VALIDATION OF DISCHARGE PREDICTION APPROACHES IN A STRAIGHT COMPOUND CHANNEL

VALIDATION OF DISCHARGE PREDICTION APPROACHES IN A STRAIGHT COMPOUND CHANNEL
VALIDATION OF DISCHARGE PREDICTION
APPROACHES IN A STRAIGHT COMPOUND
CHANNEL
A Thesis Submitted in Partial Fulfillment of the Requirements for the
Degree of
Master of Technology
In
Civil Engineering
ELLORA PADHI
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA
2014
VALIDATION OF DISCHARGE PREDICTION
APPROACHES IN A STRAIGHT COMPOUND
CHANNEL
A thesis
Submitted by
Ellora Padhi
(212CE4491)
In partial fulfillment of the requirements
for the award of the degree of
Master of Technology
In
Civil Engineering
(Water Resources Engineering)
Under The Guidance of
Dr. K.C. Patra
Department of Civil Engineering
National Institute of Technology Rourkela
Orissa -769008, India
May 2014
NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA,
ORISSA -769008, INDIA
CERTIFICATE
This is to certify that the thesis entitled, “Validation of discharge
prediction approaches in a straight compound channel” submitted by
Ellora Padhi in partial fulfillment of the requirement for the award of
Master of Technology degree in Civil Engineering with specialization in
Water Resources Engineering at the National Institute of Technology
Rourkela is an authentic work carried out by her under our supervision
and guidance. To the best of our knowledge, the matter embodied in the
thesis has not been submitted to any other University/Institute for the
award of any degree or diploma.
Research Guide
Dr. K. C. Patra
Professor
National Institute Of Technology
Place: Rourkela
Date:
ACKNOWLEDGEMENT
First and foremost, I am glad and thankful to God for the blessing that has given upon me
in all my endeavors.
I am deeply indebted to Dr. K.C. Patra Professor of Water Resources Engineering
specialization, my supervisor, for the motivation, guidance and patience throughout the
research work. Along with that I really glad to Dr. K. K. Khatua Associate Professor of
Water Resources Engineering specialization, for helping me in my research work during
my project. I appreciate their broad range of expertise and attention to detail, as well as the
constant encouragement they have given me over the years.
I am grateful to Prof. N Roy, Head of the Department of Civil Engineering for his valuable
suggestions during the synopsis meeting and necessary facilities for the research work, and
also I am sincerely thankful to Prof. Ramakar Jha, and Prof. A. Kumar for their kind
cooperation and necessary advice.
I extend my sincere thanks to Mrs Bandita Naik the senior research scholar of Water
Resources Engineering Specialization for giving a chance to work with her at the time of
experiment. I am really thankful to her for constantly encouraging me for this work. I am
grateful for friendly atmosphere of the Water Resources Engineering specialization and all
kind and helpful professors that I have met during my course.
I would like thank my parents, and family members. Without their love, patience and
support, I could not have completed this work. Finally, I wish to thank many friends
especially, Aparupa, Mona, Abinash, Santosh for the giving me support and
encouragement during these difficult years,
Ellora Padhi
Table of Contents
List of Figure................................................................................................................................................ iv
List of Tables .............................................................................................................................................. vii
List of Symbols .......................................................................................................................................... viii
Abstract ........................................................................................................................................................ xi
INTRODUCTION ........................................................................................................................................ 1
1.1
Introduction ....................................................................................................................................... 1
1.2
Types of Flow ................................................................................................................................... 2
1.2.1
Steady and unsteady flow ......................................................................................................... 2
1.2.2
Uniform and non-uniform flow................................................................................................. 2
1.2.3.
Laminar and turbulent flow....................................................................................................... 2
1.2.4.
Critical, Subcritical, Super critical flow.................................................................................... 3
1.3
Types of Channel .............................................................................................................................. 4
1.3.1.
Braided channel......................................................................................................................... 5
1.3.2.
Straight Channel........................................................................................................................ 5
1.3.3.
Meandering channel .................................................................................................................. 7
1.4.
Stage Discharge Relationship ........................................................................................................... 7
1.5.
Estimation of Stage-Discharge.......................................................................................................... 9
LITERETURE REVIEW ............................................................................................................................ 11
2.1.
Introduction ..................................................................................................................................... 11
2.2
Literature on Discharge, Momentum Transfer, Boundary Shear Stress ......................................... 12
EXPERIMENTAL SETUP AND PROCEDURE ...................................................................................... 25
3.1.1.
Introduction ................................................................................................................................. 25
3.1.2.
Design and construction of channel ............................................................................................ 25
3.1.3.
Apparatus & equipment used ...................................................................................................... 27
3.1.4.
Experimental procedure .............................................................................................................. 28
3.1.5.
Experimental channels ................................................................................................................ 29
3.1.6.
Measurement of bed slope .......................................................................................................... 30
3.1.7.
Measurement of depth of flow and discharge ............................................................................. 31
3.1.8.
Measurement of longitudinal velocity ........................................................................................ 31
3.1.9.
Measurement of boundary shear stress ....................................................................................... 32
DESCRIPTION OF DISCHARGE PREDICTION APPROACHES ......................................................... 34
3.2.1.
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Introduction ................................................................................................................................. 34
3.2.2.
Numerical methods for computation of discharge ...................................................................... 35
3.2.2.1.
Single Channel Method:- .................................................................................................... 35
3.2.2.2.
Divide Channel Method:-.................................................................................................... 35
3.2.2.2.1.
Vertical interface method .................................................................................................... 36
3.2.2.2.2.
Diagonal Interface method .................................................................................................. 36
3.2.2.3.
Interacting Divide Channel Method .................................................................................... 36
3.2.2.4.
Modified Divided Channel Method .................................................................................... 38
3.2.2.5.
Shiono knight Method......................................................................................................... 39
3.2.3.
Computational method for discharge calculation ....................................................................... 44
3.2.3.1.
Conveyance Estimation System .......................................................................................... 44
3.2.3.2.
Artificial Neural Network ................................................................................................... 45
3.2.3.2.1.
Input parameters.................................................................................................................. 47
3.2.3.2.2.
Output Parameter ................................................................................................................ 47
3.2.4.
Source of data collection:- ...................................................................................................... 48
RESULTS ................................................................................................................................................... 52
4.1
Introduction ..................................................................................................................................... 52
4.2.
Stage Discharge Results .................................................................................................................. 52
4.3.
Distribution of Longitudinal Velocity Results:- ............................................................................. 53
4.4.
Distribution of Longitudinal depth averaged Velocity Results....................................................... 59
4.5.
Distribution of boundary shear stress Results ................................................................................. 60
4.6.
Comparison of experimental results with SKM .............................................................................. 63
4.6.1.
Comparison of Depth averaged velocity with SKM ............................................................... 63
4.6.2.
Comparison of Boundary Shear Stress with SKM .................................................................. 65
4.6.3.
Comparison of Discharge with SKM ...................................................................................... 67
4.7
Comparison of discharge prediction approaches ........................................................................ 68
4.8
Determination of average absolute error ..................................................................................... 73
4.9
Determination of hydraulic parameters of collected data set .......................................................... 74
4.10
Effect of ‘n’ On MDCM ................................................................................................................. 80
4.11
Establishment of linear relationship ................................................................................................ 85
CONCLUSION ........................................................................................................................................... 86
5.1
Conclusions ..................................................................................................................................... 86
5.2
Scope for Future Work.................................................................................................................... 87
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REFERENCES ........................................................................................................................................... 89
APPENDIX-I .............................................................................................................................................. 94
List of Publication ....................................................................................................................................... 94
APPENDIX-II ............................................................................................................................................. 95
SKM Method in MATLAB ........................................................................................................................ 95
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List of Figure
Title
Page No
Fig 1.1: The specific energy curve in an open channel................................................................... 3
Fig.1.2: The Subcritical, supercritical and critical flow conditions ................................................ 4
Fig1.3. (i)-(iii): The straight channels in India as well as in abroad ............................................... 6
Fig1.4: Deposition of sediments along the path of the straight channel. ........................................ 6
Fig.1.5: Meandering River Okavango. ........................................................................................... 7
Fig.1.6: Rating curve plotted between Stage and discharge ........................................................... 8
Fig1.7: Flow structure in a compound channel (Shiono and Knight 1991) .................................. 10
Fig.3.1.1: Schematic diagram of Experimental compound channels with setup .......................... 26
Fig.3.1.2: Longitudinal dimension of the compound channel ...................................................... 26
Fig.3.1.3: Top view and Cross sectional dimensions of the compound channel. ......................... 27
Fig.3.1.4 (i to iv): Apparatus used in experimentation in the rectangular compound channel ..... 28
Fig.3.1.5: Typical grid showing the arrangement of velocity measurement points along horizontal
and in vertical direction at the test section for the rectangular compound channel. ..................... 29
Fig 3.1.6: Compound channel inside the concrete flume with measuring equipment. ................. 29
Fig.3.2.1: The vertical, horizontal, diagonal interface of a prismatic compound channel. ........... 36
Fig.3.2.2: Cross section of a two-stage channel: (a) symmetric with two identical floodplains. (b)
Asymmetric with one side floodplain. .......................................................................................... 37
Fig.3.2.3: Lateral distribution of longitudinal velocity. ................................................................ 42
Fig.3.2.4: The partition of rectangular compound channel by taking the center as origin. .......... 43
Fig. 3.2.5: Multilayer perceptron neural network. ........................................................................ 46
Fig.4.1: Stage discharge curve for the straight channel at section 1. ............................................ 53
Fig.4.2.(i): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.15 .................................................................................................................... 54
Fig.4.2.(ii): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.15 .................................................................................................................... 55
Fig.4.2.(iii): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.2 ...................................................................................................................... 55
Fig.4.2.(iv): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.2 ...................................................................................................................... 55
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Fig.4.2.(v): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.25 .................................................................................................................... 56
Fig.4.2.(vi): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.25 .................................................................................................................... 56
Fig.4.2.(vii): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.3 ...................................................................................................................... 56
Fig.4.2.(viii): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.3 ...................................................................................................................... 57
Fig.4.3.(i): Longitudinal velocity Contour for half portion of the section for relative depth of 0.15
....................................................................................................................................................... 57
Fig.4.3.(ii): Longitudinal velocity Contour for half portion of the section for relative depth of 0.2
....................................................................................................................................................... 58
Fig.4.3.(iii): Longitudinal velocity Contour for half portion of the section for relative depth of
0.25................................................................................................................................................ 58
Fig.4.3.(iv): Longitudinal velocity Contour for half portion of the section for relative depth of 0.3
....................................................................................................................................................... 58
Fig.4.4.(i): Distribution of depth averaged velocity for the relative depth of 0.15 ....................... 59
Fig.4.4.(ii): Distribution of depth averaged velocity for the relative depth of 0.2........................ 59
Fig.4.4.(iii): Distribution of depth averaged velocity for the relative depth of 0.25 .................... 60
Fig.4.4.(iv): Distribution of depth averaged velocity for the relative depth of 0.3 ....................... 60
Fig.4.5.(i): Boundary shear distribution of section 1 of the straight channel for relative depth 0.15
....................................................................................................................................................... 61
Fig.4.5.(ii): Boundary shear distribution of section 1 of the straight channel for relative depth 0.2
....................................................................................................................................................... 61
Fig.4.5.(iii): Boundary shear distribution of section 1 of the straight channel for relative depth
0.25................................................................................................................................................ 62
Fig.4.5.(iv): Boundary shear distribution of section 1 of the straight channel for relative depth 0.3
....................................................................................................................................................... 62
Fig.4.6.(i): Distribution of depth averaged velocity for the relative depth of 0.15 ....................... 63
Fig.4.6.(ii): Distribution of depth averaged velocity for the relative depth of 0.2........................ 64
Fig.4.6.(iii): Distribution of depth averaged velocity for the relative depth of 0.25 .................... 64
v|Page
Fig.4.6.(iv) Distribution of depth averaged velocity for the relative depth of 0.3 ........................ 64
Fig.4.7.(i): Boundary shear distribution of section 1 of the straight channel for relative depth 0.15
....................................................................................................................................................... 65
Fig.4.7.(ii): Boundary shear distribution of section 1 of the straight channel for relative depth 0.2
....................................................................................................................................................... 65
Fig.4.7.(iii): Boundary shear distribution of sec- 1 of the straight channel for relative depth 0.25
....................................................................................................................................................... 66
Fig.4.7.(iv): Boundary shear distribution of sec- 1 of the straight channel for relative depth 0.3 66
Fig.4.8: Error in discharge through SKM ..................................................................................... 67
Fig4.9: average absolute error in all five methods………………………………………………82.
vi | P a g e
List of Tables
Title
Page No
Table 3.1.1: Details of Geometrical parameters of the experimental runs ................................... 30
Table 3.2.1: Geometrical parameters of FCF channel .................................................................. 48
Table 3.2.2: Geometrical parameters of Knight & Demetriou channel ........................................ 50
Table 3.2.3: Geometrical parameters of Atbay channel ............................................................... 50
Table 3.2.4: Geometrical parameters of Rezai channel ................................................................ 51
Table 3.2.5: Geometrical parameters of NIT Rourkela channel ................................................... 51
Table 4.1: Percentage of error in discharge through SKM ........................................................... 67
Table 4.2(i)-4.2(xi): Percentage of error calculation for discharge through hydraulic models .... 72
Table 4.3: Average absolute error value ....................................................................................... 73
Table 4.4(i)-4.4(xi): Determination of hydraulic parameters ....................................................... 79
Table 4.5(i)-4.5(xi) Percentage of error in discharge by varying the value of Manning’s n. ....... 84
vii | P a g e
List of Symbols
A
Area of the compound channel
a
Rating curve constant
Afull bank
Area of the main channel at full bank depth
Afp
Area of the flood plain
Amc
Area of the main channel
Ar
Area ratio
Atotal
Total area of the compound channel
B
Top width of the compound channel
b
Bottom width of the main channel
b1
Rating curve constant
C
Chezy’s constant
Cd
Co-efficient of discharge
D
Hydraulic depth
d
The diameter of the pitot tube
f
Darcy- weisbach co-efficient of friction
fmc
Co efficient of friction in the main channel
ffp
Co efficient of friction in the flood plain
Fr
Froude’s number
g
Acceleration due to gravity
H
Depth of flow
h
Full bank depth
Hn
The height of water flowing above the notch
hint
Interface depth
L
The length of the notch,
n
manning’s roughness coefficient
Nfp
No of flood plain
nfp
Manning’s roughness for flood plain
nmc
Manning’s roughness for main channel
Pfull bank
Perimeter of the main channel at full bank depth
viii | P a g e
Pfp
perimeter of the flood plain
Pmc
Perimeter of the main channel
Pr
Perimeter ratio
Ptotal
Total perimeter of the compound channel
Q
Discharge of the channel
Qactual
Actual discharge of the channel
Qfull bank
Discharge of the main channel at full bank depth
Qr
Discharge ratio
Qtotal
Total discharge of the channel for a given flow
R
Hydraulic radius of the channel
Re
Reynolds number of the flowing fluid
Rfp
Hydraulic radius of the flood plain
Rmc
Hydraulic radius of the main channel
S0
Bed slope of the channel
s
lateral slope of the channel
Ud
Depth averaged velocity
Ufp
Velocity of the flood plain
Ufp,0
Velocities of flood plain when co-efficient of interface is zero
Umc
Velocity of the main channel
Umc,0
Velocities of the main channel when co-efficient of interface is zero
V
Mean velocity of the channel
Vd
Lateral depth averaged velocity
Wfull bank
Width of the main channel at full bank depth
Wfp
Width of the flood plain
Wmc
Width of the main channel
Wr
Width ratio
Wtotal
Total width of the compound channel
Xfp
Interface length for flood plain
Xmc
Interface length for the main channel
τb
Bed shear stress
γ
Co-efficient of interface
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ρ
Density of water
λ
Eddy viscosity
τint
Interface shear stress
ν
Kinematic viscosity
%Sfp
Percentage of shear force in the flood plain
∆p
Pressure difference between the total pressure and the static pressure at the
wall
β
Relative depth
Г
Secondary current
τw
Wall shear stress
α
Width ratio
x|Page
Abstract
The flow pattern of a compound channel becomes complicated due to the transfer of momentum
between the main channel and the adjoining floodplains. Experiments are carried out to compute
the velocity as well as boundary shear along the wetted perimeter of a straight compound
channel to quantify the momentum transfer along the expected interfaces originating at the
junction region between main channel and flood plain. This is helpful to evaluate the stagedischarge relationship for a compound channel accurately. Discharge calculation can be done by
using various hydraulic models. But the traditional discharge prediction models such as SCM,
DCM fail to give accurate discharge as they don’t consider the effect of momentum transfer.
Therefore some new models are being developed which makes discharge prediction more
accurate than the traditional method by considering the effect of momentum transfer. In this
study the experimental data reported by other investigators as well as data from the present series
of experiments are used through the hydraulic models such as DCM, IDCM, MDCM,CES to
evaluate the discharge estimation and the results are compared with the experimental
observations by keeping Manning’s n value constant with respect to the surface roughness. But
apart from surface roughness Manning’s n is dependent upon many other factors such as depth of
flow, shape of the channel, alignment of the channel etc.. So by varying the value of manning’s n
with respect to depth of flow the discharge is being computed through MDCM and the
percentage of error is found out. Modification to MDCM is applied for the variation of n values.
xi | P a g e
Introduction
INTRODUCTION
1.1
Introduction
There is a very close relationship exists between civilization and the rivers from the last
decades, as they provide many contribution to the human society like water for house hold work,
irrigation, navigation, hydro electricity generation, water supply for consumption and industrial
applications and disposal of waste. Therefore it is seen that the surroundings of the river have
been popular settling areas of the human civilization. Due to consequently increased use of rivers
large amount of settlements have been developed on the river flood plains and its nearby areas.
As a result the river may be a threat to the activities that has been taking places in its vicinity, at
extreme discharge condition flood may occur that may cause loss of life and damage to the
infrastructure of the surrounding area.
River engineers are therefore more and more solicited to mitigate the flood impacts.
Previously flood control work was associated with many alleviation works like improvement on
dikes and detention reservoirs. But it was cost effective and the outcome was not so effective as
the morphological response of the river is unpredictable. Therefore some sustainable solution are
being adopted such as, surrounding of the rivers are allocated with much space or made free by
withdrawing dikes and abandoning possible settlements areas or using the surrounding area of
the river seasonally (Bhattacharya and Bora 1997). Apart from this to reduce the flood risk,
hydro-dynamic models of river flow may also help in achieving better flood protection measures
against the upcoming flood. To forecast the flood is required and for that many hydraulic models
are being developed by different investigators which are helpful in estimating the discharge for
given flow condition of the rivers. There are many hydraulic models have been developed by the
researchers which are helpful in discharge prediction of a channel. Initially Single channel
method (SCM) and Divided channel method (DCM) are the two most common methods which
are used by the river engineers but these methods are that reliable as these methods do not
consider the effect of momentum transfer therefore other new discharge prediction methods are
being developed. IDCM, MDCM, EDM, SKM, MSKM LDM are the examples of the standard
hydraulic models. Apart from discharge prediction these models are helpful in velocity as well as
1|Page
Introduction
boundary shear stress measurement. But for this the hydraulic behaviors of the river is required
to be investigated. So for this investigation, the types of flow, type of channel, factor affecting
the hydraulic behavior of the channel, channel geometry etc. has to be studied.
