance
probability
2
5
10
20
50
100
200
500
1000
10000
0,50
0,80
0,90
0,95
0,98
0,99
0,995
0,998
0,999
0,9999
Normal distribution
Confidence limits Wα
WT
75%
95%
0,00
0,84
1,28
1,64
2,05
2,33
2,58
2,88
3,09
3,72
1,63
1,89
2,20
2,49
2,87
3,13
3,38
3,69
3,91
4,58
2N
2N
2N
2N
2N
2N
2N
2N
2N
2N
2,77
3,23
3,74
4,25
4,89
5,34
5,76
6,27
6,66
7,80
Exponential
distribution
2N
2N
2N
2N
2N
2N
2N
2N
2N
2N
0,69
1,61
2,30
3,00
3,91
4,61
5,30
6,21
6,91
9,21
Table 3A.3b: Values of the standardized variate WT for the Pearson Type III distribution
Return
period
(years)
2
5
10
20
50
100
200
500
1000
10000
Pearson Type III distribution (Values of WT)
g
-0,4
-0,2
0,0
0,2
0,4
-1,0
-0,8
-0,6
0,16
0,85
1,13
1,32
1,49
1,59
1,66
0,13
0,87
1,17
1,39
1,61
1,73
1,84
0,10
0,86
1,20
1,46
1,72
1,88
2,02
0,07
0,86
1,23
1,52
1,83
2,03
2,20
0,03
0,85
1,26
1,59
1,94
2,18
2,39
1,79
1,88
2,02
2,18
2,27
2,53
2,53
2,90
2,81
3,30
0,00
0,84
1,28
1,64
2,05
2,33
2,58
2,88
3,09
3,72
0,6
0,8
1,0
-0,03
0,83
1,30
1,70
2,16
2,47
2,76
-0,70
0,82
1,32
1,75
2,26
2,62
2,95
-0,10
0,80
1,33
1,80
2,36
2,76
3,13
-0,13
0,78
1,34
1,84
2,45
2,89
3,31
-0,16
0,76
1,34
1,88
2,54
3,02
3,49
3,38
4,15
3,67
4,60
3,96
5,05
4,24
5,50
4,53
5,96
Table 3A.4a: Values of the standardized variate WT for the general extreme value distribution
(EV1 & EV2)
Return
period
(years)
General extreme value (Values of WT)
g
1,14
1,2
1,4
1,6
1,8
2,0
2,5
EV1
3,0
3,5
4,0
4,5
5,0
5,5
6,0
EV2
2
0,37
0,37
0,37
0,37
0,37
0,37
0,38
0,38
0,38
0,38
0,38
0,38
0,38
0,38
5
1,50
1,51
1,55
1,58
1,60
1,63
1,68
1,72
1,75
1,77
1,79
1,80
1,82
1,83
10
2,25
2,28
2,35
2,43
2,49
2,55
2,67
2,76
2,84
2,90
2,94
2,98
3,01
3,04
20
2,97
3,01
3,15
3,28
3,40
3,50
3,73
3,91
4,05
4,16
4,25
4,33
4,39
4,45
50
3,90
3,97
4,22
4,45
4,66
4,86
5,28
5,62
5,89
6,12
6,30
6,46
6,59
6,70
100
4,60
4,71
5,05
5,38
5,68
5,97
6,59
7,10
7,52
7,86
8,15
8,39
8,59
8,77
200
5,30
5,44
5,90
6,34
6,76
7,16
8,04
8,77
9,38
9,89
10,31
10,67
10,97
11,24
500
6,21
6,41
7,05
7,68
8,29
8,87
10,19
11,32
12,26
13,06
13,74
14,32
14,81
15,24
1000
6,91
7,15
7,95
8,75
9,53
10,29
12,02
13,53
14,82
15,92
16,86
17,66
18,36
18,96
10000
9,21
9,64
11,13
12,68
14,25
15,82
19,65
23,19
26,34
29,13
31,58
33,73
35,63
37,31
A-254
Appendices
Table 3A.4b: Values of the standardized variate WT for the general extreme value distribution
(EV3)
Return
period
(years)
General extreme value (Values of WT)
g
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
EV3
2
0,33
0,34
0,34
0,34
0,35
0,35
0,36
0,36
0,36
0,37
5
1,01
1,06
1,12
1,17
1,23
1,28
1,33
1,38
1,43
1,47
10
1,28
1,37
1,46
1,57
1,67
1,78
1,89
2,00
2,10
2,19
20
1,44
1,57
1,71
1,86
2,02
2,19
2,37
2,54
2,71
2,86
50
1,58
1,74
1,93
2,15
2,38
2,64
2,90
3,18
3,45
3,72
100
1,64
1,83
2,05
2,31
2,60
2,92
3,26
3,62
3,99
4,35
200
1,68
1,89
2,14
2,44
2,77
3,16
3,58
4,02
4,49
4,97
500
1,72
1,95
2,23
2,56
2,96
3,42
3,94
4,51
5,13
5,76
1000
1,74
1,98
2,27
2,64
3,07
3,59
4,19
4,86
5,58
6,35
10000
1,76
2,02
2,36
2,78
3,32
4,00
4,83
5,81
6,96
8,24
A-255
Appendices
APPENDIX 3B
STANDARD DESIGN FLOOD METHOD
A-256
Appendices
Table 3B.1: Information required for the calculation of the SDF
Basin
SAWS
station
number
SAWS site
M
(mm)
R
(days)
C2
(%)
C100
(%)
MAP
(mm)
MAE
(mm)
1
546 204
Struan
56
30
10
40
550
1800
2
675 125
Autoriteit
62
44
5
30
450
1900
3
760 324
Siloam
64
28
5
40
470
1700
4
553 351
Waterval
58
20
10
50
630
1600
5
680 059
Leydsdorp
78
10
15
70
620
1700
6
369 030
Siloam
51
54
15
60
670
1500
7
328 726
Olivine
49
39
15
60
510
1700
8
322 071
Danielskuil
47
39
5
20
380
2100
9
258 452
Jacobsdal
43
47
15
60
380
1800
10
233 049
Wonderboom
54
55
10
50
560
1600
11
236 521
Mashai
39
66
40
80
430
1400
12
143 258
Scheurfontein
39
52
5
30
290
2100
13
284 361
Wilgenhoutsdrif
40
55
5
15
70
2600
14
110 385
Middelpos
25
13
10
30
140
2400
15
157 874
Garies
22
11
5
20
130
2100
16
160 807
Loeriesfontein
28
11
10
40
210
1900
17
84 558
Elandspoort
45
1
40
80
500
1500
18
22 113
La Motte
59
4
30
60
810
1400
19
69 483
Letjiesbos
34
16
10
35
160
2200
20
34 762
Uitenhage
53
12
15
60
480
1600
21
76 884
Albertvale
45
23
10
35
460
1700
22
80 569
Umzoniana
84
26
15
60
820
1200
23
180 439
Insizwa
60
45
10
80
890
1200
24
240 269
Newlands
76
15
15
80
910
1200
25
239 138
Whitson
55
9
10
80
830
1200
26
336 283
Nqutu
61
17
15
50
760
1500
27
339 415
Hill Farm
85
17
30
80
890
1400
28
483 193
Maliba Ranch
75
54
15
60
740
1400
29
556 088
Mayfern
66
11
15
50
740
1600
A-257
Appendices
Table 3B.2: Daily rainfall from TR102
A-258
Appendices
Table 3B.2: Daily rainfall from TR102 (continued)
A-259
Appendices
Table 3B.2: Daily rainfall from TR102 (continued)
A-260
Appendices
APPENDIX 3C
STANDARD FLOOD CALCULATION FORMS
A-261
Appendices
RATIONAL METHOD (ALTERNATIVE 1)
Description of catchment
River detail
Calculated by
Date
Physical characteristics
Size of catchment (A)
km²
Rainfall region
Longest watercourse (L)
km
Area distribution factors
Average slope (Sav)
m/m
Rural (α)
Urban (β)
Lakes (γ)
Dolomite area (D%)
%
Mean annual precipitation (MAP)#
mm
Rural
Urban
Surface slope
%
Factor
Cs
Description
%
Factor
C2
Vleis and pans
Lawns
Flat areas
Sandy, flat (<2%)
Hilly
Sandy, steep (>7%)
Steep areas
Heavy soil, flat (<2%)
Total
100
Heavy soil, steep (>7%)
Permeability
%
Factor
Cp
Residential areas
Very permeable
Houses
Permeable
Flats
Semi-permeable
Industry
Impermeable
Light industry
Total
100
Heavy industry
Vegetation
%
Factor
Cv
Business
Thick bush and plantation
City centre
Light bush and farm-lands
Suburban
Grasslands
Streets
No vegetation
Maximum flood
Total
100
Total (C2)
100
Notes:
Time of concentration (TC)
Overland flow
Defined watercourse
 rL 