1.2
Types of Flow
Generally there are two types of flow exist. One is free surface flow and another one is
pressure flow. The flow is said to be free surface flow if is subjected to atmospheric pressure and
the flow is said to be pressure flow if it is running at full flow condition with in a conduit. But in
open channel the flow type is free surface as it is open to atmosphere. But apart from this
depending upon the hydraulic characteristics the flow is again categorized such as steady and
unsteady flow, uniform and non-uniform flow, laminar and turbulent flow and lastly depending
upon the energy level it is subdivided into critical, subcritical and supercritical flow.
1.2.1 Steady and unsteady flow
When the flow velocity at a given point does not change with respect to time then the
flow is said to be steady flow. If the velocity at a given point changes with respect to time the
flow is said to be unsteady flow. This is based on variation of velocity with respect to time at a
particular location. The mean local acceleration is considered to be zero for steady state flow
condition i.e. partial derivative of the velocity components with respect to time (t) are zero.
1.2.2 Uniform and non-uniform flow
If the flow velocity at a given time does not change within a given length of the channel,
the flow is said to be uniform flow and if the flow velocity at a given time changes with respect
to space the flow is called as non-uniform flow. This is based on the variation of flow velocity
with respect to space at a particular time. Here the conservative acceleration in uniform flow is
zero i.e partial derivative of the velocity components with respect to space (x, y, z) are all zero.
1.2.3. Laminar and turbulent flow
If the flow particle of the water appear to move in a definite path and the flow appears to
be in the patterns of layer upon layer, the type of flow is said to be laminar flow. In turbulent
flow the particle of water moves in an irregular path which are not constant with respect to time
or space. Whether the flow is laminar or turbulent, it depends upon the relative magnitude of the
viscous force and the inertia force. The flow should be laminar if the viscous force is
2|Page
Introduction
predominant and the flow will be turbulent if the inertia force is predominant. The ratio of
viscous force and the inertia force is called as Reynolds number. If the Reynolds number is less
than 500, the flow comes under laminar flow category. If the Reynolds number id greater than
2000 the flow type is turbulent and if it lies between 500 and 2000, it comes under transition
zone.
1.2.4. Critical, Subcritical, Super critical flow
Depending upon the level of specific energy the flow is again characterized in to three
parts, such as critical, subcritical, super critical flow etc.
Fig 1.1 The specific energy curve in an open channel
In the fig.1.1 a graph is plotted between the depth and specific energy where y is depth of flow,
V is the mean velocity of flow, g is the acceleration due to gravity and yc denotes the critical
depth where the value of specific energy (E) is minimum. A flow is said to be critical if the
velocity of flow is equal to velocity of a gravity wave having small amplitude. A gravity wave
can be formed by changing the flow depth. The flow is said to be subcritical if the velocity of
flow is less than the critical velocity and the flow is said to be supercritical if the flow velocity is
greater than the critical velocity. If we consider critical flow in terms of depth then we can say
that the if the depth of flow is greater than critical flow depth then the flow is called as
subcritical flow and if the depth of flow is less than the critical flow depth then the flow is said to
be supercritical flow.
3|Page
Introduction
Fig.1.2 The Subcritical, supercritical and critical flow conditions
Apart from these, whether the flow is critical, subcritical or supercritical, it can be known from
the value of Froude’s number. The ratio of inertia force and gravitational force is called Froude’s
number. For an open channel,
√
, where d is hydraulic depth, V is the flow velocity and g
is the gravitational acceleration. But a rectangular channel, d term‘d’ is replaced by ‘y’ where y
is the depth of flow. As it is mentioned before depending upon the value of Froude’s number the
flow can be classified, so here the categorization is given i.e. for Froude’s number less than one
the flow is a subcritical flow, for Froude’s number greater than one, the flow is said to be a
supercritical flow and for critical flow condition the Froude’s number should be equal to one.
1.3
Types of Channel
Streams are responsible for erosion, transportation, and deposition of sediments. Energy
of the stream controls these function. the slope of the stream determines the energy of the stream
and discharge. The discharge of a stream can be measured by multiplying area of the cross
section of the stream with the velocity of the stream. there are some factors which are affecting
the discharge such as the shape of the channel, the smoothness of the channel sides and bottom,
and obstacles in the stream. Velocity of the stream determines the capability of the stream
whether it can carry large size of particle or not and as discharge is the function of velocity it
4|Page
Introduction
also determines the total capacity of the channel. Through its complete path, a river may be
classified into three different types of streams as it travels through dissimilar sites.
Three major streams are three types
1. Braided Channel
2. Straight Channel
3. Meandering Channel.
1.3.1. Braided channel
Braided streams are having less energy deficient and have a tendency to change the flow path
constantly due to deposition of large sediment loads they carry. Braided streams are often originated
in outwash plains at the head of glaciers.
1.3.2. Straight Channel
Straight stream channels are rare. The straight channels are the channels which are having
sinuosity as one. There is no much variation occurs along its flow path. These are mainly
unstable in nature. Along the lines of faults and joints, on steep slopes where the surface gradient
are closely followed by hills, the straight are developed. In the experimental laboratory it is seen
that the flume of straight channels are having uniform cross section quickly develop pool-andriffle orders.
Fig.1.3.(i)Three dimensional view of a straight channel.
5|Page
Introduction
Fig1.3.(ii) Straight reach of River
Great Ouse in United Kingdom
Fig1.3.(iii) Straight reach of
River Jhelum in Srinagar
India
Fig1.3. (i)-(iii) shows straight channels in India as well as in abroad
Straight channels are having excess of energy and mostly have a single channel. Straight streams
erode towards the downstream and thus have channels with steep walls and large slope. Even in
straight channel segments water flows in a sinuous fashion, with the deepest part of the channel
changing from near one bank to near the other. Velocity is highest in the zone overlying the
deepest part of the stream. In these areas, sediment is transported readily resulting in pools.
Where the velocity of the stream is low, sediment is deposited to form bars. The bank closest to
the zone of highest velocity is usually eroded and results in a cut-bank.
Fig1.4. Deposition of sediments along the path of the straight channel.
6|Page
Introduction
1.3.3. Meandering channel
Meandering channel are the channel which are having sinuosity more than one. These are
the channels which are having small straight reaches and the variation occurs along the flow
path. When there is an obstacle occurs the river deviates from its path and goes towards the low
resistance path due to which a meandering channel is developed. these streams have a balance of
energy. They are mainly characterized by slow moving water, low slopes, but having high
capacity. Meandering streams erode laterally across an active meandering floodplain creating
cut-banks on the outside of the bends where the bank of the stream is being eroded away, point
bars on the inside of the bends where sediments are accumulating, and oxbows where the bends
have been cut off from the main stream Oxbows may or may not have water in them. They are
often left only as depressions in the ground that have been overgrown with vegetation.
Fig.1.5: Meandering River Okavango
Depending upon the channel geometry the channels are also classified as rectangular, trapezoidal
circular etc. The compound channels are also asymmetric if there is one floodplain along the side
of the main channel. The compound channel is said to be symmetric if it has same floodplain
along both side of the main channel and it is said to be unsymmetrical if its main channel has two
flood plain but they unequal in size.
1.4. Stage Discharge Relationship
Estimation stream discharge is often area of interest of river engineers and watershed
managers. Rate of flow of water passing a point on a stream at an unit duration of time is known
as discharge; therefore, it is harder to measure the discharge of a river continuously and it is cost
effective task in hydrology. To overcome this problem an empirical or theoretical relationship is
7|Page
Introduction
being developed by the researchers between the water level and the quantity of water passing
through a point at a particular instant of time. This relationship is called as stage discharge
relationship or it is called as a rating curve. A Rating curve is a graph of discharge versus water
level (stage) for a given point on a stream. Frequent measurements of discharge of the stream are
taken over a range of stream stages. A rating curve is usually plotted as stage on y-axis versus
discharge on x-axis.
Fig.1.6: Rating curve plotted between Stage and discharge
While a rating curve is generated it includes two steps. In the first step by measuring the stage
and corresponding discharge in the river the relationship between stage and discharge is
established. In the second step, measurement of stage of river is done by gauge and then
discharge is calculated by the help of the relationship established in the first step. When the
stage-discharge relationship is constant with respect to time, it is called permanent control and
when the relationship does change, it is called shifting control. due to erosion or deposition of
sediment at the stage measurement site, situation of
shifting control occurs. Situation of
permanent controls occur where bed of the river is rock type or the bottom of the river is of
concrete, though it is not available always,
The relationship between stage and discharge can be estimated with the equation (1.1).
(1.1)
Where H represents water level (stage) for discharge Q, a and b1 are rating curve constants.
8|Page
Introduction
1.5. Estimation of Stage-Discharge
Generally the stage discharge relationship is required to predict the discharge. Therefore
an empirical relationship is established which is used for steady and uniform flow condition so
that we can get an ideal rating curve, other than this we can calculate it directly by multiplying
area with the average velocity of the river, but for this the mean velocity and the cross sectional
area of the stream should be known. Sometimes it is very difficult to go to the site and take the
measurement. So we cannot be more dependent on the rating curve formula. But apart from this
there are other traditional formulae which are used to estimate the discharge such as Manning’s
formula, Chezy’s formula and Darcy’s Weisbach formula etc.
So according to Mannings formula
⁄
(1.2)
According to Chezy’s formula
√
(1.3)
According to Darcy’s Weisbach formula
√
(1.4)
After finding out the velocity discharge can be calculated by multiplying area with it. In the
above equations V is the mean velocity, R is the hydraulic radius, S o is the bed slope, g is
acceleration due to gravity, f is the co-efficient of friction and C is the Chezy’s Constant.
The problem with three formulae is they are mainly useful to simple channel and they
fails to fails to predict the discharge large compound channels due to changes in geometry and
variability in hydraulic parameters. Therefore some new models are developed to predict the
discharge. Initially single channel method was used but as it gives overestimated discharge so
divided channel method was developed but both methods do not consider the effect of
momentum transfer.
Momentum transfer occurs at the junction of the main channel and the flood plain, due to
difference in local velocities of both main channel and flood plain. Due to this difference
formation of vortices occurs at the junction. A shear layer is formed because of these vortices.
9|Page
Introduction
Apart from this there is a secondary current develops at the boundary of the channel due to
turbulence and also there is a frictional force develops between the water and the boundary of the
channel which give resistance to flow. Due to secondary current, viscosity and shear stress the
discharge prediction was getting difficult.
Fig1.7: Flow structure in a compound channel (Shiono and Knight 1991)
So by considering these effects Shiono and Kinight developed a model which gives better
discharge prediction than those conventional methods. But later on some researchers found that
effect of secondary current is negligible therefore some new methods are being developed
without considering that. MDCM is the method which is used to predict the discharge by
quantifying the momentum transfer in terms of interface length. Interacting divided channel
method is another which is also used to measure the discharge by considering momentum
transfer in terms of shear stress.
With these numerical methods some computational are developed which also give good
discharge prediction such as HEC-RAS, MIKE11, CES, ANN etc. So here we should go for a
comparison study between these numerical and computational method so we can come to a
conclusion that which method give better discharge prediction.
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Literature Review
LITERETURE REVIEW
2.1. Introduction
Prediction of discharge is one of the important works in river flow analysis. Discharge
prediction is required to establish the stage discharge relationship in a channel which will be help
full to the River Engineers for flood forecasting, bank protection etc. Discharge calculation is
influenced by various hydraulic parameters as well as geometric parameters of the channel. But
still discharge prediction in the simple channel is easy and it can be done using manning’s
equation, chazy’s equation or by using darcy-weibach’ equation. But when it is required to
calculate the discharge in compound channel then these equations do not give adequate answers.
So for finding out the reasons of not getting good result, initially some researchers divided the
compound channel in to various segments and tried to calculate the discharge for each segment.
By integrating the discharge for the segments, the total discharge for the compound channel was
found out. But this method also did not work. So after having several investigations by the
researchers it was found that the reason behind inaccurate discharge value is due to exchange of
momentum. They stated that Momentum transfer occurs at the junction of flood plain and the
main channel due to difference in velocities. Generally in bank flow condition water flows in
certain velocity with in the main channel but due to flood, it overtops the main channel and flow
over the flood plain. As the flow area for flood plain is less than the main channel so initially the
effect of shear stress is more. Due to this there is difference in velocity generated which resulting
in the formation of vortices at the junction. This difference in velocity leads to create problem in
calculation of discharge. So now a days many researchers are trying hard to work on momentum
transfer and also to understand how it is affecting the velocity of the compound channel and
shear stress at the bed as well as on the wall for an over bank flow condition.
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Literature Review
In this chapter the works of various investigators on experimental research and studies on
discharge prediction, momentum transfer phenomenon and calculation of boundary shear stress
for straight compound channels are presented.
2.2
Literature on Discharge, Momentum Transfer, Boundary Shear
Stress
Sellin (1964) made sure the presence of the secondary current after conducting number of
laboratory studies and shown the presence of vortices at the junction of main channel and flood
plain. Here the channel velocities and discharge was being studied under both in-bank and over
bank flow conditions by putting a thin impermeable film at the junction and it was observed that
velocity in the main channel was more under in bank flow condition, than the over bank flow
condition.
Zheleznyakov (1965) investigated the interaction at the junction of main channel and the
adjoining floodplains. He studied the effect of momentum transfer mechanism by conducting
experiments in the laboratory conditions. He stated that due to momentum transfer the overall
rate of discharge is decreased for the lower floodplain depths and as the floodplain depth goes on
increasing the effect of momentum transfer goes on decreasing. Apart from this he conducted
field experiments where he had shown the importance of momentum transfer in the calculation
of overall discharge. The dragging and accelerating forces acting upon the higher main channel
flow velocity and slower flood plain flow velocity respectively are main cause of transfer of
momentum at the junction which is called as kinematics effect.
Ghosh and Kar (1975) studied the boundary shear distribution in straight compound channels
for both smooth and rough surface. The distribution of drag forces on different parts of the
channel sections were being related with the co-efficient of roughness and depth of flow.
Yen and Overton (1973) used isovel plots to get the exact position of zero shear interface plane.
By using this method data had been collected and they showed that with increase in depth of
flow over the flood plain, the angle of inclination the horizontal of the interface plane also
increased.
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Myers and Elswy (1975) reported studies on the effect of momentum transfer at the junction of
main channel and flood plain and distribution of shear stress at complex sections of a compound
channel. Here shear stress were calculated at different section of the compound channel and it is
found that with respect to in flow condition there is a decrease of 22 percent in main channel
shear stress and increase of 260 percent in flood plain shear stress. The possible area of erosion
and scour of channel bed and the flow pattern in a compound section can be known through this.
Rajaratnam and Ahmadi (1979) reported the study on the interaction of flow velocity between
main channel and floodplain with smooth boundary surface in a straight channel. The transfer of
longitudinal momentum from main channel to flood plain was presented. It is seen that due to
flow interaction at the junction of flood plain and main channel, the bed shear in floodplain
considerably increased while the main channel shear decreased at the same time. It is observed
that the effect of flow interaction was reduced as the flow depth in the floodplain increased.
Wormleaton et. al. (1982) carried out a series of laboratory experiments in straight compound
channels with symmetrical floodplains and by using "divide channel" method discharge was
estimated. By measuring boundary shear stress, apparent shear stress at the horizontal, vertical
and diagonal interface planes generated between the main channel-floodplain junction could also
be evaluated. For calculating discharge, an apparent shear stress ratio was proposed which was
useful in selecting the best method of dividing the channel. It was found that the horizontal and
diagonal interface divided channel method gave better discharge results than the vertical
interface divided channel method at lower floodplains depth.
Knight and Demetriou (1983) undertook series of experiments in straight symmetrical
compound channels to understand the characteristics of discharge, distributions of boundary
shear stress and boundary shear force in the given section. Equations for calculating the
percentage of shear force carried by floodplain were being proposed. They also presented an
equation for the proportions of total flow in various sub-parts of compound section in terms of
two dimensionless channel parameters. The apparent shear force was found to be more at lower
flow depth and also for high floodplain widths for vertical interface between main channel and
floodplain.
Knight and Hamed (1984) further extended the work of Knight and Demetriou (1983) from
smooth flood plains to rough floodplains. The floodplains were roughened through six different
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materials to study the effect of different roughness between floodplain and main channel on flow
interaction process. Using four dimensionless channel parameters, they proposed equations for
the percentage shear force carried by floodplains and the apparent shear force in vertical,
horizontal, diagonal interface planes. From the results of apparent shear force and discharge data
the efficiency of these four commonly adopted design methods for predicting discharge could be
known.
Wormleaton and Hadjipanos (1985) reported a study on flow distribution in compound
channels and showed that even though a discharge prediction method may be efficient can give
good results on overall discharge in a compound channel but the velocity flow distribution
between floodplain and main channel may not be good. In general, the floodplain flow is found
to be underestimated and the flow distribution in the main channel is overestimated.
Myers (1987) proposed the theoretical considerations of ratios of velocity of main channel and
to the velocity of floodplain and discharge of main channel to discharge of flood plain in
compound channel. The relationship was established between the ratios and the flow depth, as a
result it gave a straight line relationship. Here it was seen that the relation between ratio and flow
depth was independent of bed slope but dependent on channel geometry. Equations were
generated which describes the relationship of ratio and depth for smooth compound channel. It
was seen that at lower depths, the traditional methods overestimated the full main channel
carrying capacity and underestimated at higher depths, while floodplain flow capacity was
always underestimated for both higher and lower depths. He suggested the need for methods of
compound channel analysis which can accurately model flow proportion in floodplain and main
channel for both higher as well lower depths.
Stephenson and Kolovopoulos (1990) studied and discussed four different methods to evaluate
the discharge prediction method by considering variation of the shear stress between main
channel and flood plain with respect to different flow condition. Based on the previously
published data, they predicted discharge and ended with a conclusion that their 'area method' was
the most reliable method in predicting discharge and that Prinos-Townsend (1984) equation
gave better results for apparent shear stress at junction region of floodplain and main channel in a
compound channel.
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Shiono and Knight (1988, 1991) studied and discussed the flow of water in straight open
channels with different cross section. an analytical model for predicting depth averaged velocity
and boundary shear stress for trapezoidal channels was derived and then for any shape an
analytical model was developed by discretizing the channel boundary in to linear elements. For
this they developed the mathematical equations influencing the shear layer between a main
channel and its floodplains based on a dimensionless eddy viscosity and secondary current
model. They considered three dimensionless parameters such as
turbulence, lateral shear
turbulence and secondary flows for their model and their effects of bed-generated were studied.
Ackers (1992, 1993) developed a design formula for straight compound channels by taking into
account the effects of flow interaction between floodplain and main channel. He proposed a
parameter which keeps the consistency between the hydraulic condition of floodplain and main
channel zones. The formulations were tested in previously published experimental data set.
Myers and Lyness (1997) reported a study on the behavior of two discharge ratios, namely total
to bank full discharge and main channel to floodplain discharge in compound channels for
smooth and homogeneously roughened channels of various scales. It showed that the total to
bank full discharge ratio was independent of bed slope and scale and was fully dependent upon
cross section geometry. The other ratio was also found to be independent of bed slope and scale
but was affected by the lateral bed slope of the flood plain. The coefficients and exponents in the
equations relating to flow ratios to flow depths were being evaluated.
Pang (1998) undertook experiments on the straight compound channel under in flow and over
bank flow conditions. It was observed that the sharing of discharge between the main channel
and floodplain was in according to the flow energy loss, which can be expressed in the form of
coefficient of flow resistance. In general, Manning's roughness coefficient n not only indicated
the characteristics of channel roughness, but also influenced the loss of energy in the flow.
Depending upon the variation in water depth manning’s n also varies for same surface roughness
in a compound channel. Though the surface of the main channel and flood plain are same but as
the depth of water in both main channel as well as in the flood plain are different so manning’s n
value is also different for the section.
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Bousmar and Zech (1999) proposed a 1D model known as the exchange-discharge model
(EDM) which is suitable for prediction of stage-discharge relationship as well as simulations of
practical water-surface profile. The momentum transfer is calculated multiplying the velocity
gradient at the interface with the mass discharge exchanged through this interface generated from
the effect turbulence. They ended up with a conclusion that the model predicts the stagedischarge for both the experimental as well as natural river data. their models is being used for
flow prediction in a prototype River named as Sambre in Belgium and it works in a good
manner.
Ervine et. al. (2000) proposed a practical method for predicting depth-averaged velocity and
boundary shear stress in straight over bank flows. An analytical solution to the depth-integrated
turbulent form of the RANS equation was proposed, in which lateral shear and secondary flows
in addition to bed friction were considered. The obtained analytical solution is applied to number
of channels at both field and laboratory, and the results were compared with SKM and the lateral
distribution method (LDM).
Patra and Kar (2000) presented the test results related to the boundary shear stress, flow
velocity, shear force and discharge characteristics of a compound channel comprises of a
rectangular main channel and one or two floodplains present to its adjacent sides. Five
dimensionless channel variables were used to form equations which give the total shear force
percentage carried by the adjacent floodplains. A study was carried out on a set of smooth and
rough sections with aspect ratio varying from 2 to 5. Apparent shear forces on the anticipated
vertical, diagonal, and horizontal interface plains were found to be dissimilar. At low depths of
flow apparent shear force varies from zero and with increase in depth over floodplain the sign
changes. They suggested a variable-inclined interface where apparent shear force was considered
to be zero. Empirical equations were proposed for predicting of discharge carried by both the
main channel and floodplain.
Thrnton et. al. (2000) carried out eight numbers of experiments in a physical model of a
compound channel to estimate the apparent shear stress at the junction region of main channel
and the flood plain for both vegetated and un-vegetated floodplain flow condition. Data are being
analyzed by using a method based on turbulence for calculating the apparent shear stress as a
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function of variation in velocities in the compound channel. They gave an empirical relationship
for the calculation of the apparent shear stress at the main channel floodplain junction region
which was dependent upon the bed shear stress, depth averaged velocity, depth of flow, and the
blockage developed due to vegetation present over the floodplain.
Liu and James (2000) predicted discharge in a meandering compound channel using artificial
neural networks. This tool is having a flexible structure, capable of establishing a non-linear
relationship between the input and output data. They have showed that between predicted and the
measured discharge there is up to 15% inconsistency exist.
Myers et. al. (2001) used FCF data and presented the results for both fixed and mobile main
channel boundaries together with two types of flood plain roughness compound channel. On the
basis of mathematical modeling, the velocity and discharge ratio relationships was being
proposed which was useful for discharge estimation in over-bank flows and their results were
compared with the data of a prototype natural compound river channel. Two different graphs
were plotted, one was between the ratios of main channel to floodplain average velocities and
discharge obtained by using laboratory data and second was between ratios of main channel to
floodplain average velocities and discharge obtained by using the natural river data.it was
observed that first graph showed the logarithmic relationship whereas the second graph gave the
linear relationship. The Divided channel method overestimated the discharge in all cases and
showed good accuracy when it is applied to laboratory data with smooth floodplains, but
significant errors of 35% for rough floodplain data, and up to 27% for river data had been found
in this method. Compound discharge for all cases for low flow depths was being underestimated
by single channel method (SCM), but for the smooth boundary laboratory data as well as the
river data it became more accurate at larger depths.
Atabay and Knight (2002) established some stage discharge relationship for symmetrical
compound channel section using the experimental results of the Flood Channel Facility (FCF).
The effect of flood plain width and main channel aspect ratio to the stage discharge relationship
was being examined. Simple empirical relationships between stage and total discharge, and stage
and zonal discharge for uniform roughness and varying flood plain width ratio were being
derived. They verified broad effects on the stage –discharge relationship due to flood plain width
ratio.
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Ozbek and Cebe (2003) preferred to use experimental results of the FCF at Wallingford, for
calculating apparent shear stress and also for estimating discharge in symmetrical compound
channels with varying floodplain widths. Three vertical, horizontal, and diagonal interface planes
between the main channel and the floodplain subsections were considered for calculation of
apparent shear stresses across the interfaces. The discharge values for the whole cross-section as
well as for each sub-section of the channel were computed. It was shown that the performance
of these computation methods depend on their ability to predict apparent shear stress accurately.
They had shown that as compare to vertical division method, the diagonal and horizontal
division methods gave better results.
Weber and Menéndez (2003) presented the scope of 2D-Horizontal and 1D-Lateral models for
lateral velocity distribution is addressed, and their relative and absolute performances are tested
by making comparisons between their predictions, on the one side, and experimental and field
velocity data, on the other side. The models considered are: the Divided Channel Method
(DCM), the Lateral Distribution Method (LDM) and a 2D Horizontal hydrodynamic finiteelement model (RMA2).
Tominaga and Knight (2004) carried out numerical simulation for better understanding of
secondary flow effect on the lateral momentum transfer by linking a standard k- model with a
given secondary flow. The typical linear distribution of momentum transfer term was being
reproduced due to the simulation. The simulated secondary flow was responsible for decrease of
bed shear in main channel and increase of bad shear in flood plain shear.
Jin et. al. (2004) developed a semi analytical model to predict boundary shear distribution in
straight open channels. A simplified stream wise vorticity equation was being used for
developing the model, where the secondary Reynolds stress terms were involved. By applying
the momentum transfer model, the model incorporated the shear stresses. For computing the
effect of the channel boundary on shear stresses an empirical model was generated. To calculate
boundary shear distribution trapezoidal open channels the final equation was used the model
predictions were giving good agreement with experimental data.
Prooijen et. al. (2005) presented the effect of momentum transfer on prediction of discharge.
This process results in the so-called “kinematic effect,” a lowering of the total discharge capacity
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Literature Review
of a compound channel compared to the case where the channel and the floodplain are
considered separately. The mechanisms responsible for the momentum exchange are considered.
The transverse shear stress in the mixing region is modeled using a newly developed effective
eddy viscosity concept, that contains: (1)the effects of horizontal coherent structures moving on
an uneven bottom, taking compression and stretching of the vortices into account and (2) the
effects of the three-dimensional bottom turbulence. The model gives a good prediction of the
transverse profiles of the stream wise velocity and the transverse shear stress of the flood channel
facility experiments.
Guo and Julien (2005) proposed an analytical solution for finding out the values of bed shear
stress in an open channel for constant eddy viscosity without secondary currents. After solving
the continuity and momentum equations the average bed and sidewall shear stresses can be
determined in smooth rectangular open-channel flows. When the width–depth ratio became
large, it slightly overestimated the average bed shear stress measurements and underestimated
the average sidewall shear stress by 17% when it was compared with experimental data set.
Therefore they generated a new formula after introducing two empirical correction factors. The
second formula gave good agreement with experimental measurements over a wide range of
width–depth ratios, with an average relative error less than 6%.
Othman and Valentine (2006) studied the uniform flow in compound channels in terms of a
numerical model, called the NKE model. The model uses the three dimensional Navier-Stokes
equations in conjunction with the non-linear k-ε turbulence model. The latter is used for the
calculation of the Reynolds stress components responsible for the generation of the secondary
currents. This model is based on the SIMPLE technique, and computes the six parameters U, V,
W, P, k, and ε using wall functions on a Cartesian grid. The NKE model was used to simulate the
compound open channel flows of the UK Flood Channel Facility run 080301 (Shiono and
Knight, 1989). The Reynolds Stress Model (RSM) of FLUENT was also used as a comparison.
The results obtained have shown that the NKE and RSM models can reasonably predict the
primary mean velocity and secondary currents.
Proust et. al. (2006) had done the experimental investigation on the flow in an asymmetrically
compound channel transition reach with an abrupt floodplain contraction (mean angle 22°). To
know whether the models developed for straight and slightly converging channels are equally
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Literature Review
valid to their geometry they compared three 1D models and one 2D simulation to their
experimental data. It was shown that the due to lateral mass transfer, error on the level of water is
moderated, but it results in increase the error of discharge distribution in the sub-areas. They
recommended for further work for better understanding of the phenomena of severe mass
transfers in non-prismatic compound channels.
Knight et. al. (2007) offers a new approach to calculating the lateral distributions of depthaveraged velocity and boundary shear stress for flows in straight prismatic channels. It accounts
for bed shear, lateral shear, and secondary flow effects via 3 co-efficient (f ,λ and Г )thus
incorporating some key 3D flow feature into a lateral distribution model for stream wise motion.
The SKM incorporates the effects of secondary flows by specifying an appropriate value for the
_ parameter depending on the sense of direction of the secondary flows, commensurate with the
derivative of the term H(UV)d.
Huthoff et. al. (2008) proposed a new method to calculate flow in compound channels. The
interacting divided channel method (IDCM), based on a new parametrization of the interface
stress between adjacent flow compartments, at the junction of the main channel and floodplain of
a two-stage channel. This expression is motivated by scaling arguments and allows for a simple
analytical solution of the average flow velocities in different compartments. Good agreement is
found between the analytical model results and previously published experimental data.
Khatua (2008) reported a study on flow of energy where it is stated that distribution of energy
an important aspect needs attention adequately. From the variation of the resistance factors
Manning’s n, Chezy’s C, and Darcy –Weisbach’s f it is come to know that the energy
distribution is responsible for these variations. Channel resistance coefficients and the Stagedischarge relationship ranging from in-bank to the over-bank flow were found out. It is stated
that due to interaction mechanism as well as with sinuosity flow distribution becomes more
complicated.
Mamak (2008) carried out a comparison study on different conveyance method for compound
channels. Here he has investigated on three 1D models named as COHM (Acker), EDM and
SKM for computing the discharge capacity of the compound channel. These methods are being
validated by using the previously published experimental data. It is shown that EDM is giving
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Literature Review
more accurate result than other 1D models considered here even it is giving less error than 2D
SKM model for the data analyzed here.
Khatua (2008) presented equations to predict the section discharge carried by straight channels.
The laboratory test results related to the boundary shear stress, shear force, and discharge
characteristics of compound straight river sections composed of a rectangular main channel and
floodplains are presented. Dimensionless parameters are used to form equations representing the
total shear force percentage carried by floodplains. He proposed a curved interface for
understanding the important flow interaction for which apparent shear force is calculated as zero.
The equations give good agreement with the experimental discharge data. Using the proposed
area method, the error between the measured and calculated discharges for the meandering
compound sections is found to be the minimum when compared with that using other interfaces.
Seckin et. al. (2008) reviewed and applied two-dimensional (2-D) formulae for estimating
discharge capacity of straight compound channels for overbank flows in straight fixed and
mobile bed compound channels. The 2D formulae were generally influenced by bed shear,
lateral shear and secondary flow via three coefficients f, λ and
so by using these variables
discharge prediction was done. But then they ignored the secondary current in the new developed
2D formula. Results of both formulae were compared with the experimental result and they
found 2-D formulae almost give practically the same results for the same data when the
secondary flow term is ignored.
Tang & Knight (2009) propose a method for predicting the depth-averaged velocity in
compound channels with partially vegetated floodplains, based on an analytical solution to the
depth-integrated Reynolds-Averaged Navier-Stokes equation with a term included to account for
the effects of vegetation. The vegetation is modelled via an additional term in the momentum
equation to account for the additional drag force. The method includes the effects of bed friction,
drag force, lateral turbulence and secondary flows, via four coefficients f, CD, λ & Γ
respectively.
Khatua (2009) conducted experiments to measure the boundary shear around the wetted
perimeter of a two-stage compound channel and to quantify the momentum transfer in terms of
apparent shear stress along the assumed interfaces originating at the junction of main channel
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and flood plain of the compound channel, which is helpful for deciding the appropriate interface
plains for prediction of accurate stage-discharge relationship for a compound channel of all
geometry.
Zahiri and Dehghani (2009) estimated flow discharge in compound channels by taking nearly
400 laboratory and field data sets of geometry and flow rating curves from 30 different straight
compound sections and also by using
artificial neural networks (ANNs). For predicting
discharge through ANN he used 13 dimensionless input parameters such as relative depth,
relative roughness, relative width, aspect ratio, bed slope, main channel side slopes, flood plains
side slopes and berm inclination and flow discharge as one output variable. The ANN results
were compared with the results of traditional method (DCM) and it was found that ANN results
shows more accurate value than that of DCM.
Tang, Sterling & Knight (2010) presents a method for predicting the depth-averaged velocity
distribution in compound channels with either emergent or submerged vegetation. A general
analytical solution to the depth integrated Reynolds-Averaged Navier-Stokes (RANS) equation
has been given.. the effects of bed friction, drag force, lateral turbulence and secondary flows,
via four coefficients f, CD, λ & Γ respectively are included in this method. The analytical
solution gives better predictions of lateral velocity distribution when compared with the
experimental data of vegetated channels with submerged vegetation and with the experimental
data of emergent vegetation. By predicting the depth averaged velocity and bed shear stress
distributions, flood conveyance and sediment transport in channels with vegetation can be
calculated.
Knight, Tang and Sterling (2010) proposed a model which is based on the Shiono & Knight
method (SKM) of analysis that takes into account certain 3-D flow features that are often present
in many types of watercourse during either in-bank or overbank flow conditions. He
demonstrates the use of this model to predict lateral distributions of depth-averaged velocity and
boundary shear stress, stage-discharge relationships, as well as indicating how to deal with some
vegetation, sediment and ecological issues. Here they suggested the use of the software named as
conveyance estimation system which is largely based on the SKM, through a number of case
studies.
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Beaman (2010) undertook numerical modeling for both inbank and overbank flows regarding
the channels under various depth and width ratio values. The values of three calibration constants
f, λ & Г of SKM (1988) model were derived through large eddy simulation technique for
application in the numerical model named as Conveyance Estimation System (CES). This model
has been employed by the Environment Agency (EA) for England and Wales for estimation of
river conveyance across Europe.
Absi (2011) presented an ordinary differential equation for velocity distribution in open channel
flows based on an analytical solution of the Reynolds-Averaged Navier-Stokes equations and a
log-wake modified distribution of eddy viscosity. The proposed equation helps in predicting the
maximum velocity below the free surface. Here he presented two different degrees of
approximations one is semi-analytical solution of the proposed ordinary differential equation, i.e.
the full dip-modified-log-wake law and second one is simple dip-modified-log-wake law.
Numerical solution of the ordinary differential equation and velocity profiles of the two laws are
compared with the previously published experimental data. In this study it is shown that the dip
correction is not sufficient for an accurate prediction as it requires larger value of the dip
correction parameter. The simple dip-modified-log-wake law shows reasonable agreement and
seems to be an interesting tool of intermediate accuracy. The full dip-modified-log-wake law,
with a parameter for dip-correction obtained from an estimation of dip positions, provides
accurate velocity profiles.
Khatua and Patra (2012) carried out a series of laboratory tests for both smooth and rigid
compound channels and a mathematical equation was developed using dimension analysis for
evaluating the roughness coefficients. Velocity, hydraulic radius, viscosity, gravitational
acceleration, bed slope, sinuosity, and aspect ratio were considered as the important variables
which were affecting the stage-discharge relationship in a compound channel.
Khatua et. al. (2012) gave a modified expression to predict the boundary shear distribution in
compound channels and it is found to provide significant improved results. The practical method
to predict the stage-discharge relationship uses the one-dimensional (1D) approach by taking due
care of the momentum transfer. The proposed approach is tested for its validity using available
experimental data. Error statistics including standard error and coefficient of determination (R2)
are applied to ascertain the effectiveness of the model.
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Fernandes, Leal and Cardoso (2012) stated that the momentum transfer generates a complex
3D flow due to velocity difference between the main channel and the flood plain flows at
extreme flood condition which makes the discharge prediction difficult. They took comparison
study on prediction of discharge by using several models and their accuracy was measured.
They took four different flow conditions corresponding to uniform flows for relative depths of
0.15 and 0.3 for smooth and rough floodplains. The effect of relative depth and roughness of the
flood plain evaluated and the flow characteristics were shown. Their study included the
longitudinal velocity distribution in lateral direction and Reynolds stresses in horizontal plane.
Yang et al (2014) proposed a new method for the discharge distribution and estimating the
stage-discharge relationship in a compound channels by considering the flow interaction between
the upper and lower main channel and that between the upper main channel and its adjoining
floodplain data from the laboratory channels and three natural rivers were being tested and it was
shown that the proposed method made a good agreement with the experimental as well as with
the field data. The computed results showed that apart from predicting discharge distribution of
flood plain and the whole main channel the presented method was well capable of predicting the
discharge distributions in the inbank flow condition.
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Methodology Part-I
EXPERIMENTAL SETUP AND PROCEDURE
3.1.1. Introduction
Generally, experimentation on open channel models is bit difficult in a laboratory in
practical point of view if the scaling of the prototype is properly done and for this case only a
model should be designed according to the prototype so that the hydraulic characteristics can be
studied in a laboratory and the different improvement techniques can be implemented. Discharge
means rate of flow per unit duration of time and measurement of discharge in a channel is the
most important work in river engineering study. Prediction of discharge is required to establish
the stage discharge relationship which is helpful for river engineers who are working on
sediment transport, bank protection, erosion of bed and flood forecasting. To predict the
discharge there are various methods being developed by the researchers from last decades. But
all the methods do not give satisfactory results. Some of the methods overestimate the discharge
and some of them underestimate it, but still with the development of technology there are new
standard methods are being developed with give better result and apart from discharge estimation
these methods are truly useful for velocity measurement and boundary shear stress calculation
for that channel for a given flow condition. To predict Stage-Discharge relationships in straight
channel is easier but till date no hydraulic model is good enough which can give accurate
discharge value. So in our present work a comparison study is being done where discharge being
calculated using different numerical as well as computational methods and the obtained results
are compared with the experimental results by conducting experiment on a straight rectangular
prismatic channel in hydraulic engineering laboratory, NIT Rourkela. So for comparison study a
straight open channel model has been constructed and flow conditions are studied by varying the
flow depth. According the requirement the construction of the channel is done as follows.