TC  0,604 
 S 
 av 
0,467
 0,87L2 

TC  
 1000Sav 
hours
hours
Return period (years), T
Run-off coefficient, C1
(C1 = CS + CP + CV)
Adjusted for dolomitic areas, C1D
(= C1(1 - D%)+C1D%(∑(Dfactor x CS%))
Adjustment factor for initial saturation, Ft
Adjusted run-off coefficient, C1T
(= C1D x Ft)
Combined run-off coefficient CT
(= αC1T + βC2 + γC3)
Return period (years), T
Point precipitation (mm), PT
Point intensity (mm/hour), PiT (= PT/TC)
Area reduction factor (%), ARFT
Average intensity (mm/hour), IT
(= PiT x ARFT)
Return period (years), T
0,385
Run-off coefficient
2
5
10
20
50
100
Max
2
Rainfall
5
10
20
50
100
Max
2
5
10
20
50
100
Max
C I A
Peak flow (m³/s), Q T  T T
3,6
Note: # Reference to the appropriate figures and tables is made in the legend table of this method.
A-262
R1 - Page1/2
Appendices
RATIONAL METHOD (ALTERNATIVE 1)
LEGEND TABLE
Rational method (Alt 1)
ID
Reference
Figure 3.5 or SA

Weather Services

Table 3C.1

Table 3C.2

Table 3C.3

Table 3C.4

Table 3C.5

Figure 3.7
Figure 3.8 (or

Figure 3.26 DM)
Table 3C.1
Rural (C1)
Component
Classification
Vleis and pans (<3%)
Flat areas (3 to 10%)
Hilly (10 to 30%)
Steep areas (>30%)
Very permeable
Permeable
Semi-permeable
Impermeable
Thick bush and plantation
Light bush and farm-lands
Grasslands
No vegetation
Surface slope
(CS)
Permeability
(CP)
Vegetation
(CV)
Table 3C.3
Surface description
Table 3C.2
Urban (C2)
Use
Lawns
Sandy, flat (< 2%)
Sandy, steep (>7%)
Heavy soil, flat (< 2%)
Heavy soil, steep (>7%)
Residential areas
Houses
Flats
Industry
Light industry
Heavy industry
Business
City centre
Suburban
Streets
Maximum flood
Return period (years)
Adjustment factor (Ft) for
steep and impermeable
catchments
Adjustment factor (Ft) for
flat and permeable
catchments
Mean annual precipitation (mm)
600
600 - 900
900
0,01
0,03
0,05
0,06
0,08
0,11
0,12
0,16
0,20
0,22
0,26
0,30
0,03
0,04
0,05
0,06
0,08
0,10
0,12
0,16
0,20
0,21
0,26
0,30
0,03
0,04
0,05
0,07
0,11
0,15
0,17
0,21
0,25
0,26
0,28
0,30
Factor
Paved areas
Clean compacted soil, no stones
Sparse grass over fairly rough surface
Medium grass cover
Thick grass cover
0,05 - 0,10
0,15 - 0,20
0,13 - 0,17
0,25 - 0,35
0,30 - 0,50
0,50 - 0,70
0,50 - 0,80
0,60 - 0,90
0,70 - 0,95
0,50 - 0,70
0,70 - 0,95
1,00
2
Recommended
value of r
0,02
0,1
0,3
0,4
0,8
Table 3C.4
Adjustment factor to Cs
Surface slope classification
Dfactor
Steep areas (slopes >30%)
0,50
Hilly (10 to 30%)
0,35
Flat areas (3 to 10%)
0,20
Vleis and pans (slopes <3%)
0,10
Table 3C.5
5
10
20
50
100
0,75
0,80
0,85
0,90
0,95
1,00
0,50
0,55
0,60
0,67
0,83
1,00
R1 - Page 2/2
A-263
Appendices
RATIONAL METHOD (ALTERNATIVE 2)
Description of catchment
River detail
Calculated by
Date
Physical characteristics
Size of catchment (A)
km²
Days of thunder per year (R)
days/year
Longest watercourse (L)
km
Weather Service station
Average slope (Sav)
m/m
Weather Service number
Dolomite area (D%)
%
Area distribution factors
Mean annual precipitation (MAP)#
mm
Rural (α)
Urban (β)
Lakes (γ)
2-year return period rainfall (M) 
mm
Rural
Urban
Surface slope
%
Factor
Cs
Description
%
Factor
C2
Vleis and pans
Lawns
Flat areas
Sandy, flat (<2%)
Hilly
Sandy, steep (>7%)
Steep areas
Heavy soil, flat (<2%)
Total
100
Heavy soil, steep (>7%)
Permeability
%
Factor
Cp
Residential areas
Very permeable
Houses
Permeable
Flats
Semi-permeable
Industry
Impermeable
Light industry
Total
100
Heavy industry
Vegetation
%
Factor
Cv
Business
Thick bush and plantation
City centre
Light bush and farm-lands
Suburban
Grasslands
Streets
No vegetation
Maximum flood
Total
100
Total (C2)
100
Notes:
Time of concentration (TC)
Overland flow
Defined watercourse
 rL 