3.1.2. Design and construction of channel
For carrying out study in straight channels, experimental setup was built in Fluid
mechanics and Hydraulics Laboratory of NIT, Rourkela. Experiments was conducted in
prismatic compound channels made of concrete having dimension as 15m×.95m×0.55m (Bandita
Channel).The width ratio of the channel is α>1.8 and the aspect ratio is δ>5. The channel is made
up of cement concrete. The main channel was rectangular in shape having bottom width 0.5m,
25 | P a g e
Methodology Part-I
depth 0.1m with a vertical side slope, and the flood plains were having bottom width 0.2m and
also having vertical side walls (Fig shows the overall view of the channel.) Fig.3.1 shows the
schematic diagram of experimental setup and fig 3.2 and fig 3.3 represent the dimensions of
channel with test section respectively). By the help of centrifugal pump (15Hp) the water is
supplied to the flume from an underground sump via an overhead tank. This water is re
circulated through the downstream volumetric tank fitted with closure valves for calibration
purpose. Water entered the channel through bell mouth section via an upstream rectangular notch
specifically built to measure discharge in such a wide laboratory channel. At the downstream end
an adjustable tail gate was provided to control the flow depth and maintain a uniform flow in the
channel. . A movable bridge was provided across the flume for both span wise and stream wise
movements over the channel area so that each location on the plan of compound channel could
be accessed for taking measurements. The broad parameters of this channel are aspect ratio of
main channel (δ), width ratio (α). In all the experimental channels, the flow has been maintained
uniform i.e. the water surface is parallel to bed of channel.
Fig.3.1.1 Schematic diagram of Experimental compound channels with setup
Fig.3.1.2 Longitudinal dimension of the compound channel
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Methodology Part-I
Fig.3.1.3. Top view and Cross sectional dimensions of the compound channel.
3.1.3. Apparatus & equipment used
For this study measuring devices such as a pointer gauge having least count of 0.1 mm,
rectangular notch, one pitot tubes having 4.6 mm external diameter and one manometer were
used in the experiments. These measuring devices are used to measure longitudinal velocity in
the direction of flow within the channels. In the experiments structures like baffle walls,
travelling bridge, sump, tail gate, volumetric tank, overhead tank arrangement, water supply
devices, two parallel pumps etc. are used. The proper arrangement of the measuring equipment
and the devices were done to carry out experiments in the channels.
(i) Overhead tank
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(ii) Baffle wall at the
Inlet of the channel
Methodology Part-I
(iii) Point gauge and Pitot
tube measuring velocity
(iv) Series of manometer
used for measuring pressure
Fig.3.1.4 (i to iv): Apparatus used in experimentation in the rectangular compound channel
3.1.4. Experimental procedure
All the observations are recorded at section 1 of the compound channel. Point velocities
were measured along verticals spread across the main channel as well as flood plain so as to
cover the width of entire cross section. Also at a number of horizontal layers in each vertical for
both main channel as well as flood plain, point velocities were measured. Measurements were
thus taken from left edge point to the right edge of the main channel as well as for the flood plain
bed and side vertical walls. The lateral spacing of grid points over which measurements were
taken was kept 5cm inside the main channel and also Pitot tube is moved from the bottom of the
channel to upwards by 0.2H, 0.4H, 0.6H, 0.8H (H=total depth of flow of water)(Fig.3.5 shows
the grid diagram used for experiments). Velocity measurements are taken by Pitot static tube
(outside diameter 4.77mm) and two piezometers fitted inside a transparent fiber block fixed to a
wooden board and hung vertically at the edge of flume. The ends of which were open to
atmosphere at one end and the other end connected to total pressure hole and static hole of Pitot
tube by long transparent PVC tubes. Before taking the readings the Pitot tube along with the long
tubes measuring about 5m were to be properly immersed in water and caution was exercised for
complete expulsion of any air bubble present inside the Pitot tube or the PVC tube. Even the
presence of a small air bubble inside the static limb or total pressure limb could give erroneous
28 | P a g e
Methodology Part-I
readings in piezometers used for recording the pressure. Steady uniform discharge was
maintained in each run of the experiment and the differences in pressure were measured at each
allocated points.
Fig.3.1.5: Typical grid showing the arrangement of velocity measurement points along horizontal and
in vertical direction at the test section for the rectangular compound channel.
3.1.5. Experimental channels
The main channel is constructed of 500 mm wide at bottom, having a full bank level of
100 mm with a vertical wall. Two symmetrical flood plains are constructed of 200mm width
with side vertical walls along both side of the main channel. Channel has the width ratio of 1.8,
and having aspect ratio of 5. For better information the details of geometrical parameters for the
experimental channels are tabulated below (Table 3.1) and also fig.3.6 shows details overview of
compound channels.
Fig 3.1.6: Compound channel inside the concrete flume with measuring equipment.
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Table 3.1.1: Details of Geometrical parameters of the experimental runs
Sl
No
Item description
Present Experimental Channels
1
Channel Type
Straight compound channel
2
Flume size
15m×.95m×0.55m
3
Geometry of Main channel section
Rectangular with vertical side wall
4
Geometry of Flood plain section
Rectangular with vertical side wall
5
Main channel width (b)
0.5m
6
Flood plain width
0.2m
7
Top width of the channel along with the
flood plain (B)
0.9m
8
Bed Slope of the channel
0.001
8
Bank full depth of channel (h)
0.1m
3.1.6. Measurement of bed slope
There are several methods exists for the measuring the bed slope of the flume, which are
used depending upon the practical conditions and interest of the researcher. In the present work
the bed slope is measured by the help of water level piezometric tube. So at first with reference
to the bed of the channel the water level in piezometric tube was maintained at the upstream side
as well as in the downstream side of the compound channel at a distance of 15m. Piezometric
tube was properly leveled at both the sides. Vertical distance between the water level and the
bottom of the bed excluding the thickness of the Perspex sheet is measured at both upstream as
well as in the downstream referred points. The channel bed slope was calculated by simply
dividing difference between the leveled heights measured at the two ends with the distance
between the two referred points of the given channel (15m). For getting better and accurate result
this procedure was repeated for three times and then by averaging slope of the channel was found
to be 0.001.
30 | P a g e
Methodology Part-I
3.1.7. Measurement of depth of flow and discharge
Pointer gauge is being used above the bed of the channel for the measurement of depth of
flow for all the series of experiments. A vernier caliper is fitted with the point gauge with least
count of 0.1 mm and the total measuring device is fitted with the movable bridge and it was
operated manually. For measuring the discharge in the channel, the construction of rectangular
notch is provided at the upstream side. At the downstream side of channel a volumetric tank was
constructed to receive the incoming water flowing through the channels. For each run the
discharge ‘Qactual’ is calculated as the equation given below.
√
⁄
(3.1.1)
Where, Qactual is the actual discharge, Cd is known as coefficient of discharge obtained from
notch calibration, L is the length of the notch, Hn is the height of water flowing above the notch
and g is acceleration due to gravity.
3.1.8. Measurement of longitudinal velocity
Generally energy loss occurs in the open channel when water flows from one point to
another point. The total energy depends upon kinetic energy, potential energy and pressure
energy. Among all kinetic energy affects the total energy more especially in case of open channel
flow condition. Kinetic energy is the ratio of square of the velocity to twice of acceleration due
to gravity. So it is required to find out the mean velocity of the fluid flowing in the channel. In
the present study, by the help of Pitot tube and manometer, total pressure head as well as static
pressure head readings were taken and their differences were calculated. From these observed
data corresponding velocities at each point within the channel were calculated. Normally Pitot
tube was placed with in the channel in the direction of flow and then allowed to move along a
plane parallel to the bed to get the longitudinal velocity with respect to bed along lateral
direction. At required interval pitot tube was placed and kept it their until the head difference
obtained in manometer remained constant. To measure the magnitude of point velocity vector a
simple formula was being used i.e. v=2gh, where g is the acceleration due to gravity. Here the
tube coefficient is taken as unit and the error due to turbulence considered was being neglected at
the time of measuring velocity. Velocities were being calculated in main channel as well as in
flood plains at the given grid points at an interval of 0.05m in horizontal direction. Apart from
this velocities were measured in the vertical direction at an interval of 0.2H, 0.4H, 0.6H, 0.8H for
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Methodology Part-I
main channel and 0.2(H-h), 0.4(H-h), 0.6(H-h), 0.8(H-h) for flood plain depending upon the
depth of flow in the compound channel. Each experimental runs of the channel are conducted by
maintaining the water surface slope parallel to the bed slope of the channel to achieve the steady
and uniform flow conditions.
3.1.9. Measurement of boundary shear stress
Shear stress is the stress develops between the two layers of water at flowing condition.
Boundary shear stress is the stress that is developed between the water flowing in the channel
and its bed as well as wall of the channel. Generally it is denoted by the symbol τ. Boundary
shear develops due to resistance offered by the channel upon the fluid flowing through the
channel. Due to this shears stress there is a reduction in velocity occurs. So it’s a parameter
which is required to find out. So for finding out the boundary shear stress there are few formula
existing. Patel’s formula (1965) is most common formula which is being used for finding out the
boundary shear stress. There are three equations are proposed by patel’s to find out the shear
stress depending upon the range of the Reynolds number.
(3.1.2)
When y*<1.5, uτd/2ν < 5.6
(3.1.3)
When 1.5< y*<3.5, 5.6 < uτd/2ν < 55
(3.1.4)
When 3.5< y*<5.3, 55 < uτd/2ν < 800
Where
and
Here τw is the wall shear stress, d is the diameter of the pitot tube, ρ is the density of water, ν is
the kinematic viscosity of water at standard temperature which is equal to 0.801x10-6, ∆p is the
pressure difference between the total pressure and the static pressure at the wall which is
measured by the pitot tube. So by using pitot tube boundary shear stress can be calculated along
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Methodology Part-I
the cross section as well as wall of the channel at different point if the pressure difference of that
point is known.
Apart from this the shear stress at each point of the channel can also be calculated by using depth
averaged velocity or mean velocity of the channel if the co-efficient friction of the fluid is
known. The equation for finding shear stress is given below.
(3.1.6)
Where
ud and f are mean velocity and co-efficient of friction of the channel respectively.
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Methodology Part-II
DESCRIPTION OF DISCHARGE PREDICTION APPROACHES
3.2.1. Introduction
During floods, part of the river discharge is carried by the main channel and the rest is
carried by the adjacent flood plains. Once water in the river overtops the banks, the cross
sectional geometry of flow goes on changing. The channel section becomes compound and the
flow structure for such section is affected by large shear layers generated by the difference in
velocities of water in the main channel and the floodplain due to the transfer of momentum
between them. In a compound channel formation of vortices at the junction of main channel and
flood plain was first shown by Sellin [1964] and Zheleznvakov [1965]. Wormleaton et. al.
(1982) have stated that the total draging force on the main channel flow due to floodplain flow at
the interfaces is equal to the accelerating force on the flood plain flow due to the main channel
flow due to which transfer of momentum occurs. At lower depths of flow over the floodplain,
momentum transfer takes place from the main channel to the floodplain resulting in decrement of
the main channel velocity and discharge, while its floodplain components are being increased
and at higher depths of flow over the floodplains the process of momentum transfer is reversed,
i.e. the momentum is supplied to the main channel from the floodplain and this momentum
transfer makes the discharge prediction difficult. The effect of flow interaction between the
floodplain and main channel for various depths of flow over floodplain should adequately take
care while calculating discharge in the compound channel. There are various traditional methods
through which discharge can be predicted. Patra (1999), and Patra and Kar (2000) proposed a
variable interface plane of separation of compound channel
which nullify the momentum
transfer for a better estimate of discharge in straight compound river sections. Ackers (1992)
proposed a method by making some correction to the DCM named as coherence method
(COHM). Huthoff et. al. (2008) parameterized the interface stress in terms of velocity of the
main channel and floodplains. Later Khatua et.al (2012) quantified momentum transfer in terms
of interface length which makes discharge prediction more accurate. Apart from these one
dimensional mathematical models, there is some 1D software such as HEC-RAS, ANN, MIKE
11, and CES which also do better discharge prediction in a compound channel.
34 | P a g e
Methodology Part-II
The traditional discharge prediction models such as SCM, DCM fail to give accurate
discharge as they don’t consider the effect of momentum transfer. Therefore some new models
are developed which does discharge prediction more accurately by considering the effect of
momentum transfer. This chapter includes discharge computation by numerical models such as
SCM, DCM, IDCM, MDCM, SKM as well as computational methods such as CES and ANN.
3.2.2. Numerical methods for computation of discharge
3.2.2.1. Single Channel Method:It treats the channel cross-section as a whole channel without division to subsections.
This method usually fails to give a good estimate of the stage-discharge relationship, as it over
estimates the discharge.
⁄
(3.2.1)
Where Q= discharge
R=Hydraulic Radius
So=Bed slope of the channel
3.2.2.2. Divide Channel Method:This classical method employs division of the compound channel to two subsections i.e.
the main channel (bank full) and floodplains (berms).The conveyance is calculated for each sub
sections considering the interfaces. Again, this method is modified into a few versions
distinguishing each other by the way how they consider verticals dividing the compound channel
into sub-sections. This includes horizontal interface, vertical interface, diagonal interface, curved
interface, variable interface (Fig. 3.2.1). However vertical interface and diagonal interface are
the two methods which are commonly used. Discharge for each sub-section can be calculated by
using the Eq.(3.2.1) given below.
[
]
(3.2.2)
Where Q = Discharge through the compound channel,
floodplain respectively,
= Bed slope of the channel,
plain respectively.
35 | P a g e
= Area of the main channel and
= perimeter of the main channel and floodplain respectively,
= manning’s co-efficient for main channel and flood
Methodology Part-II
Fig.3.2.1: The vertical, horizontal, diagonal interface of a prismatic compound channel.
3.2.2.2.1.
Vertical interface method
In this method the flood banks are separated from the main channel by means of vertical
interface (Fig. 3.2.1), but the interface length is not included in the calculation of wetted
perimeter of either of the over bank flow or main channel flow as this interface is considered as a
surface of zero shear stress and no momentum transfer takes place through junction of main
channel and flood plain.
3.2.2.2.2.
Diagonal Interface method
In this method a diagonal interface is considered from the top of the main channel bank to the
centerline of the water surface. This interface is considered to be the surface of zero shear stress
and due to that the length is not included in the calculation of wetted perimeter of the over bank
flow and main channel flow. The problem with both the methods is, they overestimate the
discharge to some extent.
3.2.2.3.
Interacting Divide Channel Method
This method developed by Fredrik Huthoff in the year 2007. Here the channel is divided
in to two parts by vertical interfaces and the effect of momentum transfer occurring at the
junction of main channel and flood plain is considered in terms of interface stress (τint).
36 | P a g e
Methodology Part-II
Fig.3.2.2: Cross section of a two-stage channel: (a) symmetric with two identical floodplains. (b)
Asymmetric with one side floodplain. (Hutoff 2007)
The following equations have been developed to find out the velocity of the main channel as well
as flood plain given as
(
(3.2.3)
)
(
)
(
Where
(3.2.4)
)
(
)
(
)
(3.2.5)
are the velocities of main channel and the flood-plain respectively assumed
steady and longitudinally uniform, = co-efficient of interface.
= number of flood plains.
= velocities of the main channel and flood plain when
= interface
stress developed at the interface of the main channel and flood plain. The value of co-efficient of
interface
(3.2.6)
(3.2.7)
(3.2.8)
37 | P a g e
Methodology Part-II
Where
are co-efficient of friction.
flood plain respectively.
respectively.
are the perimeter of the main channel and
are the area for main channel and flood plain
are the hydraulic radius of main channel and flood plain respectively.
=difference between the water depth and the full bank level (Fig.3.2.2).
After finding out the velocities, discharge (Q) of the total section can be predicted through inter
acting divided channel method by using equation (3.2.9).
(3.2.9)
“The interface stress parameterization yields a set of model equations that is linear in the squared
velocities, leading to an analytical solution” is a practical property of IDCM. When generalizing
IDCM to compound channels with several numbers of compartments, this property is retained.
This generalization is required as the interface co-efficient γ has either a universal value or an
explicit dependency on the geometry as well as on the roughness of the nearby compartments.
Based on the results from their study, Huthoff et.al has recommend a constant value of γ =0 .020.
3.2.2.4.
Modified Divided Channel Method
This is another method developed by Khatua et. al (2012), which quantified the momentum
transfer in terms of interface length. According to Wormleaton et. al. (1982), the total dragging
force on the main channel flow due to floodplain flow at the interfaces is equal to the
accelerating force on the floodplain flow due to the main channel flow due to which transfer of
momentum occurs which makes the discharge prediction difficult. So for balancing the force,
here the main channel boundary shear to be increased and that of the floodplain decreased
suitably to account for main channel and floodplain flow interaction. Let
length for inclusion in the main channel wetted perimeter and
= the interface
= the length of interface to be
subtracted from the wetted perimeter of the floodplain termed as interaction length. So according
to this method, the value of
(
38 | P a g e
(3.2.10)
]
)[
(
are found out from Equation (3.2.10) and Equation (3.2.11).
)[
]
(3.2.11)
Methodology Part-II
Where α = width ratio = B/b; β = relative depth =
b = width of main channel bottom; B =
total width of compound channel; h = bank full depth; and H = total depth of flow.
percentage of shear force in the flood plains. Knowing
interface lengths
and
=
and the channel geometry, the
are evaluated. Next, the discharges for the main channel and
floodplain are calculated using Manning’s equation and added together to give total discharge as
[
(
) ]
(3.2.12)
Where So = bed slope of both main channel and floodplain (assumed to be the same in 1D
= manning’s co-efficient of main channel and floodplain subsections
models) and
respectively. For rectangular channel and floodplains having homogeneous roughness (i.e.,
Manning’s n value is equal for both the main channel and floodplains).
is calculated from
the equation (3.2.13), developed by Khatua & Patra(2012).
[
]
(3.2.13)
So by putting the value of %Sfp, the value of
and
can be calculated. After finding out
the values of interface length the discharge of the straight compound channel can be estimated.
3.2.2.5.
Shiono knight Method
The SKM is based on a depth averaged form of Navier-Stokes equation, expressed for steady
flow as
[
√
]
[
]
(3.2.14)
Where ρ=density, g=acceleration due to gravity, So= longitudinal slope, H= depth of water
flowing, s= lateral slope, f=co-efficient of friction, Ud=depth averaged velocity in longitudinal
direction, Vd=depth averaged velocity in lateral direction, λ= dimensionless eddy viscosity, y=
lateral direction co-ordinate.
39 | P a g e
Methodology Part-II
Here in the equation the 1st left hand side term is gravitational term for a uniform flow, the
second term is bed shear stress and the third term is the Reynolds’s shear stress and the term
which is present in the right hand side is the secondary current. The given equation is dependent
upon depth averaged velocity, bed shear stress and Reynolds’s stress, but these parameters are
influenced by three calibration co-efficient f, λ, Г, which are related to local bed friction,
Reynolds’s stress and the secondary flow respectively.
Shiono and Knight proposed an analytical solution to find out depth averaged velocity as well as
boundary shear stress by considering the effect of secondary current. From their experimental
results they conclude that the depth averaged velocity varies linearly in y direction therefore they
replaced the right hand side term in the equation by a constant, Г. The derivation (Rezai 2006) is
given below.
[
]
(3.2.15)
√
[
]
(3.2.16)
For a flatbed region or when there is no lateral slope the above equation (3.2.16) can be written
as
√
[
Here
]
(3.2.17)
are assumed to be constant in each channel sub section.
(
(
)
(
))
So we can write the equation (3.2.17) in the following form
[
Let
√
√
]
(3.2.18)
,
So we can rewrite the above equation in terms of A, B, C.