TC  0,604 
 S 
 av 
0,467
 0,87L2 

TC  
 1000Sav 
hours
hours
Return period (years), T
Run-off coefficient, C1
(C1 = CS + CP + CV)
Adjusted for dolomitic areas, C1D
(= C1(1 - D%)+C1D%(∑(Dfactor x CS%))
Adjustment factor for initial saturation, Ft
Adjusted run-off coefficient, C1T
(= C1D x Ft)
Combined run-off coefficient CT
(= αC1T + βC2 + γC3)
Return period (years), T
Point precipitation (mm), PT
Point intensity (mm/hour), PiT (= PT/TC)
Area reduction factor (%), ARFT
Average intensity (mm/hour), IT
(= PiT x ARFT)
Peak flow (m³/s) Q T 
0,385
Run-off coefficient
2
5
10
20
50
100
Max
Rainfall
5
10
20
50
100
Max
2
CT IT A
3,6
Note: # Reference to the appropriate figures and tables is made in the legend table of this method.
A-264
R2 - Page 1/2
Appendices
RATIONAL METHOD (ALTERNATIVE 2)
n-day rainfall data
Weather Service station
Weather Service station number
Mean annual precipitation (MAP)
mm
Coordinates
&
Duration
Return period (years), T
(days)
2
5
10
20
50
100
1 day
2 days
3 days
7 days
200
LEGEND TABLE
Rational method (Alt 2)
ID
Reference
Figure 3.5 or SA

Weather Services

TR102 or other

Figure 3.9

Table 3C.1

Table 3C.2

Table 3C.3

Table 3C.4

Table 3C.5

Table 3C.6

Figure 3.10

TR102
Selection criteria
TC < 6 hours
6 hours ≤ TC < 24 hours
TC ≥ 24 hours
Table 3C.6
Calculation method
Modified Hershfield equation

Pt, T  1,130,41  0,64lnT   0,11  0,27lnt  0,79M 0,69 R 0,20

Linear interpolation between calculated modified Hershfield
equation point rainfall and 1-day point rainfall from TR102
Linear interpolation between n-day point rainfall values from TR102
R2 - Page 2/2
A-265
Appendices
RATIONAL METHOD (ALTERNATIVE 3)
Description of catchment
River detail
Calculated by
Date
Physical characteristics
Size of catchment (A)
km²
Weather Service station
Longest watercourse (L)
km
Weather Service number 
Average slope (Sav)
m/m
Area distribution factors
Dolomite area (D%)
%
Rural (α)
Urban (β)
Lakes (γ)
Mean annual precipitation (MAP)#
mm
Rural
Urban
Surface slope
%
Factor
Cs
Description
%
Factor
C2
Vleis and pans
Lawns
Flat areas
Sandy, flat (<2%)
Hilly
Sandy, steep (>7%)
Steep areas
Heavy soil, flat (<2%)
Total
100
Heavy soil, steep (>7%)
Permeability
%
Factor
Cp
Residential areas
Very permeable
Houses
Permeable
Flats
Semi-permeable
Industry
Impermeable
Light industry
Total
100
Heavy industry
Vegetation
%
Factor
Cv
Business
Thick bush and plantation
City centre
Light bush and farm-lands
Suburban
Grasslands
Streets
No vegetation
Maximum flood
Total
100
Total (C2)
100
Notes:
Time of concentration (TC)
Overland flow 
Defined watercourse
 rL 

TC  0,604 
 S 
 av 
0,467
 0,87L2 

TC  
 1000Sav 
hours
hours
Return period (years), T
Run-off coefficient, C1
(C1 = CS + CP + CV)
Adjusted for dolomitic areas, C1D
(= C1(1 - D%)+C1D%(∑(Dfactor x CS%))
Adjustment factor for initial saturation, Ft
Adjusted run-off coefficient, C1T
(= C1D x Ft)
Combined run-off coefficient CT
(= αC1T + βC2 + γC3)
Return period (years), T
Point precipitation (mm), PT 
Point intensity (mm/hour), PiT (= PT/TC)
Area reduction factor (%), ARFT 
Average intensity (mm/hour), IT
(= PiT x ARFT)
Peak flow (m³/s) Q T 
0,385
Run-off coefficient
2
5
10
20
50
100
Max
Rainfall
5
10
20
50
100
Max
2
CT IT A
3,6
Note: # Reference to the appropriate figures and tables is made in the legend table of this method.
A-266
R3 - Page 1/2
Appendices
RATIONAL METHOD (ALTERNATIVE 3)
Table 3C.7
Rural (C1)
LEGEND TABLE
Rational method (Alt 3)
Reference
ID

Figure 3.5 or SA
Weather Services

Table 3C.7

Table 3C.8

Table 3C.9

Table 3C.10

Table 3C.11
#
Figure 3.12 and Figure
3.13

Figure 3.8 (or Figure
3.26 DM)