(3.2.19)
40 | P a g e
Methodology Part-II
(Auxiliary equation)
√
√
√
(3.2.20)
[
]
√
( )
Now
√
√
( )
√
Putting the value of
√
(
(3.2.21)
and
√
in equation (3.2.18) we can get
)
(
√
√
)
(3.2.22)
(
)
[
]
Again (B/A) can be simplified
41 | P a g e
Methodology Part-II
(
)
(
( )
( )
√ )
( )( )
( )
( )
( )=
So the general solution for depth averaged velocity for a rectangular channel can be written as
[
Where
]
(3.2.23)
( ) ( ) ( )
(3.2.24)
The cross section of a prismatic compound channel is then divided into number of panels, in
which the three calibration co-efficient f, λ, Г are calculated and then
can be evaluated
within each panel as a function of y.
Fig.3.2.3: Lateral distribution of longitudinal velocity (Bousmar 2002)
42 | P a g e
Methodology Part-II
Boundary condition
1.
, Continuity of depth averaged velocity.
2.
(
)
(
)
3.
The boundary condition for a rigid side wall (No slip condition) may be written as
, Continuity of the lateral gradient of the depth averaged velocity
Fig.3.2.4: The partition of rectangular compound channel by taking the center as origin
Here the compound channel is divided into 3 panels
Applying boundary condition to 1st and 2nd pannel
(3.2.25)
(3.2.26)
(3.2.27)
Likewise boundary condition applied to 1st and 3rd panel
(3.2.28)
(3.2.29)
(3.2.30)
In all the above equations the A1, A2,…..A6 are the six unknowns which can be found out by using
elimination method or by matrix method (Rezai 2006).
Elimination method is quite lengthy as well as complex to get the values of unknowns so here we
are using matrix method for finding out the values of A1, A2, ….. A6.
43 | P a g e
Methodology Part-II
] [
[
]
[
]
From this matrix method the values of unknowns can be found out which will be useful for
finding out the depth averaged velocity, bed shear stress and discharge for that particular depth
can be found out.
3.2.3. Computational method for discharge calculation
3.2.3.1.
Conveyance Estimation System
The Conveyance and Afflux Estimation System (CES/AES) is a software tool which is
used for estimation of flood and drainage water levels in the rivers, watercourses and drainage
channels. This software is being developed by the hydraulic engineers of United Kingdom.
This software helps in estimation of hydraulic roughness, water levels corresponding to channel
conveyance, flow for a given slope, sectional averaged velocity as well as spatial velocities,
backwater profiles of a known flow-head control like weir (steady), afflux at upstream of bridges
and culverts, uncertainties of input and out data etc.
The CES software involves roughness advisor, conveyance generator, uncertainty estimator,
backwater module, afflux estimator etc. The roughness advisor carries the information
regarding the roughness values for a range of natural and man-made roughness types along with
description and photographs related to that roughness. . The roughness values are obtained from
over 700 references (River Habitat Survey) and it also contain aquatic vegetation, crops, grasses,
hedges, trees, substrates, bank protection and irregularities. The Roughness Advisor has also the
information regarding seasonal variations in vegetation roughness, cutting and recommended
regrowth patterns following the cutting. Based on the roughness information and cross section
geometry the conveyance generator estimates the conveyance of the channel. By the help of
lateral distribution method the conveyance is calculated. Here unit flow rate is calculated at 100
points across the channel section and then by integrating the flow rate across the section over all
flow is found out. Water level, flow, rating curves, velocity, area, perimeter, Froude Number,
Reynolds Number etc. are the available outputs with respect to given depth. Spatial distributions
44 | P a g e
Methodology Part-II
of velocity, boundary shear and shear velocity can also be obtained across the section. The
uncertainty estimator gives some measure of the uncertainty associated with each predicted
water level. The upper and lower values of the uncertainty estimator depend upon the upper and
lower roughness values estimated from the roughness advisor. Backwater module consists of a
modest calculation for forming a backwater profile at upstream with known stage and flow
value. This is based on the concept of balancing the energy between the upstream and
downstream and it has an option to include the velocity head term. For gradually varied flow
condition a code is used which is called as afflux generator. This code is helpful in finding out
the afflux at upstream of the bridge and culvert at high flow condition. This code also provides
longitudinal water surface profile.
Apart from these main tools, there is another tool named as afflux advisor which helps in
quick calculation of afflux at simple culvert and bridge in a uniform flow condition. Like afflux
generator, here also calculation is based on laboratory data as well as on field data but the
problem with afflux advisor is it cannot provide longitudinal water surface profile.
The CES software tools help in calculating water levels, flows and velocities for rivers for
given flow condition. It provides upper and lower uncertainty situations regarding the flow. It
helps in measuring the flood at high water levels and requirement of channel reconstruction or
management option. It evaluates the influence of timing and type of cutting of vegetation. It
shows the impact of blockage generated from unwanted vegetation and debris. Now a days it
provides guidance for channel preservation and performance.
Along with all above advantages there are some limitations of this software. It can only
work with steady flow condition. It cannot work for sluice gates, weirs etc. Except within bridge
and culvert it cannot consider super critical flow conditions.
3.2.3.2.
Artificial Neural Network
Artificial neural network (ANN) is a soft computing tool, which is attempting to signify
low-level intelligence in natural organisms. This tool is having a flexible structure, capable of
establishing a non-linear relationship between the input and output data. Here multilayer
perceptron network (MLP) based on back propagation rule were used. The MLP network is also
called as Back Propagation (BP) network. It involves three layers, like wise input layer, hidden
layer and output layer. The data values were received by input nodes and input nodes pass them
45 | P a g e
Methodology Part-II
to the nodes of first hidden layer. Each hidden layer collects the input from all input nodes after
multiplying a weight with each input value, attaches a bias to this sum, and the results were
passed through a nonlinear transformation like the sigmoid transfer function. This helps in
forming the input either for the second hidden layer or it forms an output layer that operates
same to the hidden layer. The subsequent transformed output generated from each output node is
the network output. The network required to be trained by using a training algorithm such as
back propagation, conjugate gradient, cascade correlation etc.
Fig. 3.2.5: Multilayer perceptron neural network
The main motive of training the patterns is to decrease the global error, which can be found out
by using the formula given below.
∑
∑
(
)
Where Tij is the jth element of the target output associated to the ith pattern, Oij is the computed
output of jth neuron linked to the ith pattern, np is the number of patterns and no is the number of
neurons in the layer of output.
Previously Liu and James (2000) predicted discharge in a meandering compound channel using
ANN and they have showed that between predicted and the measured discharge there is up to
15% inconsistency exist. But still now a days ANN has wide applications in prediction of
46 | P a g e
Methodology Part-II
sediment concentration in the rivers, modeling of river flow, modelling of rainfall and runoff. It
helps in simulation of stage discharge relationship in rivers and computation of flow resistance in
smooth channels.
Flow pattern and momentum transfer between the flood plain and main channel in
straight compound channels is governed by geometric and hydraulic variables significantly. Here
the important dimensionless geometric ratios are taken as input parameters for ANN model. For
this analysis four dimensionless parameters and one output variable are chosen.
The input dimensionless variables are area ratio, perimeter ratio, width ratio, slope and
discharge ratio is considered as a output dimensionless parameter.
3.2.3.2.1.
Input parameters
1. The area ratio defines the ratio between area of the compound channel to the area of main
channel at full bank flow condition.
(3.2.31)
2. The perimeter ratio defines the ratio between perimeter of the compound channel to the
perimeter of main channel at full bank flow condition.
(3.2.32)
3. The width ratio defines the ratio between width of the compound channel to the bottom
width of main channel.
(3.2.33)
4. The bed slope (So) of the channel which is already a dimensionless quantity.
3.2.3.2.2.
Output Parameter
The discharge ratio is the only one dimensionless output parameter which is used in this ANN
model. Flow discharge ratio can be expressed as the ratio of the total observed discharge to the
bank full flow discharge.
(3.2.34)
47 | P a g e
Methodology Part-II
3.2.4. Source of data collection:Experimental discharge data have been collected from FCF (Large scale Flood channel
facility created at Wallingford UK) series data(S-1, S-2, S-3, S-8, S-10), Kinght & Demetriou
(1983) (K&D-1, K&D-2, K&D-3), Atbay (2002), Rezai (2006) & NIT Rourkela Hydraulic lab
data with varying width ratio α (B/b).
Table 3.2.1: Geometrical parameters of FCF channel
Series
name
So
Wmc
(m)
Wfp
(m)
Nfp
Smc
Wtotal
(m)
h
(m)
H
(m)
Sfp
0.001027
1.5
4.1
2
1
10
0.15
0.15899
1
0.001027
1.5
4.1
2
1
10
0.15
0.16519
1
0.001027
1.5
4.1
2
1
10
0.15
0.17563
1
FCF 0.001027
Series0.001027
1
1.5
4.1
2
1
10
0.15
0.18656
1
1.5
4.1
2
1
10
0.15
0.19881
1
0.001027
1.5
4.1
2
1
10
0.15
0.21411
1
0.001027
1.5
4.1
2
1
10
0.15
0.21443
1
0.001027
1.5
4.1
2
1
10
0.15
0.25012
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.15649
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.16873
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.1699
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.17784
1
FCF 0.001027
Series0.001027
2
1.5
2.25
2
1
6.3
0.15
0.18676
1
1.5
2.25
2
1
6.3
0.15
0.18695
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.19796
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.21355
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.24855
1
0.001027
1.5
2.25
2
1
6.3
0.15
0.28795
1
48 | P a g e
Methodology Part-II
Series
name
FCF
Series
-3
FCF
Series
-8
FCF
Series
-10
0.001027
Wmc
(m)
1.5
Wfp
(m)
0.75
1
Wtotal
(m)
3.3
h
(m)
0.15
H
(m)
0.158
0.001027
1.5
2
1
3.3
0.15
0.16627
1
0.001027
0.75
2
1
3.3
0.15
0.17712
1
1.5
0.75
2
1
3.3
0.15
0.18779
1
0.001027
1.5
0.75
2
1
3.3
0.15
0.19804
1
0.001027
1.5
0.75
2
1
3.3
0.15
0.21454
1
0.001027
1.5
0.75
2
1
3.3
0.15
0.2477
1
0.001027
1.5
0.75
2
1
3.3
0.15
0.2484
1
0.001027
1.5
0.75
2
1
3.3
0.15
0.29922
1
0.001027
1.5
0.75
2
1
3.3
0.15
0.30014
1
0.001027
1.5
2.25
2
v
6
0.15
0.15796
1
0.001027
1.5
2.25
2
v
6
0.15
0.167
1
0.001027
1.5
2.25
2
v
6
0.15
0.17653
1
0.001027
1.5
2.25
2
v
6
0.15
0.18757
1
0.001027
1.5
2.25
2
v
6
0.15
0.20008
1
0.001027
1.5
2.25
2
v
6
0.15
0.21483
1
0.001027
1.5
2.25
2
v
6
0.15
0.25022
1
0.001027
1.5
2.25
2
v
6
0.15
0.29973
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.15803
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.1666
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.17654
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.18701
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.20033
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.20051
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.21481
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.2493
1
0.001027
1.5
2.25
2
2
6.6
0.15
0.2797
1
So
Nfp
Smc
2
0.75
1.5
0.001027
49 | P a g e
Sfp
1
Methodology Part-II
Table 3.2.2: Geometrical parameters of Knight & Demetriou channel
Series
Name
So
Knight &
Demetrio
u -1
Knight &
Demetrio
u -2
Knight &
Demetrio
u -3
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
0.000966
Wmc
(m)
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
0.152
Wfp
(m)
0.076
0.076
0.076
0.076
0.076
0.076
0.076
0.152
0.152
0.152
0.152
0.152
0.152
0.228
0.228
0.228
0.228
0.228
Nfp
Smc
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Wtotal
(m)
0.304
0.304
0.304
0.304
0.304
0.304
0.304
0.456
0.456
0.456
0.456
0.456
0.456
0.608
0.608
0.608
0.608
0.608
h
(m)
0.076
0.076
0.076
0.076
0.076
0.076
0.076
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
H
(m)
0.0855
0.09453
0.10026
0.11343
0.12583
0.1511
0.08746
0.09608
0.10093
0.11209
0.125
0.14931
0.08501
0.095597
0.102151
0.114286
0.127303
0.153846
Sfp
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Table 3.2.3: Geometrical parameters of Atbay channel
Series
Name
So
Wmc
(m)
Wfp
(m)
Nfp
Smc
Wtotal
(m)
h
(m)
H
(m)
Sfp
Atbay's
Data
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.002024
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
0.407
2
2
2
2
2
2
2
2
2
2
2
2
2
2
v
v
v
v
v
v
v
v
v
v
v
v
v
v
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.805
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.0538
0.0596
0.0641
0.0682
0.0713
0.0686
0.0733
0.0764
0.0788
0.0846
0.0876
0.0923
0.0946
0.0980
v
v
v
v
v
v
v
v
v
v
v
v
v
v
50 | P a g e
Methodology Part-II
Table 3.2.4: Geometrical parameters of Rezai channel
So
Wmc
(m)
Wfp
(m)
Nfp
Smc
Wtotal
(m)
h
(m)
H
(m)
Sfp
0.002003
0.398
0.1
2
v
0.598
0.05
0.0528
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.05556
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.058824
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.0603
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.0625
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.0667
v
Rezai's 0.002003
Data 0.002003
0.398
0.1
2
v
0.598
0.05
0.0718
v
0.398
0.1
2
v
0.598
0.05
0.0762
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.08
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.08333
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.0852
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.0933
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.1015
v
0.002003
0.398
0.1
2
v
0.598
0.05
0.1077
v
Series
Name
Table 3.2.5: Geometrical parameters of NIT Rourkela channel
Series
Name
So
Wmc
(m)
Wfp
(m)
Nfp
Smc
Wtotal
(m)
h
(m)
H
(m)
Sfp
NIT
Rourkela
Data
20132014
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
2
2
2
2
2
2
2
2
2
2
2
v
v
v
v
v
v
v
v
v
v
v
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1111
0.1147
0.117647
0.125
0.128
0.1334
0.137
0.142857
0.15
0.16667
0.2
v
v
v
v
v
v
v
v
v
v
v
All the channels taken here are smooth and symmetrical type. All FCF channels are having main
channel trapezoidal shape but some of their flood plains are rectangular and some of them are
trapezoidal, whereas all others channels are rectangular in shape for both main channel and in the
flood plain.
51 | P a g e
Result and Discussion
RESULTS
4.1
Introduction
In chapter 3 the experimental procedures as well as discharge predicting methods have
been described. Eleven sets of data are presented in that chapter. The geometrical parameters of
those data sets which are influencing the discharge are tabulated in there. In this chapter the
results of experiments conducted in NIT Rourkela will be presented in terms of local velocity
distribution, stage discharge relationship, and boundary shear stress distribution. Apart from this
a comparison study is being done between five different methods and their results are compared
with the experimental results and percentage of error is found out.
4.2. Stage Discharge Results
Stage discharge relationship is one of the most important relationships for a River
Engineer which is required for design and flood management purposes. From the stage-discharge
data, it is possible to capacity of the channel and to predict the discharge. In order to understand
the influence of the momentum transfer on discharge prediction five different methods are used
for predicting the discharge at different flow conditions on eleven numbers of data sets. To
achieve uniform flow the gate was adjusted to get M1 and M2 profiles. The depth related to this
tailgate setting was then considered as the normal depth. This procedure was repeated for every
single experiment in order to obtain accurate stage discharge relationships for the meandering
channels.
In the present work stage discharge relationship is achieved by maintaining steady
uniform flow in the prismatic part of the experimental channel (sec-1) shown in the fig 3.2. in
chapter 3. From the experiment it was found that the discharge is influenced the hydraulic
parameters and the geometrical parameters of the experimental channel. It was tried to maintain
the water surface profile parallel to the valley slope. Discharge is measured for 16 different depth
of flow, out of them 9 numbers are in bank flow depths and rest is over bank flow. Initially the
rate of flow was less but as the depth of flow goes on increasing the rate of flow also increasing
subsequently. The stage discharge curve is given in fig.4.1.
52 | P a g e
Result and Discussion
0.16
0.14
Stage in m
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.01
0.02
0.03
0.04
Discharge in m³/s
0.05
0.06
Fig.4.1: Stage discharge curve for the straight channel at section 1
4.3. Distribution of Longitudinal Velocity Results:In order to find out the local velocities and to determine the discharge, a velocity measuring
device commonly used is the Pitot tube. The Pitot tube is connected to a U-tube manometer by the
help of two pipes. Among these two pipes one gives static pressure and another gives the total
pressure. The static and total pressure values are measured in the U-tube manometer. The difference
between these reading gives the dynamic pressure of the moving fluid. The velocity of any point of
the moving fluid is related to the dynamic pressure of that point. The velocity can be found out by
using the equation 4.1 given below.
√
(4.1)
Where V = the velocity of flow
h = the difference between the total pressure and static pressure or the dynamic pressure.
g = acceleration due to gravity
C = the non-dimensional constant.
53 | P a g e
Result and Discussion
The non-dimensional constant C is dependent upon the degree of imperfection in the Pitot tube,
and on method of using the Pitot tube. The Pitot tube also helps in calculating the discharge in
the channel but for this it is required to have sufficient velocity measurements. Depending upon
the nature of velocity distribution across the channel, the local velocity measurements are taken.
If the flow pattern is complex then more number of velocity measurements is required. The depth
averaged velocity is required to be found out over a small area. Once the depth averaged velocity
with respect to its area is found out, the discharge of the channel can be calculated by numerical
integration.
The pitot tube which is used in the experiment has outside diameter as 4.6mm. The pitot
tube is fixed to a trolley which helps in the movement of the pitot tube in both horizontal and
vertical direction. Adequate care should be taken while taking the reading as there is always a
chance of formation of air bubbles in the tube if it is exposed to air. The longitudinal velocities at
specified points are taken by pitot tube at section 1 of the straight channel, which is prismatic.
Velocity distributions along lateral direction are taken for 4 different depths. The points where
the velocity is measured is shown in the fig 3.5 in chapter three. The velocity distribution of both
main channel and flood plain along lateral direction are shown in fig 4.2.(i)-4.2.(viii), apart from
this the velocity contours are also presented in the fig4.3.(i)-4.3.(iv).
Fig.4.2.(i): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.15
54 | P a g e
Result and Discussion
Fig.4.2.(ii): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.15
Fig.4.2.(iii): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.2
Fig.4.2.(iv): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.2
55 | P a g e
Result and Discussion
Fig.4.2.(v): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.25
Fig.4.2.(vi): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.25
Fig.4.2.(vii): Longitudinal velocity distribution along lateral direction in the main channel for
relative depth of 0.3
56 | P a g e
Result and Discussion
Fig.4.2.(viii): Longitudinal velocity distribution along lateral direction in the Flood plain for
relative depth of 0.3
From this velocity profile it is seen that velocity is increasing as the depth goes on increasing.
Most of the case it is seen that height value occurs at 0.8H depth from the bottom for the main
channel. Likewise for the flood plain height value of the velocity occurs at the top point where
the velocity measurements are taken. Most of the cases the highest value occurs at 0.6(H-h) from
the bottom of the flood plain depending upon the depth of water flowing over the flood plain and
the condition of the pitot tube.