Figure 3.10, Figure
3.13 or other
Component
Classification
Wetlands and pans (<3%)
Flat areas (3 to 10%)
Hilly (10 to 30%)
Steep areas (>30%)
Very permeable
Permeable
Semi-permeable
Impermeable
Thick bush and plantation
Light bush and farm-lands
Grasslands
No vegetation
Surface slope
(CS)
Permeability
(CP)
Vegetation
(CV)
Table 3C.9
Surface description
Table 3C.8
Urban (C2)
Use
Lawns
Sandy, flat (< 2%)
Sandy, steep (>7%)
Heavy soil, flat (< 2%)
Heavy soil, steep (>7%)
Residential areas
Houses
Flats
Industry
Light industry
Heavy industry
Business
City centre
Suburban
Streets
Maximum flood
Return period (years)
Adjustment factor (Ft) for
steep and impermeable
catchments
Adjustment factor (Ft) for
flat and permeable
catchments
Mean annual rainfall (mm)
600
600 - 900
900
0,01
0,03
0,05
0,06
0,08
0,11
0,12
0,16
0,20
0,22
0,26
0,30
0,03
0,04
0,05
0,06
0,08
0,10
0,12
0,16
0,20
0,21
0,26
0,30
0,03
0,04
0,05
0,07
0,11
0,15
0,17
0,21
0,25
0,26
0,28
0,30
Factor
Paved areas
Clean compacted soil, no stones
Sparse grass over fairly rough surface
Medium grass cover
Thick grass cover
0,05 - 0,10
0,15 - 0,20
0,13 - 0,17
0,25 - 0,35
0,30 - 0,50
0,50 - 0,70
Table 3C.10
Adjustment factor to Cs
Surface slope classification
Dfactor
Steep areas (slopes >30%)
0,50
Hilly (10 to 30%)
0,35
Flat areas (3 to 10%)
0,20
Wetlands and pans (slopes <3%)
0,10
0,50 - 0,80
0,60 - 0,90
0,70 - 0,95
0,50 - 0,70
0,70 - 0,95
1,00
2
Recommended
value of r
0,02
0,1
0,3
0,4
0,8
Table 3C.11
5
10
20
50
100
0,75
0,80
0,85
0,90
0,95
1,00
0,50
0,55
0,60
0,67
0,83
1,00
Note: # Calculate the point intensity rainfall by making use of the provided Design Rainfall estimation software.
The exact point intensity can be calculated by means of linear interpolation between two consecutive values
considering the time of concentration.
R3 - Page 2/2
A-267
Appendices
UNIT HYDROGRAPH METHOD
Description of catchment
River detail
Calculated by
Size of catchment (A)
Longest watercourse (L)
Average slope (Sav)
Length to catchment centroid (LC)
Mean annual precipitation(MAP)#
L LC
Catchment
IC 
index
S
Date
Physical characteristics
km²
Veld type
km
Lag (TL)
m/m
Coefficient (KU) 
km
Peak discharge
K A
Qp  U
of unit
mm
TL
hydrograph (QP)
m³/s
av
Return period (years), T
Storm duration (hours), TSD
Point precipitation (mm), PT
Point intensity (mm/hour), PiT (= PT/TSD)
Area reduction factor, ARFiT
Average rainfall (mm), PAvgiT (= PT x ARFiT)
Flood run-off factor (%), fiT
Effective rain (mm), heiT (= fiT x PAvgiT)
TSD = 1 hour
t 
Time
Q 
S-curve,
TL
(hours), t
Qp
S1
T=
TSD =
Lagged Scurve, S2T
hours
S1 – S2T
Return period (years)
Storm duration (hours), TSD
Unit Hydrograph peak (m³/s), QPiT
Peak discharge (m³/s), QiT (= QPiT x heiT)
Adjusted peak for QPiT/Qp < 1 (m³/s)
ID





S1 - S 2T
TSD
TSD =
Lagged Scurve, S2T
hours
S1 – S2T
S1 - S 2T
TSD
T=
LEGEND TABLE
Unit Hydrograph method
Reference
ID
Reference

Figure 3.8 (or Figure 3.26 DM for large areas)
Figure 3.5 or SA Weather Services

Figure 3.17
Figure 3.15

Table 3.9
Figure 3.16

Table 3.6
Paragraph 3.5.2.5 in DM

Design rainfall Database or Figure 3.7
QPiT = Qp x [(S1 – S2T)/TSD]max
U - Page 1/1
A-268
Appendices
STANDARD DESIGN FLOOD METHOD
Description of catchment
River detail
Calculated by
Date
Physical characteristics
km²
Time of
km
concentration
(TC)
m/m
Size of catchment (A)
Longest watercourse (L)
Average slope (Sav)
SDF basin#
2-year return period rainfall (M)
 0,87L2 

TC  
 1000Sav 
0,385
hours
Time of concentration, t (= 60TC)
mm
Days of thunder per year (R)
TR102 n-day rainfall data
Mean annual precipitation (MAP)
Coordinates
Return period (years)
2
5
10
20
50
Weather Service station
Weather Service station no.
Duration (days)
minutes
days/year
mm
&
100
200
100
200
1 day
2 days
3 days
7 days
Return period (years), T
Point precipitation depth (mm), Pt,T
Area reduction factor (%), ARF
0,4
 90000  12800lnA  9830lnt
Average intensity (mm/hour), IT
(= Pt,T x ARF / TC)

2
Rainfall
5
10
20
50

Run-off coefficients
Calibration factors C2 (2-year return period) (%)
C100 (100-year return period) (%)
Return period (years)
2
5
10
20
50
100
Return period factors (YT)
0
0,84
1,28
1,64
2,05
2,33
Run-off coefficient (CT),
C
C 
 Y  C
C T  2   T  100  2 
100  2,33  100 100 
Peak flow (m³/s), Q T 
ID


200
2,58
CT IT A
3,6
LEGEND TABLE
Standard Design Flood method
Reference
ID
Reference

Figure 3.21
Table 3C.12
Table 3B.1
Criteria
TC < 6 hours
6 hours ≤ TC < 24 hours
TC ≥ 24 hours
Table 3C.12
Calculation method
Modified Hershfield equation

Pt, T  1,130,41  0,64lnT   0,11  0,27lnt  0,79M 0,69 R 0,20

Linear interpolation between calculated modified Hershfield
equation point rainfall and 1-day point rainfall from TR102
Linear interpolation between n-day point rainfall values from TR102
Note: # Reference to the appropriate figures and tables is made in the legend table of this method.
A-269
S - Page 1/1
Appendices
SCS-SA METHOD
Description of catchment
River detail
Calculated by
Date
Physical characteristics
Size of catchment (A)
Time of Concentration (TC)
Defined watercourse
km²
0,385
Longest watercourse (L)
km
Average slope (Sav)
m/m
Lag estimation
L  0,6T c
Return period (years)
 0,87L2 

TC  

 1000Sav 
Overland flow
 rL 

TC  0,604
 S 
 av 
1:10
1:20
hours
1:2
hours
0,467
1:5
1:50
1:100
Daily rainfall depth (one-day design
rainfall, P) (mm) 
Area reduction facture (only applied
for large catchments, ARF) (%) 
Catchment design rainfall
(P x ARF/100) (mm)
SOIL
HRU
Area
(Ai)
(%)
Form
Series
Typical
Textural
Class
LAND COVER
Depth
(m)
SCS
Grouping
Land
Cover
Class
Cover
Category
(S/I/D)
Practice/
Treatment
StormFlow
Potential