Fig.4.3.(i): Longitudinal velocity Contour for half portion of the section for relative depth of 0.15
57 | P a g e
Result and Discussion
Fig.4.3.(ii): Longitudinal velocity Contour for half portion of the section for relative depth of 0.2
Fig.4.3.(iii): Longitudinal velocity Contour for half portion of the section for relative depth of
0.25
Fig.4.3.(iv): Longitudinal velocity Contour for half portion of the section for relative depth of 0.3
The velocity contours shows that maximum velocity occurs either at the center of the main
channel or just adjacent to it. For lower depth of flow maximum velocity is occurred at the
58 | P a g e
Result and Discussion
center but as the depth of flow goes higher the maximum velocity is occurred just adjacent to the
center position of the channel, this is clearly visible for the relative depth of 0.3.
4.4. Distribution of Longitudinal depth averaged Velocity Results
The depth averaged longitudinal velocity for the section 1 along lateral direction is
measured for 4 different depth of flow and presented in the fig.4.4.(i)-4.4(iv). It is required to
know the average velocity of flow at each specified section of the channel which is helpful in
calculating the discharge.
0.7
0.6
Velocity in m/s
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Width in m
Fig.4.4.(i): Distribution of depth averaged velocity for the relative depth of 0.15
0.7
Velocity in m/s
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Width in m
Fig.4.4.(ii): Distribution of depth averaged velocity for the relative depth of 0.2
59 | P a g e
Result and Discussion
0.7
Velocity in m/s
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Width in m
Fig.4.4.(iii): Distribution of depth averaged velocity for the relative depth of 0.25
0.7
0.6
Velocity in m/s
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
Width in m
Fig.4.4.(iv): Distribution of depth averaged velocity for the relative depth of 0.3
4.5.
Distribution of boundary shear stress Results
Shear stress distribution along the cross section of the channel is required to find out to
know the variation of shear stress along the bed and it is also helpful in finding out the apparent
shear stress in the channel section. In general Patel’s equation is used to find out the shear stress
develop at the bed and wall of the channel. Boundary shear stress at the bed and wall of the main
channel and the flood plain are presented in the fig4.5.(i)-fig.4.5(iv).
60 | P a g e
Result and Discussion
Fig.4.5.(i): Boundary shear stress distribution of section 1 of the straight channel for relative
depth 0.15
Fig.4.5.(ii): Boundary shear stress distribution of section 1 of the straight channel for relative
depth 0.2
61 | P a g e
Result and Discussion
Fig.4.5.(iii): Boundary shear stress distribution of section 1 of the straight channel for relative
depth 0.25
Fig.4.5.(iv): Boundary shear stress distribution of section 1 of the straight channel for relative
depth 0.3
62 | P a g e
Result and Discussion
4.6. Comparison of experimental results with SKM
Shiono Knight Method is one of the methods which include three important parameters
while calculating the discharge. The three important parameters are frictional resistance, eddy
viscosity and lastly secondary current. This method uses RANS equation for predicting
discharge. The analytical solution is already described in the chapter 3. A MATLAB code being
written for calculating the depth averaged velocity and boundary shear stress through SKM, but
the limitation with this code is, it is valid for rectangular compound channel only. So here we
need to compare the experimental result with the results obtained from SKM.
The results of depth averaged velocity of both experimental as well as SKM are presented in the
fig 4.6.(i)-4.6.(iv). Experimental results as well as results of SKM for boundary shear
distributions are shown in the fig.4.7(i)-4.7(iv). The discharge results for both experimental and
SKM are tabulated in the table 4.1 and the percentage of error between the actual discharge and
the discharge obtained from SKM are calculated there.
4.6.1. Comparison of Depth averaged velocity with SKM
0.7
SKM
0.6
Experimental Result
Velocity in m/s
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Width in m
Fig.4.6.(i): Distribution of depth averaged velocity for the relative depth of 0.15
63 | P a g e
Result and Discussion
SKM
Experimental Result
0.7
Velocity in m/s
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Width in m
Fig.4.6.(ii): Distribution of depth averaged velocity for the relative depth of 0.2
SKM
Experimental Result
0.7
Velocity in m/s
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
Width in m
0.6
0.7
0.8
0.9
Velocity in m/s
Fig.4.6.(iii): Distribution of depth averaged velocity for the relative depth of 0.25
0.7
SKM
0.6
Experimental Result
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
Width in m
0.6
0.7
0.8
0.9
Fig.4.6.(iv) Distribution of depth averaged velocity for the relative depth of 0.3
64 | P a g e
Result and Discussion
4.6.2. Comparison of Boundary Shear Stress with SKM
1
0.9
0.8
Stress in N/m²
0.7
0.6
0.5
0.4
SKM
0.3
Experimental Result
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Width in m
Fig.4.7.(i): Boundary shear distribution of section 1 of the straight channel for relative depth 0.15
1
0.9
0.8
stress in N/m²
0.7
0.6
0.5
0.4
SKM
0.3
Experimental Result
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Width in m
Fig.4.7.(ii): Boundary shear distribution of section 1 of the straight channel for relative depth 0.2
65 | P a g e
Result and Discussion
1.2
Stress in N/m²
1
0.8
0.6
SKM
Experimental Result
0.4
0.2
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Width in m
Fig.4.7.(iii): Boundary shear distribution of section 1 of the straight channel for relative depth
0.25
1.2
Stress in N/m²
1
0.8
0.6
SKM
Experimental Result
0.4
0.2
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Width in m
Fig.4.7.(iv): Boundary shear distribution of section 1 of the straight channel for relative depth 0.3
66 | P a g e
Result and Discussion
4.6.3. Comparison of Discharge with SKM
Table 4.1: Percentage of error in discharge through SKM
Depth of flow
α
β
(m)
Observed
discharge
% of error
(m³/s)
Discharge
obtained from
SKM (m³/s)
0.119
1.8
0.15
0.037594
0.03516
-6.47426
0.127
1.8
0.20
0.039444
0.040672
3.113372
0.138
1.8
0.25
0.04618
0.04708
1.950242
0.149
1.8
0.30
0.052165
0.052774
1.167085
Here the percentage of error in discharge is found out and the graph (Fig 4.8) is plotted between
percentage of error and the relative depths of the channel.
3
% of error in discharge
2
1
0
-1
-2
-3
-4
-5
-6
-7
0.15
0.2
0.25
0.3
Relative depth
Fig.4.8: Error in discharge through SKM
From the error analysis the average percentage of error is found to be 3%.
67 | P a g e
0.35
Result and Discussion
4.7
Comparison of discharge prediction approaches
In the early years discharge prediction was done by single channel method. In this
method, it considers the channel section as a single channel and discharge is predicted by using
manning’s formula. This method gives good result for simples channels but when it is used for
compound channel it over estimated the discharge for which it could not be in river flow
analysis. After this Divided Channel method was developed where it divided the channel in both
horizontal and vertical interfaces and depending upon the division the discharge was estimated.
Though it gives better discharge prediction than Single channel method but it over estimated the
discharge for the main channel and under estimated the discharge for the flood plain. This was
happened both the method did not quantify the momentum transfer. So many researchers worked
on this, they developed some new models where they quantified the momentum transfer.
Modified divided channel method, Interacting Divided channel method are two hydraulic model
where the momentum exchange is quantified by interface length and shear stress respectively,
due to which these models are able to predict the discharge in a better manner than divided
channel method and single channel method. But Interacting divided channel method is limited to
straight channels. Apart from these numerical methods some software are being developed which
also do discharge prediction. Conveyance estimation system software developed by hydraulic
engineers of United Kingdom which gives output in terms of discharge, water level, water
surface profile, boundary shear stress, depth average d velocity, spatial velocity etc. Artificial
neural network is the mathematical tool which can also be used to predict the discharge by using
multilayer programming or back propagation technique. This method is reliable if the number of
hidden layers is more so that number of iteration will be more.
Therefore we consider divided channel method, modified divided channel method,
interacting divided channel method, CES and ANN for a comparison study on prediction of
discharge. So here eleven sets of data of varying cross sections are being presented in the table
4.2.(i)-4.2(xi) where actual discharge and predicted discharge obtained through all these methods
are tabulated. The percentage of error calculation is done for each of the method so that we can
know that which methods are good in predicting discharge and which method is giving best
discharge prediction result among these numerical as well as computational methods.
68 | P a g e
Result and Discussion
Table 4.2(i)
Series
Name
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.2082
0.213
2.405
0.233
11.688
0.237
13.807
0.252
20.897
0.187
-9.998
0.2337
0.240
2.622
0.258
10.408
0.265
13.431
0.282
20.859
0.233
-0.353
0.2852
0.298
4.566
0.316
10.726
0.327
14.662
0.347
21.799
0.324
13.779
0.3535
0.373
5.626
0.389
10.172
0.405
14.452
0.429
21.471
0.353
-0.094
0.4511
0.472
4.634
0.486
7.792
0.505
12.011
0.536
18.719
0.326
-27.630
0.6001
0.614
2.328
0.626
4.358
0.650
8.239
0.690
14.924
0.596
-0.629
0.6046
0.617
2.093
0.629
4.100
0.653
7.967
0.690
14.104
0.607
0.444
1.0145
1.021
0.658
1.030
1.528
1.061
4.603
1.113
9.663
1.464
44.294
Series1 FCF
data
Table 4.2(ii)
Series
Name
observed
discharge
0.225
Series2 FCF
data
0.214
% of
error
-4.959
0.220
% of
error
-2.409
0.241
0.235
0.268
0.268
-2.589
0.241
-0.097
0.248
3.010
0.267
10.528
0.205
-15.168
-0.033
0.273
1.910
0.284
6.243
0.304
13.759
0.230
-13.914
0.303
0.304
0.163
0.308
1.484
0.323
6.471
0.345
13.869
0.258
-14.839
0.332
0.341
2.757
0.344
3.570
0.362
9.025
0.387
16.459
0.287
-13.579
0.392
0.408
4.102
0.409
4.190
0.431
9.909
0.458
16.711
0.339
-13.542
0.558
0.562
0.760
0.556
-0.290
0.586
5.085
0.624
11.925
0.463
-16.979
0.558
0.566
1.353
0.560
0.275
0.590
5.675
0.628
12.519
0.466
-16.488
0.836
0.847
1.356
0.825
-1.291
0.867
3.667
0.925
10.599
0.710
-15.035
0.835
0.853
2.157
0.830
-0.540
0.872
4.450
0.931
11.544
0.715
-14.307
MDCM
IDCM
0.224
% of
error
-0.665
DCM
0.242
% of
error
7.458
0.187
% of
error
-17.117
CES
ANN
Table 4.2(iii)
Series
Name
observed
discharge
MDC
M
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.225
0.214
-4.959
0.220
-2.409
0.224
-0.665
0.242
7.458
0.187
-17.117
0.241
0.235
-2.589
0.241
-0.097
0.248
3.010
0.267
10.528
0.205
-15.168
0.268
0.268
-0.033
0.273
1.910
0.284
6.243
0.304
13.759
0.230
-13.914
0.303
0.304
0.163
0.308
1.484
0.323
6.471
0.345
13.869
0.258
-14.839
0.332
0.341
2.757
0.344
3.570
0.362
9.025
0.387
16.459
0.287
-13.579
0.392
0.408
4.102
0.409
4.190
0.431
9.909
0.458
16.711
0.339
-13.542
0.558
0.562
0.760
0.556
-0.290
0.586
5.085
0.624
11.925
0.463
-16.979
0.558
0.566
1.353
0.560
0.275
0.590
5.675
0.628
12.519
0.466
-16.488
0.836
0.847
1.356
0.825
-1.291
0.867
3.667
0.925
10.599
0.710
-15.035
0.835
0.853
2.157
0.830
-0.540
0.872
4.450
0.931
11.544
0.715
-14.307
Series
-3
FCF
data
69 | P a g e
Result and Discussion
Table 4.2(iv)
Series
Name
observed
discharge
MDCM
0.186
0.186
0.132
0.197
6.261
0.201
8.209
0.208
12.123
0.208
11.864
0.206
0.212
2.829
0.225
8.799
0.232
12.263
0.254
23.125
0.219
6.258
0.238
0.248
4.252
0.260
9.122
0.270
13.476
0.296
24.319
0.244
2.644
0.284
0.298
4.927
0.308
8.493
0.322
13.266
0.355
25.023
0.295
3.989
0.344
0.363
5.608
0.371
7.991
0.388
12.813
0.432
25.717
0.383
11.398
0.427
0.451
5.517
0.457
6.864
0.476
11.426
0.526
23.187
0.512
19.841
0.690
0.703
1.798
0.702
1.645
0.726
5.169
0.804
16.470
0.771
11.776
1.103
1.142
3.492
1.127
2.101
1.155
4.649
1.241
12.506
1.230
11.463
Series8 FCF
data
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
Table 4.2(v)
Series
Name
observed
discharge
MDCM
0.237
0.226
-4.432
0.239
1.114
0.243
2.675
0.277
16.795
0.236
-0.244
0.263
0.257
-2.075
0.272
3.613
0.279
6.380
0.312
18.826
0.258
-1.911
0.301
0.303
0.675
0.317
5.618
0.329
9.299
0.364
21.189
0.292
-2.787
0.351
0.359
2.077
0.373
6.027
0.387
10.216
0.427
21.642
0.344
-2.065
0.429
0.440
2.653
0.452
5.469
0.471
9.882
0.518
20.776
0.439
2.248
0.429
0.442
2.880
0.454
5.688
0.473
10.111
0.519
21.032
0.440
2.550
0.522
0.541
3.619
0.551
5.483
0.574
9.897
0.629
20.418
0.574
9.988
0.807
0.824
2.087
0.827
2.418
0.858
6.303
0.932
15.432
0.874
8.303
1.094
1.119
2.336
1.114
1.804
1.151
5.235
1.238
13.170
1.094
0.038
Series10
FCF
data
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
Table 4.2(vi)
Series
Name
K&D2
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.005
0.005
-6.621
0.005
-6.372
0.005
-1.451
0.006
11.538
0.005
-12.981
0.006
0.006
-5.803
0.006
-5.999
0.006
-0.506
0.007
15.625
0.005
-15.673
0.007
0.007
-5.956
0.007
-6.195
0.007
-0.840
0.009
16.753
0.006
-17.201
0.009
0.009
-5.021
0.009
-5.280
0.009
-0.256
0.011
19.481
0.008
-17.023
0.012
0.011
-4.702
0.011
-5.055
0.012
-0.165
0.014
20.598
0.010
-14.829
0.017
0.016
-6.341
0.016
-7.142
0.017
-2.039
0.020
19.298
0.016
-8.355
70 | P a g e
Result and Discussion
Table 4.2(vii)
Series
Name
K&D3
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.007
0.007
2.64
0.007
3.498
0.007
8.79
0.008
23.522
0.007
4.25
0.008
0.008
-1.85
0.008
-1.131
0.008
3.45
0.010
19.006
0.008
-0.53
0.011
0.011
-5.55
0.011
-4.860
0.011
-1.46
0.013
15.695
0.011
-3.67
0.015
0.014
-7.90
0.014
-7.176
0.014
-4.64
0.017
13.531
0.015
-1.30
0.023
0.021
-9.18
0.021
-8.482
0.022
-6.66
0.026
12.650
0.029
24.01
Table 4.2(viii)
Series
Name
K&D4
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.008
0.007
-1.135
0.008
0.126
0.008
4.789
0.009
20.667
0.010
29.918
0.009
0.009
1.400
0.009
2.434
0.010
6.379
0.011
24.286
0.012
31.768
0.014
0.013
-2.906
0.013
-2.005
0.014
0.502
0.016
19.259
0.017
29.304
0.018
0.018
-0.620
0.018
0.294
0.018
1.979
0.022
21.944
0.022
24.380
0.029
0.029
-0.756
0.029
0.090
0.030
0.964
0.035
19.694
0.031
6.963
Table 4.2(ix)
Series
Name
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.012
0.012
-0.236
0.012
-0.564
0.012
1.441
0.010
-17.670
0.012
-0.487
0.015
0.016
1.075
0.015
-1.902
0.016
1.545
0.013
-17.911
0.016
7.020
0.018
0.019
4.392
0.018
0.323
0.019
4.245
0.015
-16.726
0.020
10.935
0.021
0.022
5.791
0.021
1.272
0.022
5.287
0.018
-16.003
0.023
11.476
0.024
0.025
3.387
0.024
-1.128
0.025
2.731
0.020
-18.059
0.026
8.131
0.024
0.022
-5.639
0.022
-9.688
0.022
-6.111
0.021
-11.186
0.024
-0.665
0.027
0.027
-1.334
0.026
-5.651
0.027
-2.034
0.024
-13.236
0.028
2.795
0.030
0.030
-1.128
0.028
-5.411
0.029
-1.910
0.025
-15.401
0.031
2.724
0.034
0.032
-6.777
0.031
-10.753
0.032
-7.554
0.032
-8.333
0.033
-3.053
0.040
0.038
-4.518
0.037
-8.382
0.038
-5.363
0.033
-17.992
0.040
0.367
0.045
0.042
-7.554
0.040
-11.180
0.041
-8.381
0.037
-17.333
0.044
-2.269
0.050
0.047
-5.854
0.045
-9.356
0.047
-6.696
0.040
-21.041
0.050
-0.331
0.055
0.050
-9.341
0.048
-12.627
0.049
-10.149
0.043
-22.470
0.053
-4.352
0.060
0.054
-9.783
0.052
-12.930
0.054
-10.578
0.045
-24.996
0.057
-5.459
Atbay
71 | P a g e
Result and Discussion
Table 4.2(x)
Series
Name
Rezai
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.012
0.014
12.617
0.014
16.344
0.014
13.662
0.013
4.250
0.012
-3.664
0.013
0.015
15.193
0.015
20.138
0.015
15.654
0.014
13.490
0.013
-0.022
0.014
0.016
18.098
0.017
23.806
0.016
17.951
0.016
16.296
0.014
3.450
0.015
0.017
13.334
0.018
18.966
0.017
12.997
0.018
19.553
0.015
-0.436
0.015
0.018
17.420
0.019
23.406
0.018
16.839
0.017
8.260
0.016
3.523
0.018
0.021
14.687
0.022
20.651
0.020
13.857
0.020
13.296
0.018
1.724
0.021
0.024
12.396
0.025
18.246
0.023
11.429
0.023
11.000
0.021
0.502
0.024
0.026
10.067
0.028
15.757
0.026
9.048
0.026
8.583
0.024
-0.712
0.027
0.029
7.240
0.030
12.743
0.029
6.199
0.029
5.696
0.026
-2.359
0.029
0.031
7.902
0.033
13.404
0.031
6.814
0.031
6.221
0.029
-0.811
0.030
0.033
8.602
0.034
14.121
0.032
7.481
0.032
6.853
0.030
0.431
0.035
0.039
10.149
0.040
15.685
0.038
8.875
0.038
8.057
0.037
5.078
0.040
0.045
12.698
0.047
18.335
0.044
11.203
0.044
10.276
0.045
11.939
0.045
0.050
10.967
0.053
16.517
0.049
9.318
0.049
8.371
0.052
14.328
Table 4.2(xi)
Series
Name
observed
discharge
MDCM
% of
error
IDCM
% of
error
DCM
% of
error
CES
% of
error
ANN
% of
error
0.029
0.029
-2.053
0.029
-0.490
0.030
3.129
0.035
21.104
0.032
10.220
0.033
0.030
-0.080
0.031
-0.068
0.032
-0.028
0.039
0.193
0.033
0.014
0.034
0.032
-0.073
0.032
-0.063
0.034
-0.019
0.041
0.204
0.035
0.005
0.039
0.036
-0.081
0.036
-0.075
0.038
-0.027
0.047
0.199
0.038
-0.043
0.041
0.038
-0.073
0.038
-0.068
0.040
-0.018
0.046
0.136
0.039
-0.049
0.044
0.041
-0.061
0.041
-0.058
0.044
-0.007
0.054
0.230
0.041
-0.061
0.046
0.044
-0.057
0.044
-0.055
0.046
-0.003
0.055
0.198
0.043
-0.070
0.049
0.043
-0.117
0.048
-0.027
0.050
0.026
0.062
0.274
0.026
-0.464
0.052
0.052
0.006
0.052
0.006
0.055
0.061
0.069
0.322
0.050
-0.047
0.059
0.065
0.109
0.065
0.108
0.068
0.167
0.086
0.460
0.060
0.025
NIT
Rourkela
Data
20132014
Table 4.2(i)-4.2(xi): Percentage of error calculation for discharge through hydraulic models
72 | P a g e
Result and Discussion
4.8
Determination of average absolute error
The by averaging the percentage of error in discharge for all sets of data average absolute
error is found out. The average absolute error value is shown in the table 4.4 and it is shown in
the form of bar chart in the fig4.9.