1
2
3
4
5
HRU 1
Initial Curve Number (CN) 
Final Curve Number 
Potential maximum soil water
retention (S, mm) 
Initial losses (mm)
Ia = 0,12S
Return period (years)
HRU
1
2
3
4
5
1:2
HRU 2
1:5
HRU 3
HRU 4
1:10
1:20
Design Stormflow depth (Qi) 
HRU 5
1:50
1:100
Total stormflow depth (∑
)
(mm)
Total runoff volume (V, m3x106) 
Peak discharge (qp, m3/s) 
Note: # Reference to the appropriate figures and tables is made in the legend table of this method.
C - Page 1/2
A-270
Appendices
SCS-SA METHOD
ID










LEGEND TABLE
SCS-SA method
Reference
Figure 3.12 or Figure
3E.1 to Figure 3E.6
Figure 3.25 or 3.26
Table 3E.1 or 3E.2
Table 3E.3
Table 3E.3
Table 3C.8
Table 3C.9
Table 3C.10
Table 3C.11
Table 3C.12
Table 3C.8
Adjustment of Curve Numbers
1100
1100
ΔS

CN  II 25,4
CN  II
CN w 
0,4036  0,0059CN  II
CN f 
Median Condition Method
Wet/saturated Conditions
Table 3C.9
Potential maximum soil water retention
S
25400
 254
CN
Table 3C.10
Stormflow depth
Q
(P  Ia) 2
for P > Ia
P  Ia  S
Table 3C.11
Stormflow volume
V=
QA
1000
Table 3C.12
Peak discharge estimation
qp =
0,2083AQ
1,83L
C - Page 2/2
A-271
Appendices
EMPIRICAL METHODS
Description of catchment
River detail
Calculated by
Date
Physical characteristics
km²
Veld type
km
Catchment parameter (C)
with regard to reaction time
km
Size of catchment (A)
Longest watercourse (L)
Length to catchment centroid (LC)
Average slope (Sav)
m/m
Kovács region
Mean annual precipitation (P)
mm
Return period (years), T
10
Constant value for KT 
Peak flow (m³/s), QT based
Q T  0,0377KT PA 0,6 C 0,2
on Midgley & Pitman
Peak flow (m³/s), QRMF based on Kovács
Return period (years), T
50
QT/QRMF ratios
Peak flow (m³/s), based on QT/QRMF ratios
ID


Return
period T
in years
10
20
50
100
Kovács
region
LEGEND TABLE
Empirical methods
Reference
ID
Reference
Figure 3.5 or SA
Weather Services
Figure 3.15
C
Α S
L LC
20
50
100
200
ID
100
Reference