Table 4.3: Average absolute error value
Average
MDCM
IDCM
DCM
CES
ANN
4.070955
5.782871
6.549618
14.50004
9.11942
Absolute
error
16
Average Absolute Error (%)
14
12
10
8
6
4
2
0
MDCM
IDCM
DCM
CES
ANN
Fig4.9: average absolute error in all five methods.
In all the above numerical methods the value of n is kept constant with respect to the surface
roughness. Historically both the Chézy and the Manning coefficients were expected to be
constant and functions of the roughness only. But it is now well known that these coefficients are
only constant for a range of flow rates. Though surface roughness is most influencing factor but
it is seen that there are some other factors which influence the value of manning’s n. Therefore it
is required to know how it affects the discharge if the value of n is changed. The variation of n
value with flow rate is required to be studied and discharge is predicted by varying n values. But
before that the other hydraulic parameters of the channels has to be found out to know flow
characteristics.
73 | P a g e
Result and Discussion
4.9
Determination of hydraulic parameters of collected data set
Discharge prediction is one of the most uncertain area of hydraulic engineering as it is
influenced by both geometrical parameter as well as hydraulic parameters. As geometrical
parameters we can consider the relative depth, width ratio and shape of the channel etc. and as
hydraulic parameter channel roughness, Reynolds number, Froude’s number etc. So it is required
to find out these parameters.
The channel roughness is commonly known as manning’s n. The channel roughness is required
to find out to know the type of bed material is available.. Generally the value of manning’s n is
depends upon various factors such as surface roughness, channel shape, type of vegetation, the
depth of flow etc. many researchers have given the range of n value for open channels depending
upon the surface characteristics. Manning’s n can be found out using the equation given below
(4.2)
Where Q= discharge of the channel
A= total cross sectional area of the channel
R= Hydraulic radius of the channel
So= bed slope of the channel
Reynolds number is the ratio of inertia force to viscous force. By the help of Reynolds number,
whether the fluid flowing in the channel is laminar or turbulent is known. As we know if the
Reynolds number values is less than 500, the flowing fluid is considered to be laminar, if its
value is greater than 2000 then it comes under turbulent flow category and if its values lies in
between 500 to 2000 then it comes under transition zone. So to understand this we need to find
out the Reynolds number for each experimental run. The Reynolds number can be calculated
using the formula given below for open channel.
(4.3)
Where ρ= density of flowing fluid
V= mean velocity of the flowing fluid
R= hydraulic radius of the channel
ν= kinematic viscosity of the flowing fluid
74 | P a g e
Result and Discussion
Darcy-Weisbach co-efficient of friction is required to find out to evaluate the shear stress at the
boundary. So to understand the effect of shear stress or effect of friction on fluid flowing through
the channel it is required to find out by using the formula given below
⁄
(4.4)
Where f= co-efficient of friction of the channel
g= acceleration due to gravity
R= hydraulic radius of the channel
n= manning’s n for the channel
To know the profile of the channel it is required to find out the Froude’s number. By knowing
the values of Froude’s number we can conclude that whether the flow type is subcritical or
supercritical. The Froude’s number is calculated by using the formula given below.
(4.5)
√
Where Fr = Froude’s number
V= mean velocity of the flowing fluid
g= acceleration due to gravity
D= hydraulic depth of the channel
Chezy’s C is required to find out the velocity of the channel and it can be found out by using the
formulae given below.
√
(4.6)
(4.7)
Where C = Chezy’s constant
R= hydraulic radius of the channel
g= acceleration due to gravity
n= manning’s n for the channel
f= co-efficient of friction of the channel
Here hydraulic parameters of the eleven data sets are presented in the Table 4.4.(i)-4.4(xi).
75 | P a g e
Result and Discussion
Table 4.4(i)
Series
name
FCF
Series1
Manning's n
Chezy's C
Darcy's f
R(m)
mean
velocity
V (m/s)
Reynolds
number
(Re)
Froude’s
Number
(Fr)
0.033416
0.617072
0.005387863
105.3356
0.007073
73642.43
1.073541
0.3994
0.039332
0.585128
0.006334273
92.06483
0.009259
82193.22
0.936205
0.2852
0.5038
0.049511
0.566098
0.007632992
79.38811
0.012452
100100.1
0.807306
0.3535
0.6131
0.060123
0.576578
0.008530127
73.37559
0.014577
123806.3
0.746174
0.4511
0.7356
0.071963
0.613241
0.009041239
71.333
0.015423
157610
0.725413
0.6001
0.8886
0.086672
0.675332
0.009293644
71.5803
0.015317
209043.4
0.727941
0.6046
0.8918
0.086978
0.677955
0.009279517
71.73149
0.015252
210597.8
0.729479
1.0145
1.2487
0.120945
0.812445
0.009646814
72.89777
0.014768
350933.5
0.741371
Observed
discharge
Q (m3/s)
A (m2)
0.2082
0.3374
0.2337
Area
Radius
Table 4.4(ii)
Series
name
FCF
Series2
Manning's n
Chezy's C
Darcy's f
R(m)
mean
velocity
V (m/s)
Reynolds
number
(Re)
Froude’s
Number
(Fr)
0.28842
0.0448
0.736056
0.005491928
108.5145
0.006665
117768.3
1.099446
0.36585
0.056564
0.678694
0.006957767
89.0471
0.009897
137105.1
0.901873
0.2492
0.37326
0.057684
0.66762
0.00716622
86.73981
0.010431
137538.2
0.878463
0.2821
0.42366
0.065262
0.665853
0.007801516
81.33249
0.011864
155195.3
0.823403
Observed
discharge
Q (m3/s)
Area
Radius
A (m2)
0.2123
0.2483
0.3237
0.48043
0.073731
0.673758
0.008363365
77.42727
0.013091
177417.4
0.783502
0.32382
0.48165
0.073911
0.672313
0.008394966
77.16715
0.013179
177468.9
0.780862
0.3832
0.55194
0.084299
0.694268
0.008874445
74.61559
0.014096
209023
0.754562
0.48
0.65190
0.09889
0.736305
0.009307418
73.06279
0.014702
260047.5
0.738141
0.763
0.87807
0.131146
0.868944
0.009519845
74.87369
0.013999
406994.6
0.754659
1.1142
1.13561
0.16665
0.981142
0.009891394
74.99694
0.013953
583956.2
0.753806
Table 4.4(iii)
Series
name
FCF
Series3
Manning's n
Chezy's C
Darcy's f
R(m)
mean
velocity
V (m/s)
Reynolds
number
(Re)
Froude’s
Number
(Fr)
0.273964
0.079616
0.821641
0.00721833
90.865
0.009505
233627.6
0.912658
0.2412
0.301456
0.08713
0.800118
0.00787184
84.58336
0.01097
248979.1
0.849367
0.2676
0.337731
0.09688
0.792345
0.008531502
79.43524
0.012437
274150.3
0.797244
0.3031
0.373635
0.10635
0.811219
0.008867561
77.62206
0.013025
308117.3
0.778492
0.3323
0.40834
0.115339
0.813783
0.009330969
74.77145
0.014037
335216.7
0.749294
0.3922
0.464647
0.129591
0.844081
0.009722652
73.16631
0.01466
390662.2
0.73211
0.5579
0.579455
0.157448
0.962801
0.009705267
75.71505
0.01369
541397.7
0.754989
0.5581
0.581903
0.158025
0.959095
0.009766554
75.28581
0.013846
541290.7
0.75065
0.836
0.762193
0.19876
1.096836
0.009950927
76.76998
0.013316
778598
0.760907
0.8349
0.765504
0.199477
1.090654
0.010031377
76.20001
0.013516
777002.5
0.755174
Observed
Discharge
Q (m3/s)
Area
Radius
A (m2)
0.2251
76 | P a g e
Result and Discussion
Table 4.4(iv)
Series
name
FCF
Series8
Manning's n
Chezy's C
Darcy's f
Reynolds
number
(Re)
Froude’s
Number
(Fr)
0.681027
0.005792292
102.2603
0.007505
105038.9
1.021033
0.051626
0.630635
0.007045634
86.60804
0.010463
116276
0.864531
0.384884
0.060472
0.618758
0.007979313
78.51629
0.01273
133633.3
0.783446
0.451832
0.070653
0.628686
0.008711714
73.80476
0.014408
158636.6
0.736019
0.34398
0.527988
0.082104
0.651492
0.009292224
70.94818
0.015591
191036.5
0.707022
0.42726
0.618183
0.095492
0.691155
0.009686959
69.7922
0.016112
235712.9
0.694865
0.69018
0.836364
0.127118
0.825215
0.009817974
72.22358
0.015045
374640.3
0.717375
1.1034
1.145799
0.170223
0.962996
0.010221302
72.83333
0.014794
585443.2
0.720921
Observed
Discharge
Q (m3/s)
Area
Radius
R(m)
mean
velocity
V (m/s)
A (m2)
0.1858
0.272823
0.043186
0.2064
0.327289
0.23815
0.28406
Table 4.4(v)
Series
name
FCF
Series10
Reynolds
number
Froude’s
Number
(Re)
(Fr)
0.007246
126448.4
1.059052
90.69987
0.00954
139846.5
0.92277
0.007779209
81.76128
0.01174
159412.7
0.831488
0.681489
0.00845546
77.01325
0.013232
185573.9
0.782792
0.088929
0.70943
0.00899988
74.23411
0.014241
225316.3
0.75398
0.605917
0.089099
0.708348
0.00902516
74.04984
0.014312
225404.4
0.7521
0.522
0.701946
0.102603
0.743647
0.009444787
72.4438
0.014954
272501.5
0.735149
0.8071
0.93524
0.13471
0.862987
0.009758458
73.37005
0.014579
415189.2
0.742878
1.0939
1.142842
0.16248
0.957175
0.00996919
74.09803
0.014294
555434
0.748698
Darcy's f
Reynolds
number
Froude’s
Number
(Re)
(Fr)
Observed
discharge
Area
Radius
mean
velocity
Q (m3/s)
A (m2)
R(m)
V (m/s)
0.2368
0.323062
0.048303
0.732985
0.005798837
104.0691
0.2627
0.379836
0.056617
0.691615
0.006832047
0.3006
0.445868
0.066206
0.67419
0.3514
0.515636
0.076246
0.429
0.604711
0.4292
Manning's n
Chezy's C
Darcy's f
Table 4.4(vi)
Series
name
Knight
&
Demet
riou -1
Observed
discharge
Area
Radius
mean
velocity
Q (m3/s)
A (m2)
R(m)
V (m/s)
0.005200
0.01444
0.0304
0.360111
0.008406879
66.45242
0.017772
39097.74
0.527539
0.006400
0.017184
0.031394
0.372433
0.008304932
67.62974
0.017159
41757.3
0.500131
0.007300
0.018928
0.034853
0.385668
0.008598712
66.46701
0.017764
48005.66
0.49347
0.009450
0.022932
0.037517
0.412095
0.008452279
68.4537
0.016748
55215.92
0.479052
0.011700
0.0267
0.043197
0.438208
0.008731884
67.83705
0.017054
67603.87
0.472095
0.017100
0.034382
0.048051
0.497347
0.008259656
72.99975
0.014727
85349.67
0.472165
0.005000
0.015035
0.056718
0.33256
0.013796388
44.92844
0.038879
67364.68
0.477444
77 | P a g e
Manning's n
Chezy's C
Result and Discussion
Table 4.4(vii)
Series
name
Knight
&
Demet
riou -2
Manning's n
Chezy's C
Darcy's f
Reynolds
number
(Re)
Froude’s
Number
(Fr)
0.323532
0.008217234
65.81321
0.018119
28906.28
0.484716
0.03195
0.351223
0.008910207
63.22048
0.019636
40077.31
0.500178
0.028011
0.03484
0.398057
0.008329064
68.61469
0.01667
49529.89
0.512777
0.033896
0.041181
0.446955
0.008292604
70.86401
0.015628
65736.41
0.523405
0.023400
0.044982
0.048011
0.520203
0.007892445
76.38575
0.01345
89198.7
0.528809
0.004900
0.015661
0.059609
0.312877
0.015158495
41.23151
0.046164
66608.21
0.539027
Observed
discharge
Q (m3/s)
Area
Radius
R(m)
mean
velocity
V (m/s)
A (m2)
0.006700
0.020709
0.025017
0.008050
0.02292
0.011150
0.015150
Table 4.4(viii)
Series
name
Knight
&
Demet
rious 3
Manning's n
Chezy's C
Darcy's f
R(m)
mean
velocity
V (m/s)
Reynolds
number
(Re)
Froude’s
Number
(Fr)
0.029364
0.319594
0.009256137
60.00745
0.021795
33515.87
0.519379
0.027452
0.033795
0.331493
0.009800465
58.01784
0.023315
40009.8
0.498091
0.013500
0.03483
0.041634
0.3876
0.009632432
61.11838
0.021009
57633.2
0.517042
0.018000
0.042744
0.049553
0.421108
0.009957231
60.86567
0.021184
74524.97
0.507075
0.029400
0.058882
0.064304
0.4993
0.009991211
63.35117
0.019555
114667.3
0.512254
Darcy's f
Reynolds
number
Froude’s
Number
(Re)
(Fr)
Observed
discharge
Q (m3/s)
A (m2)
0.007500
0.023467
0.009100
Area
Radius
Table 4.4(ix)
Series
name
Atbay'
s Data
Observed
discharge
Area
Radius
mean
velocity
Q (m3/s)
A (m2)
R(m)
V (m/s)
0.012
0.024506
0.01857
0.489684
0.006442751
79.87284
0.012302
32477.37
0.403679
0.015349
0.031535
0.023689
0.48673
0.007624042
70.29214
0.015883
41179.63
0.401243
0.018013
0.036989
0.0276
0.486977
0.008437236
65.15544
0.018487
48001.62
0.401447
0.020953
0.041998
0.031145
0.498911
0.008926331
62.83835
0.019875
55494.78
0.411285
0.024042
0.045716
0.033748
0.525896
0.008933891
63.63093
0.019383
63386.31
0.433531
0.023836
0.04246
0.03147
0.561385
0.007988031
70.3411
0.015861
63095.23
0.462787
0.027085
0.048179
0.035461
0.562173
0.008637713
66.35782
0.017823
71196.28
0.463436
0.030012
0.051906
0.038031
0.578207
0.008799348
65.90323
0.018069
78535.89
0.476654
0.034429
0.054837
0.040037
0.627839
0.008386257
69.74444
0.016134
89775.26
0.517569
0.040052
0.061859
0.044785
0.64747
0.008762814
68.00579
0.016969
103561.5
0.533752
0.044939
0.065427
0.047167
0.686857
0.008550672
70.29754
0.015881
115704.7
0.566222
0.050026
0.071169
0.050959
0.702921
0.008797208
69.21363
0.016382
127928.4
0.579464
0.055037
0.073955
0.05278
0.744192
0.008506145
72.00212
0.015138
140279.9
0.613486
0.060025
0.078076
0.055452
0.768804
0.008509411
72.56931
0.014902
152255.4
0.633776
78 | P a g e
Manning's n
Chezy's C
Result and Discussion
Table 4.4(x)
Series
name
Rezai's
Data
Reynolds
number
Froude’s
Number
(Re)
(Fr)
0.015966
70761.93
0.458524
67.77966
0.018647
79460.45
0.45256
0.008793296
65.0976
0.020537
86313.07
0.45048
0.575608
0.008518539
67.53793
0.019898
88657.29
0.474511
0.037863
0.565187
0.008928778
64.89989
0.021686
100838.7
0.465921
0.029887
0.040862
0.598931
0.008864992
66.20263
0.018495
105852.3
0.493738
0.021
0.032936
0.044413
0.637592
0.008803085
67.60043
0.017579
118993.9
0.525609
0.024
0.035568
0.047398
0.674771
0.008686769
69.25248
0.016412
134680
0.556258
0.027
0.03784
0.049921
0.713531
0.008503854
71.35612
0.015174
155629.8
0.58821
0.028968
0.039831
0.05209
0.727267
0.00858324
71.19916
0.015728
160363.9
0.599534
0.03
0.04095
0.053292
0.732608
0.008651215
70.90877
0.016048
170954.5
0.603937
0.035
0.045793
0.058365
0.764302
0.008810726
70.68828
0.015541
178497.7
0.630065
0.0399
0.050697
0.063292
0.787029
0.009031288
69.8997
0.015014
199491.9
0.648799
0.0451
0.054405
0.066885
0.828974
0.008895845
71.62007
0.014003
221806.6
0.683378
Darcy's f
Reynolds
number
Froude’s
Number
(Re)
(Fr)
Observed
discharge
Area
Radius
mean
velocity
Q (m3/s)
A (m2)
R(m)
V (m/s)
0.012
0.021574
0.030663
0.556215
0.007882668
70.9734
0.01275
0.023225
0.032752
0.54898
0.008345255
0.013758
0.025177
0.03518
0.546457
0.015
0.026059
0.036264
0.015472
0.027375
0.0179
Manning's n
Chezy's C
Darcy's f
Table 4.4(xi)
Series
name
NIT
Rourkela
Data
20132014
Observed
discharge
Area
Radius
mean
velocity
Q (m3/s)
A (m2)
R(m)
V (m/s)
0.02919
0.05999
0.053457
0.486577
0.009222618
66.54987
0.01772
32473.39
0.401117
0.033
0.06323
0.055985
0.521904
0.008867329
69.75142
0.016131
36478.22
0.43024
0.034403
0.065882
0.058031
0.522189
0.009077077
68.54841
0.016702
37831.67
0.430474
0.039207
0.0725
0.063043
0.540787
0.009262619
68.10927
0.016918
42563.17
0.445806
0.04081
0.0752
0.065052
0.542682
0.009425284
67.28458
0.017335
44073.05
0.447369
0.043891
0.08006
0.068615
0.548232
0.009667518
66.18428
0.017916
46962.49
0.451944
0.046164
0.0833
0.070954
0.554186
0.009779774
65.79113
0.018131
49090.81
0.456852
0.048861
0.088571
0.074699
0.551657
0.01016731
63.82823
0.019263
51445.8
0.454767
0.052165
0.095
0.079167
0.549105
0.010617916
61.7141
0.020606
54270.7
0.452663
Manning's n
Chezy's C
Table 4.4(i)-4.4(xi): Determination of hydraulic parameters
From the tables it is found that the values of n are changing very significantly with respect to
flow depths. So now it is required to find out the discharge for all the eleven channels data by
using MDCM with the varying n values.