Figure 3.26

Table 3C.14

Table 3C.13

Table 3D.1 or 3D.2
Table 3C.13
Constant values of KT
Veld type (Figure 3.15)
1
0,17
0,23
0,32
0,40
K*
2
Winter
All
year
3
4&
5A
5
0,42
0,52
0,68
0,80
0,83
1,04
1,36
1,60
0,29
0,40
0,55
0,70
0,59
0,68
0,95
1,20
0,59
0,80
1,11
1,40
6
Winter
All
year
7
8
9
0,33
0,45
0,63
0,80
0,67
0,91
1,26
1,60
0,67
0,91
1,26
1,60
0,42
0,57
0,79
1,00
0,50
0,68
0,95
1,20
Table 3C.14
RMF region classification in southern Africa
Number of
Transition zone
Flood zone
floods #
Area range
QRMF
Area range
QRMF
(km²)
(m³/s)
(km²)
(m³/s)
6
1 – 500
30A0,262
500 – 500 000
1,74A0,72
0,265
12
1 – 300
50A
300 – 500 000
5,25A0,66
0,34
26
1 – 300
70A
300 – 300 000
15,9A0,60
55
1 – 100
100A0,38
100 – 100 000
47,9A0,54
0,50
155
1 – 100
100A
100 – 100 000
100A0,50
0,56
61
1 – 100
100A
100 – 30 000
145A0,48
34
1 – 100
100A0,62
100 – 20 000
209A0,46
0,68
25
1 – 100
100A
100 – 10 000
302A0,44
2,8
K1
3,4
K2
4,0
K3
4,6
K4
5,0
K5
5,2
K6
5,4
K7
5,6
K8
Notes:
*
RMF K value as used in Equation 3.32
#
Recorded flood data are reflected in the DWAF report TR105 – Maximum flood peak discharges
in South Africa: An empirical approach
E -Page 1/1
A-272
Appendices
APPENDIX 3D
QT/QRMF RATIOS FOR DIFFERENT CATCHMENT AREAS
A-273
Appendices
Table 3D.1: QT/QRMF ratios for different catchment areas in South Africa, Lesotho and
Swaziland (3.13)
Region
K8
(5,6)
K7
(5,4)
K6
(5,2)
K5
(5 - except in
SW Cape)
K5
(5 - G, H in
SW Cape)
K4
(4,6)
K3
(4)
K2
(3,4)**
Note:
Return
period
(years)
KT
50
100
200
50
100
200
50
100
200
50
100
200
50
100
200
50
100
200
50
100
200
50
100
200
5,06
5,25
5,41
4,70
4,89
5,04
4,50
4,69
4,86
4,30
4,48
4,64
4,45
4,63
4,78
3,84
4,04
4,20
3,26
3,50
3,68
2,40
2,66
2,91
Effective catchment area - Ae (km2)
 10*
0,537
0,668
0,803
0,447
0,556
0,661
0,447
0,556
0,676
0,447
0,550
0,661
0,531
0,654
0,777
0,416
0,524
0,629
0,426
0,562
0,692
0,317
0,428
0,570
30*
0,508
0,645
0,788
0,416
0,525
0,635
0,416
0,528
0,650
0,416
0,521
0,636
0,502
0,629
0,758
0,385
0,495
0,603
0,426
0,562
0,692
0,317
0,428
0,570
100
0,474
0,617
0,769
0,380
0,492
0,607
0,380
0,494
0,624
0,380
0,488
0,608
0,468
0,600
0,738
0,350
0,462
0,576
0,426
0,562
0,692
0,317
0,428
0,570
300
0,503
0,640
0,784
0,411
0,523
0,633
0,411
0,524
0,650
0,411
0,517
0,633
0,497
0,625
0,757
0,381
0,491
0,602
0,390
0,529
0,665
0,281
0,391
0,536
1 000
0,537
0,668
0,803
0,447
0,556
0,661
0,447
0,556
0,676
0,447
0,550
0,661
0,531
0,654
0,777
0,416
0,524
0,629
0,426
0,562
0,692
0,317
0,428
0,570
3 000
0,570
0,695
0,821
0,482
0,588
0,687
0,482
0,588
0,701
0,482
0,582
0,687
0,564
0,680
0,795
0,453
0,558
0,660
0,463
0,595
0,718
0,353
0,463
0,600
10 000
0,607
0,724
0,838
0,523
0,623
0,716
0,526
0,626
0,733
0,525
0,619
0,718
30 000
100 000
0,566
0,660
0,758
0,567
0,657
0,748
0,617
0,699
0,780
0,496
0,597
0,692
0,506
0,631
0,745
0,398
0,506
0,638
0,541
0,636
0,724
0,548
0,666
0,771
0,444
0,549
0,672
0,591
0,679
0,758
0,602
0,710
0,804
0,500
0,598
0,710
300 000
0,651
0,749
0,831
0,560
0,651
0,753
* Estimated ratios
** Ratios of this region may also be used in region K1 (2,8)
Table 3D.2: QT/QRMF ratios for different catchment areas in Namibia and Zimbabwe (3.13)
Region
Return
period
(years)
KT
Effective catchment area - Ae (km2)
 10*
30*
100
300
1 000
3 000
10 000
30 000
100 000
0,594
0,732
0,855
0,620
0,763
0,883
0,595
0,703
0,788
0,585
0,669
0,758
0,631
0,759
0,871
0,654
0,787
0,895
0,631
0,731
0,809
0,619
0,698
0,779
0,690
0,811
0,909
0,666
0,759
0,829
0,656
0,729
0,803
0,727
0,835
0,920
0,710
0,793
0,856
0,696
0,762
0,828
0,564
0,702
0,838
0,603
0,731
0,855
0,640
0,759
0,871
300 000
Namibia
K5
(5)
K4
(4,6)
K3
(4)
K2
(3,4)
50
100
200
50
100
200
50
100
200
50
100
200
4,50
4,70
4,85
4,14
4,34
4,48
3,50
3,66
3,77
2,88
3,01
3,13
0,562
0,708
0,841
0,589
0,741
0,871
0,562
0,676
0,767
0,550
0,639
0,733
0,534
0,686
0,828
0,561
0,721
0,860
0,562
0,676
0,767
0,550
0,639
0,733
0,501
0,661
0,813
0,530
0,699
0,848
0,562
0,676
0,767
0,550
0,639
0,733
0,529
0,683
0,826
0,558
0,719
0,860
0,529
0,648
0,746
0,517
0,610
0,711
0,562
0,708
0,841
0,589
0,741
0,871
0,562
0,676
0,767
0,550
0,639
0,733
Zimbabwe
K6
(5,2)**
Note:
50
100
200
4,65
4,86
5,03
0,531
0,676
0,822
0,502
0,652
0,807
0,468
0,625
0,791
0,497
0,649
0,806
0,531
0,676
0,822
* Estimated ratios
** In region K5 use the same ratios as those applicable to South Africa
A-274
Appendices
APPENDIX 3E
SCS-SA ADDITIONAL INFORMATION
A-275
Appendices
Table 3E.1: Example of classification of soils in southern Africa into hydrological soil
groups by soil form, family and textural class (taxonomic classification)
Soil
Form
ADDO
B
ADDO
B
Code
Ad 1111
Ad 1111
Ad 1111
Ad 1111
Ad 1112
Ad 1112
Ad 1112
Ad 1112
Ad 1121
Ad 1121
Ad 1121
Ad 1121
Ad 1122
Ad 1122
Ad 1122
Ad 1122
Ad 1211
Ad 1211
Ad 1211
Ad 1211
Ad 1212
Ad 1212
Ad 1212
Ad 1212
Ad 1221
Ad 1221
Ad 1221
Ad 1222
Ad 1222
Ad 1222
Ad 1222
Ad 2111
Ad 2111
Ad 2111
Ad 2111
Ad 2112
Ad 2112
Ad 2112
Ad 2112
Ad 2121
Ad 2121
Ad 2121
Ad 2121
Ad 2122
Ad 2122
Ad 2122
Ad 2122
Ad 2211
Ad 2211
Ad 2211
Ad 2211
Ad 2212
Ad 2212
Ad 2212
Ad 2212
Ad 2221
Ad 2221
Ad 2221
Ad 2221
Ad 2222
Ad 2222
Ad 2222
Soil Family
Glenconnor
Glenconnor
Glenconnor
Glenconnor
Dalby
Dalby
Dalby
Dalby
Centlivres
Centlivres
Centlivres
Centlivres
Kentvale
Kentvale
Kentvale
Kentvale
Spekboom
Spekboom
Spekboom
Spekboom
Gorah
Gorah
Gorah
Gorah
Walkraal
Walkraal
Walkraal
Sylvania
Sylvania
Sylvania
Sylvania
Maurmond
Maurmond
Maurmond
Maurmond
Airedale
Airedale
Airedale
Airedale
Felsenheim
Felsenheim
Felsenheim
Felsenheim
Longhill
Longhill
Longhill
Longhill
Mimosa
Mimosa
Mimosa
Mimosa
Peperboom
Peperboom
Peperboom
Peperboom
Suttondale
Suttondale
Suttondale
Suttondale
Tregaron
Tregaron
Tregaron
Typical
Textural
Class
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaClLm
SaCl
SCS
Grouping
A/B
B
B
B/C
A/B
B
B
B/C
B
B/C
B/C
C
B
B/C
B/C
C
A/B
B
B
B/C
A/B
B
B
B/C
B
B/C
C
B
B/C
B/C
C
A/B
B
B
B/C
A/B
B
B
B/C
B
B/C
B/C
C
B
B/C
B/C
C
A/B
B
B
B/C
A/B
B
B
B/C
B
B/C
B/C
C
B
B/C
C
Soil Form
Code
Soil Family
Typical
Textural
Class
Cl
Cl
Cl
Cl
Cl
Cl
Cl
Cl
Cl
Cl
Cl
Cl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
SaLm
SaClLm
SaCl
LmSa
ARCADIA Ar 1100 Lonehill
C/D
Ar 1100 Lonehill
Ar 1200 Rustenburg
Ar 1200 Rustenburg
Ar 2100 Minerva
Ar 2100 Minerva
Ar 2200 Diepsloot
Ar 2200 Diepsloot
Ar 3100 Bospoort
Ar 3100 Bospoort
Ar 3200 Deercroft
Ar 3200 Deercroft
ASKHAM Ak 1000 Aroab
B
Ak 1000 Aroab
Ak 1000 Aroab
Ak 1000 Aroab
Ak 2000 Noenieput
Ak 2000 Noenieput
Ak 2000 Noenieput
Ak 2000 Noenieput
AUGRABIE Ag 1110 Hefnaar
B
Ag 1110 Hefnaar
Ag 1110 Hefnaar
Ag 1110 Hefnaar
Ag 1120 Giyani
Ag 1120 Giyani
Ag 1120 Giyani
Ag 1120 Giyani
Ag 1210 Khubus
Ag 1210 Khubus
Ag 1210 Khubus
Ag 1210 Khubus
Ag 1220 Shilowa
LEGEND
A
low runoff potential
B
moderately low potential
C
moderately high potential
D
high runoff potential
Sa
sand
Cl
clay
Lm
loam
A-276
SCS
Grouping
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
A/B
B
B
B/C
B
B/C
B/C
B/C
A/B
B
B
B/C
B
B/C
B/C
C
A/B
B
B
B/C
B
Appendices
Table 3E.2: Example of classification of soils in southern Africa into hydrological
soil groups by soil form and series (binomial classification)
Soil Form
ARCADIA
C/D
Code
Ar 40
Ar 11
Ar 21
Ar 41
Ar 20
Ar 10
Ar 32
Ar 12
Ar 31
Ar 30
Ar 42
Ar 22
AVALON
Av 13
B
Av 26
Av 12
Av 27
Av 37
Av 33
Av 34
Av 20
Av 14
Av 24
Av 10
AVALON
Av 32
B
Av 31
Av 25
Av 17
Av 22
Av 16
Av 36
Av 21
Av 30
Av 23
Av 11
Av 35
Av 15
BAINSVLEI Bv 23
A/B
Bv 36
Bv 12
Bv 20
Bv 30
Bv 13
Bv 16
Bv 10
Bv 34
Bv 31
Bv 26
Bv 25
Bv 11
Bv 27
Bv 22
Bv 37
Bv 24
Bv 32
Bv 15
Bv 33
Bv 21
Bv 35
Bv 17
Typical
Textural
Class
Arcadia
Cl
Bloukrans
Cl
Clerkness
Cl
Eenzaam
Cl
Gelykvlakte
Cl
Mngazi
Cl
Nagana
Cl
Noukloof
Cl
Rooidraai
Cl
Rydalvale
Cl
Wanstead
Cl
Zwaarkrygen Cl
Ashton
SaLm
Avalon
SaClLm
Banchory
Sa
Bergville
SaCl
Bezuidenhout SaCl
Bleeksand
SaLm
Heidelberg
SaLm
Hobeni
LmSa
Kanhym
SaLm
Leksand
SaLm
Mastaba
LmSa
Middelpos
Sa
Mooiveld
LmSa
Newcastle
SaLm
Normandien
SaCl
Rossdale
Sa
Ruston
SaClLm
Soetmelk
SaClLm
Uithoek
LmSa
Viljoenskroon LmSa
Villiers
SaLm
Welverdien
LmSa
Windmeul
SaLm
Wolweberg
SaLm
Ashkelon
SaLm
Bainsvlei
SaClLm
Camelot
Sa
Chelsea
LmSa
Delwery
LmSa
Dunkeld
SaLm
Elysium
SaClLm
Hlatini
LmSa
Kareekuil
SaLm
Kingston
LmSa
Lonetree
SaClLm
Maanhaar
SaLm
Makong
LmSa
Metz
SaCl
Oosterbeek
Sa
Ottosdal
SaCl
Redhill
SaLm
Trekboer
Sa
Tygerkloof
SaLm
Vermaas
SaLm
Vungama
LmSa
Wedgewood
SaLm
Wilgenhof
SaCl
Soil Series
SCS
Grouping
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
C/D
A/B
B
A
B/C
C
B/C
B/C
A/B
A/B
B
A
B
B
A/B
B
A/B
B
B/C
A/B
B
B
A
B
A
A/B
B
A
A
A/B
A/B
A/B
A
B
A/B
A/B
A
A
B
A
B/C
A/B
A/B
A
B
A
A/B
B
Soil Form
BAINSVLEI
BONHEIM
C
Code
Soil Series
Typical
Textural
Class
SaLm
LmSa
SaClLm
SaClLm
SaCl
SaClLm
SaCl
SaCl
SaClLm
LmSa
SaClLm
SaCl
SaLm
SaClLm
Sa
SaLm
SaClLm
SaLm
LmSa
SaLm
SaClLm
SaLm
SaClLm
SaLm
Cl
LmSa
SaClLm
SaCl
Cl
SaLm
SaClLm
LmSa
SaLm
SaCl
Cl
LmSa
Bv 14
Wykeham
Bo 41
Bonheim
Bo 20
Bushman
Bo 30
Dumasi
Bo 31
Glengazi
Bo 10
Kiora
Bo 21
Rasheni
Bo 11
Stanger
Bo 40
Weenen
CARTREF
Cf 10
Amabele
C
Cf 12
Arrochar
Cf 13
Byrne
Cf 21
Cartref
Cf 22
Cranbrook
Cf 30
Grovedale
Cf 31
Kusasa
Cf 32
Noodhulp
Cf 11
Rutherglen
Cf 20
Waterridge
CHAMPAGNE Ch 11
Champagne
D
Ch 21
Ivanhoe
Ch 10
Mposa
Ch 20
Stratford
CLOVELLY Cv 33
Annandale
A/B
Cv 18
Balgowan
Cv 40
Bleskop
Cv 36
Blinkklip
Cv 17
Clovelly
Cv 28
Clydebank
Cv 35
Denhere
Cv 46
Dudfield
Cv 11
Geelhout
Cv 25
Gutu
Cv 47
Klippan
Cv 38
Klipputs
Cv 10
Lismore
LEGEND
A
low stormflow potential
B
moderately low potential
C
moderately high potential
D
high stormflow potential
Sa
sand
Cl
clay
Lm
loam
A-277
SCS
Grouping
A/B
C/D
C
C
C/D
C
C/D
C/D
C
B/C
C
C/D
C
C
B/C
B/C
C
C
B/C
D
D
D
D
B
B
A
B
B
B
A/B
A/B
A
A
B
B/C
A
Appendices
Table 3E.3 Initial Curve Numbers for selected land cover and treatment classes,
stormflow potentials and hydrological soil groups (various sources)
Land Cover
Class
Fallow
Row Crops
Garden Crops
Small Grain
Close Seeded
Legumes or
Rotational
Meadow
Sugarcane
Land Treatment/ Practice/Description
1 = Straight row
2 = Straight row + conservation tillage
3 = Straight row + conservation tillage
1 = Straight row
2 = Straight row
3 = Straight row + conservation tillage
4 = Straight row + conservation tillage
5 = Planted on contour
6 = Planted on contour
7 = Planted on contour + conservation tillage
8 = Planted on contour + conservation tillage
9 = Conservation structures
10 = Conservation structures
11 = Conservation structures + conservation tillage
12 = Conservation structures + conservation tillage
1 = Straight row
2 = Straight row
1 = Straight row
2 = Straight row
3 = Straight row + conservation tillage
4 = Straight row + conservation tillage
5 = Planted on contour
6 = Planted on contour
7 = Planted on contour + conservation tillage
8 = Planted on contour + conservation tillage
9 = Planted on contour - winter rainfall region
10 = Conservation structures
11 = Conservation structures
12 = Conservation structures + conservation tillage
13 = Conservation structures + conservation tillage
1 = Straight Row
2 = Straight Row
3 = Planted on contour
4 = Planted on contour
5 = Conservation structures
6 = Conservation structures
1 = Straight row: trash burnt
2 = Straight row: trash mulch
3 = Straight row: limited cover
4 = Straight row: partial cover
5 = Straight row: complete cover
6 = Conservation structures: limited cover
7 = Conservation structures: partial cover
8 = Conservation structures: complete cover
A-278
Stormflow
Potential
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
Low
High
High
Low
High
Low
High
Low
High
Low
Low
High
Low
High
Low
High
Low
High
Low
High
Low
A
77
75
74
72
67
71
64
70
65
69
64
66
62
65
61
45
68
65
63
64
60
63
61
62
60
63
61
59
60
58
66
58
64
55
63
51
43
45
67
49
39
65
25
6
Hydrological Soil Group
A/B B B/C C C/D
D
82 86 89 91
93
94
80 84 87 89
91
92
79 83 85 87
89
90
77 81 85 88
90
91
73 78 82 85
87
89
75 79 83 86
88
89
70 75 79 82
84
85
75 79 82 84
86
88
69 75 79 82
84
86
74 78 81 83
85
87
70 74 78 80
82
84
70 74 77 80
82
82
67 71 75 78
80
81
70 73 76 79
80
81
66 70 73 76
78
79
56 66 72 77
80
83
71 75 79 81
83
84
71 76 80 84
86
88
69 75 79 83
85
87
70 74 78 82
84
86
67 72 76 80
82
84
69 74 79 82
84
85
67 73 78 81
83
84
68 73 77 81
83
84
66 72 76 79
81
82
66 70 75 78
80
81
67 72 76 79
81
82
65 70 75 78
80
81
67 71 75 78
80
81
64 69 73 76
78
79
72 77 81 85
87
89
65 72 75 81
84
85
70 75 80 83
84
85
63 69 74 78
81
83
68 73 77 80
82
83
60 67 72 76
78
80
55
56
73
60
50
70
46
14
65
66
78
69
61
75
59
35
72
72
82
73
68
79
67
59
77
77
85
79
74
82
75
70
80
80
87
82
78
84
80
75
82
83
89
84
80
86
83
79
Appendices
Table 3E.3 Initial Curve Numbers for selected land cover and treatment classes,
stormflow potentials and hydrological soil groups (various sources) (continued)
Land Cover
Land Treatment/ Practice/Description
Class
Stormflow
Hydrological Soil Group
Potential
High
Moderate
Low
High
Moderate
Low
A A/B B B/C C C/D
68 74 79 83 86 88
49 61 69 75 79 82
39 51 61 68 74 78
47 57 67 75 81 85
25 46 59 67 75 80
6 14 35 59 70 75
Irrigated Pasture
Low
35
41 48
57 65
68
70
Meadow
Low
30
45 58
65 71
75
81
1 = Woods
2 = Woods
Woods and Scrub
3 = Woods
4 = Brush - Winter rainfall region
High
Moderate
Low
Low
45
36
25
28
56
49
47
36
72
68
64
53
77
73
70
60
80
77
74
64
83
79
77
66
39
44 53
61 66
69
71
52
48
37
48
42
32
41
34
23
37
30
18
62
58
49
58
54
45
53
47
37
49
43
33
72
68
60
68
65
57
64
59
50
60
56
47
77
73
66
73
70
62
69
64
56
66
61
52
82
78
71
78
75
67
74
69
61
71
66
57
85
82
74
82
78
71
77
72
64
74
69
61
87
85
77
85
81
74
80
75
67
77
72
65
39
49
89
81
77
61
57
54
51
98
98
76
72
74
51
61
91
85
81
69
65
63
61
98
98
81
77
79
61
69
92
88
85
75
72
70
68
98
98
85
82
84
68
75
93
90
88
80
77
76
75
98
98
88
85
88
74
79
94
91
90
83
81
80
78
98
98
89
87
90
78
82
95
92
91
85
84
83
82
98
98
90
88
91
80
84
95
93
92
87
86
85
84
98
98
91
89
92
Veld (range)
and Pasture
Orchards
Forests &
Plantations
1 = Veld/pasture in poor condition
2 = Veld/pasture in fair condition
3 = Veld/pasture in good condition
4 = Pasture planted on contour
5 = Pasture planted on contour
6 = Pasture planted on contour
1 = Winter rainfall region, understory of crop cover
1 = Humus depth 25mm; Compactness:
2= "
"
"
3= "
"
"
4 = Humus depth 50mm; Compactness:
5= "
"
"
6= "
"
"
7 = Humus depth 100mm; Compactness:
8= "
"
"
9= "
"
"
10 = Humus depth 150mm; Compactness:
11 = "
"
"
12 = "
"
"
1 = Open spaces, parks, cemeteries 75% grass cover
2 = Open spaces, parks, cemeteries 75% grass cover
3 = Commercial/business areas
85% grass cover
4 = Industrial districts
72% impervious
5 = Residential: lot size 500m2
65% impervious
6= "
"
1000m2
38% impervious
Urban/Sub7= "
"
1350m2
30% impervious
urban Land Uses
8= "
"
2000m2
25% impervious
9= "
"
4000m2
20% impervious
10 = Paved parking lots, roofs, etc.
11 = Streets/roads: tarred, with storm sewers, curbs
12 = "
gravel
13 = "
dirt
14 = "
dirt-hard surface
A-279
compact
moderate
loose/friable
compact
moderate
loose/friable
compact
moderate
loose/friable
compact
moderate
loose/friable
66
60
55
44
D
89
84
80
88
83
79
Appendices
Figure 3E.1: One-day design rainfall distribution over southern Africa for 2 year return
period
Figure 3E.2: One-day design rainfall distribution over southern Africa for 5 year return
period
A-280
Appendices
Figure 3E.3: One-day design rainfall distribution over southern Africa
for 10 year return period
Figure 3E.4: One-day design rainfall distribution over southern Africa
for 20 year return period
A-281
Appendices
Figure 3E.5: One-day design rainfall distribution over southern Africa
for 50 year return period
Figure 3E.6: One-day design rainfall distribution over southern Africa
for 100 year return period
A-282
Appendices