79 | P a g e
Result and Discussion
Effect of ‘n’ On MDCM
4.10
From the comparison study it is seen that MDCM is the best method among those five
methods for predicting discharge by keep n value constant with respect to surface roughness of
the channel. Therefore in the present work all eleven data sets are validated by MDCM for
discharge prediction by changing the value of n with respect to the depth of flow.. From the
calculation it is found that the MDCM is overestimating the discharge with a maximum error of
35% for lower depth of flow while for higher depth of flow, the error has been reduced to 2%. So
there is a large variation in error is occurring for all depth of flow. Therefore this method needs
few modifications.
Khatua (2007) proposed an equation for %Sfp (equation 3.2.12, as shown in chapter-3) for a
compound channel section having a width ratio varying from 2-6.67 as
[
]
But the equation valid for a constant value of manning’s n. therefore on the basis of simulation of
the experimental data an empirical factor (Ef )is multiplied to it.
(
)
(4.8)
So the %Sfp is now re written as
(
[
]
)
(4.9)
So the value obtain from equation (4.8) has been put in the equation (3.2.9) and (3.2.10) to get
the values of
and
. The discharge is again computed through the equation (3.2.11) and the
results are compared with MDCM and experimental data sets. The error obtained from both the
methods is presented in the table 4.5.(i)-4.5(xi).
80 | P a g e
Result and Discussion
Table 4.5(i)
Series
name
Depth of
flow H (m)
Manning's n
FCF
Series-1
0.15899
0.16519
0.17563
0.18656
0.19881
0.21411
0.21443
0.25012
0.005388
0.006334
0.007633
0.00853
0.009041
0.009294
0.00928
0.009647
Observed
discharge Q
(m3/s)
0.2082
0.2337
0.2852
0.3535
0.4511
0.6001
0.6046
1.0145
Discharge
through
MDCM
0.36895
0.378637
0.3907
0.437736
0.52207
0.660719
0.665143
1.058544
% of error
77%
62%
37%
24%
16%
10%
10%
4%
Discharge
through Revised
MDCM
0.228586
0.233336
0.261201
0.331313
0.451171
0.620229
0.625064
1.048342
% of error
10%
0%
-8%
-6%
0%
3%
3%
3%
Table 4.5(ii)
Series
name
Depth of
flow H
(m)
Manning's n
Observed
discharge Q
(m3/s)
Discharge
through
MDCM
% of error
Discharge
through Revised
MDCM
% of error
FCF
Series2
0.15649
0.16873
0.1699
0.17784
0.18676
0.18695
0.19796
0.21355
0.24855
0.28795
0.005492
0.006958
0.007166
0.007802
0.008363
0.008395
0.008874
0.009307
0.00952
0.009891
0.2123
0.2483
0.2492
0.2821
0.3237
0.32382
0.3832
0.48
0.763
1.1142
0.346245
0.354987
0.351242
0.367429
0.396214
0.395904
0.444645
0.531133
0.800636
1.140711
63%
43%
41%
30%
22%
22%
16%
11%
5%
2%
0.252167
0.269628
0.27042
0.293044
0.335757
0.33592
0.40206
0.506803
0.793965
1.139081
19%
9%
9%
4%
4%
4%
5%
6%
4%
2%
% of error
Discharge
through Revised
MDCM
% of error
32%
24%
18%
13%
11%
7%
4%
5%
2%
2%
0.264499
0.270035
0.286337
0.320486
0.350409
0.411967
0.574455
0.58202
0.852699
0.851377
18%
12%
7%
6%
5%
5%
3%
4%
2%
2%
Table 4.5(iii)
Series
name
FCF
Series3
81 | P a g e
Depth of
flow H
(m)
0.158
0.16627
0.17712
0.18779
0.19804
0.21454
0.2477
0.2484
0.29922
0.30014
Manning's n
Observed
discharge Q
(m3/s)
0.007218
0.007872
0.008532
0.008868
0.009331
0.009723
0.009705
0.009767
0.009951
0.010031
0.2251
0.2412
0.2676
0.3031
0.3323
0.3922
0.5579
0.5581
0.836
0.8349
Discharge
through
MDCM
0.296722
0.299077
0.314461
0.34351
0.367321
0.421612
0.577445
0.584956
0.853225
0.851885
Result and Discussion
Table 4.5(iv)
Depth of
flow H
(m)
Series
name
0.15796
0.167
0.17653
0.18757
0.20008
0.21483
0.25022
0.29973
FCF
Series8
Manning's n
Observed
discharge Q
(m3/s)
0.005792
0.007046
0.007979
0.008712
0.009292
0.009687
0.009818
0.010221
0.1858
0.2064
0.23815
0.28406
0.34398
0.42726
0.69018
1.1034
Discharge
through
MDCM
0.281377
0.30152
0.311474
0.342514
0.391371
0.465878
0.715908
1.116371
% of error
Discharge
through Revised
MDCM
% of error
51%
46%
31%
21%
14%
9%
4%
1%
0.210059
0.226227
0.241262
0.288397
0.355588
0.445184
0.710426
1.115431
13%
10%
1%
2%
3%
4%
3%
1%
% of error
Discharge
through Revised
MDCM
% of error
Table 4.5(v)
Depth of
flow H
(m)
Series
name
FCF
Series10
Manning's n
Observed
discharge Q
(m3/s)
Discharge
through
MDCM
0.15803
0.005799
0.2368
0.360451
52%
0.272253
15%
0.1666
0.006832
0.2627
0.376866
43%
0.297139
13%
0.17654
0.007779
0.3006
0.389485
30%
0.314824
5%
0.18701
0.008455
0.3514
0.424746
21%
0.365663
4%
0.20033
0.009
0.429
0.489967
14%
0.450984
5%
0.20051
0.009025
0.4292
0.489913
14%
0.451253
5%
0.21481
0.009445
0.522
0.573401
10%
0.550406
5%
0.2493
0.009758
0.8071
0.845071
5%
0.838662
4%
0.2797
0.009969
1.0939
1.123388
3%
1.121219
2%
% of error
Discharge
through Revised
MDCM
% of error
Table 4.5(vi)
Depth of
flow H
(m)
Manning's n
Observed
discharge Q
(m3/s)
0.085500
0.008407
0.005200
0.005776
11%
0.00522
0%
0.094527
0.008305
0.006400
0.007259
13%
0.006788
6%
0.100263
0.008599
0.007300
0.007984
9%
0.007647
5%
0.113433
0.008452
0.009450
0.010619
12%
0.010476
11%
0.125828
0.008732
0.011700
0.012769
9%
0.012711
9%
0.151100
0.008260
0.017100
0.01939
13%
0.019378
13%
Series
name
Knight
&
Demetr
iou -1
82 | P a g e
Discharge
through
MDCM
Result and Discussion
Table 4.5(vii)
Manning's n
Observed
discharge Q
(m³/s)
% of error
Discharge
through Revised
MDCM (m³/s)
% of error
0.096081
0.008217
0.006700
0.00837
25%
0.007627
14%
0.100930
0.008910
0.008050
0.008867
10%
0.008356
4%
0.112094
0.008329
0.011150
0.012643
13%
0.012397
11%
0.125000
0.008293
0.015150
0.016826
11%
0.016732
10%
0.149312
0.007892
0.023400
0.026926
15%
0.026907
15%
% of error
Discharge
through Revised
MDCM (m³/s)
% of error
Depth of
flow H
(m)
Series
name
Knight
&
Demetr
iou -2
Discharge
through
MDCM
Table 4.5(viii)
Depth of
flow H
(m)
Series
name
Knight
&
Demetr
iou -2
Manning's n
Observed
discharge Q
(m3/s)
Discharge
through
MDCM
0.095597
0.009256
0.007500
0.008011
7%
0.007056
-6%
0.102151
0.009800
0.009100
0.009415
3%
0.008822
-3%
0.114286
0.009632
0.013500
0.013608
1%
0.013369
-1%
0.127303
0.009957
0.018000
0.017965
0%
0.017882
-1%
0.153846
0.009991
0.029400
0.029203
-1%
0.02919
-1%
% of error
Discharge
through Revised
MDCM (m³/s)
% of error
Table 4.5(ix)
Series
name
Atbay's
Data
83 | P a g e
Depth of
flow H
(m)
Manning's n
Observed
discharge Q
(m3/s)
Discharge
through
MDCM
0.0538
0.006443
0.012
0.017676
47%
0.014791
23%
0.0596
0.007624
0.015349
0.01898
24%
0.016038
4%
0.0641
0.008437
0.018013
0.020807
16%
0.018781
4%
0.0682
0.008926
0.020953
0.023146
10%
0.021839
4%
0.0713
0.008934
0.024042
0.026005
8%
0.025056
4%
0.0686
0.007988
0.023836
0.026253
10%
0.024848
4%
0.0733
0.008638
0.027085
0.028975
7%
0.028188
4%
0.0764
0.008799
0.030012
0.031678
6%
0.031128
4%
0.0788
0.008386
0.034429
0.036034
5%
0.035593
3%
0.0846
0.008763
0.040052
0.041299
3%
0.041078
3%
0.0876
0.008551
0.044939
0.046085
3%
0.04592
2%
0.0923
0.008797
0.050026
0.050952
2%
0.050854
2%
0.0946
0.008506
0.055037
0.055907
2%
0.055828
1%
Result and Discussion
Table 4.5(x)
Series
name
Depth of
flow H
(m)
Rezai's
Data
0.0528
0.05556
0.058824
0.0603
0.0625
0.0667
0.0718
0.0762
0.08
0.08333
0.0852
0.0933
0.1015
0.1077
Manning's n
Observed
discharge Q
(m3/s)
0.007883
0.008345
0.008793
0.008519
0.008929
0.008865
0.008803
0.008687
0.008504
0.008583
0.008651
0.008811
0.009031
0.008896
0.012
0.01275
0.013758
0.015
0.015472
0.0179
0.021
0.024
0.027
0.028968
0.03
0.035
0.0399
0.0451
Discharge
through
MDCM
% of error
Discharge
through Revised
MDCM (m³/s)
% of error
13%
15%
18%
13%
17%
15%
12%
10%
7%
8%
9%
10%
13%
11%
0.012846
0.013774
0.015307
0.016104
0.017373
0.019957
0.023253
0.026195
0.028807
0.031153
0.032495
0.038514
0.044949
0.050036
7%
8%
11%
7%
12%
11%
11%
9%
7%
8%
8%
10%
13%
11%
0.013514
0.014687
0.016248
0.017
0.018167
0.020529
0.023603
0.026416
0.028955
0.031257
0.032581
0.038552
0.044967
0.050046
Table 4.5(xi)
Series
name
Depth of
flow H
(m)
Manning's n
Observed
discharge Q
(m3/s)
Discharge
through
MDCM
% of error
Discharge
through Revised
MDCM (m³/s)
% of error
NIT
Rourke
la Data
20132014
0.1111
0.1147
0.117647
0.125
0.128
0.1334
0.137
0.142857
0.15
0.16667
0.2
0.009223
0.008867
0.009077
0.009263
0.009425
0.009668
0.00978
0.010167
0.010618
0.011851
0.014651
0.02919
0.033
0.034403
0.039207
0.04081
0.043891
0.046164
0.048861
0.052165
0.058596
0.0684
0.0341
0.037666
0.038664
0.042807
0.044162
0.046882
0.048966
0.051353
0.054365
0.060326
0.069773
17%
14%
12%
9%
8%
7%
6%
5%
4%
3%
2%
0.03116
0.034468
0.035592
0.040281
0.041934
0.045154
0.047523
0.050319
0.053684
0.060076
0.069734
7%
4%
3%
3%
3%
3%
3%
3%
3%
3%
2%
Table 4.5(i)-4.5(xi) Calculation of percentage of error in discharge by varying the value of
Manning’s n.
From the table 4.4(i)-4.4(xi) we observed that the percentage of error is found to be less when
the empirical factor is used in MDCM. The average absolute errors for Revised MDCM are
found to be 5% whereas for MDCM it is observed to be 13%.
84 | P a g e
Result and Discussion
4.11 Establishment of linear relationship
Through Revised MDCM, and MDCM the discharge is calculated for all eleven numbers of
data sets by considering the variation in manning’s n. So a linear relationship is established
between the discharge obtained from these methods and the actual discharge obtained from each
experimental run. The Fig 4.10(i)-4.10(ii) the linear relationship is presented.
1.4
1.2
y = 1.0273x + 0.0029
R² = 0.9989
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
Fig.4.10.(i): Correlation plot of actual discharge and Discharge predicted by Revised MDCM
1.4
y = 1.0514x + 0.0188
R² = 0.9645
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
Fig.4.10.(ii): Correlation plot of actual discharge and Discharge predicted by MDCM
85 | P a g e
Conclusion
CONCLUSION
5.1
Conclusions
Experiments are carried out to analyze the flow pattern in a straight compound channel
having narrow flood plains for four different relative depths. Observations are made at section-1
of the channel (as shown in the figure 3.2) for depth averaged velocity and wall shear data at
different depth of flow. Apart from this, eleven data sets are tested through five different
methods for predicting discharge and the obtained results are compared with the experimental
results (as described in chapter 4). Based on analysis and discussions of the experimental
investigations certain conclusions from the present work are drawn below.
 Form the stage discharge curve it is observed that the rate of flow increases with the
increase in flow depth. The maximum discharge is recorded as 0.0526m3/s for 0.1487m
of depth flow.
 Velocity measurements are made for four relative depths such as 0.15, 0.2, 0.25, and 0.3.
Maximum velocity is observed just below the free water surface. This may be due to
formation of boundary layer between the free water surface and air which restrict the
flow of top layer.
 The depth averaged velocity is measured at a depth of 0.6H and 0.6(H-h) from the free
water surface of the main channel and flood plain respectively. From the depth averaged
velocity graph it is observed that the depth averaged velocity goes on decreasing with
decrease in depth of flow.
 It is observed from the boundary shear stress graphs that, the boundary shear stress at the
bed of the main channel remains higher at center while decreasing towards the wall. In
the flood plain it is observed to remain lower at its wall while gradually increasing
towards the junction of main channel and flood plain.
 From the values of Reynolds number and Froude’s number, it is found that the flow type
is turbulent for all eleven channels and they are having subcritical flow conditions.
86 | P a g e
Conclusion
 Discharge has been computed through five different methods. The results are compared
with the actual data that has been collected from different sources. The percentage of
error for all the methods is found to be more or less than 10%.
 From the absolute error graph it is clearly visible that MDCM is giving better result as
compared to other four methods.
 From the comparison study we got that among the three numerical methods, both IDCM
and MDCM gives better discharge prediction as compared to DCM as both IDCM and
MDCM considers the effect of momentum transfer in terms of interface stress and
interface length respectively, at the junction of the main channel and the flood plain
whereas DCM does not consider this effect.
 Between MDCM and IDCM, we can say that from the calculation point of view MDCM
is much better than IDCM, as it has less number of computational steps for calculation of
discharge which leads to less computational error.
 By varying the values of manning’s n with respect to depth of flow, discharge is
computed through MDCM. It is found that MDCM fails to predict the discharge for
lower depth of flow. But as the higher depth of it works well.
 Modification is applied to MDCM for predicting discharge for lower depth of flow.
 The discharge is calculated through the Revised MDCM and the results are compared
with the experimental discharge data. It is found that the Revised MDCM is doing better
discharge prediction as compared to MDCM with a percentage of error of 5%.
5.2
Scope for Future Work
The present research is restricted to straight prismatic channel. The work thereof leaves a
broad spectrum for other investigators to explore many intricate flow phenomena such as
secondary currents, turbulent intensities and vortices that significantly affects the distribution of
boundary shear stress in simple and compound non prismatic straight channels as well as the
meandering channel. The determination of discharge, velocity, boundary shear stress
calculations involves limited number of data.
87 | P a g e
Conclusion
The future scope of the present work may be summarized as:
 The work is applied to straight prismatic channels only, while its applicability to other
channels such as meandering, curved channel can be be incorporated and tested.
 The present work lacks shear force analysis for trapezoidal straight and meandering
compound channel. The percentage of floodplain and main channel shear can be
estimated for non-prismatic straight compound channels and models can be developed
incorporating present data.
 The current data can be used to validate with data of other investigators.
 The channel here is smooth and rigid. Further investigation for the calculation of
discharge, velocity and boundary shear stress may also be carried out for mobile beds and
by roughening the channel bed.
 Discharge prediction through SKM is limited to prismatic rectangular straight channel in
this work. So SKM can be used for trapezoidal as well as non-prismatic channel and for
that some modification is required in the formulae.
 IDCM is restricted to straight prismatic channel only so it can be used for meandering
channel by simply modifying the formulae for discharge and velocity calculation.
 By the help of dimensional analysis the given model can be further verified.
88 | P a g e
References
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Appendix-I
APPENDIX-I
List of Publication

Published “Stage Discharge Prediction in a Prismatic Compound Channel” in
International Journal of Civil Engineering Research. ISSN 2278-3652 Vol (5), Number 3
(2014), pp. 227-232

Published “Experimental & Validation of Discharge Prediction Approaches In Straight
Two Stage Compound Channels” International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622. pp 39-44
Accepted for Publication

Paper “Analysis of Depth Averaged Velocity in Meandering Compound Channels”
accepted for 7th International Conference in Fluvial Hydraulics – River Flow 2014, Lausanne,
Switzerland.
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Appendix-II
APPENDIX-II
SKM Method in MATLAB
The experiments are conducted in NIT Rourkela 2013-2014 (Bandita channel), by considering
different water depth and the depth averaged velocity and discharge is calculated for each
relative depth. SKM is being used and a program is being written for rectangular compound
channel through MATLAB to calculate the depth average velocity, boundary shear stress and
discharge for each flow depth. The code for finding out the velocity, boundary shear stress is
being written for one relative depth and is given below.
clear all
clc
lamdamc ;
% all units are in meter
f;
%coefficent of friction;
H;
%overall depth of water
h;
%depth of the main channel
w;
%total width of the channel
S;
%bed slope of the channel
g;
%accelaration due to gravity
taumc;
%boundary shear stress in the main channel
taufp;
%boundart shear stress in flood plain
Dr=(H-h)/H;
% relative depth
B1;
%half width of the main channel
B2;
%width of the right flood plain
B3;
%width of the left flood plain
ro=1000;
%calculation of lamda for flood plain
lamdafp=lamdamc*(-0.2+1.2*(Dr^(-1.44)));
% calculation of gamma for the compound channel
Y1=sqrt(2/lamdamc)*((f/8)^0.25)*(1/H);
%Y1 indicates the gamma value for the main
channel
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Appendix-II
Y2=sqrt(2/lamdafp)*((f/8)^0.25)*(1/(H-h));
%Y2 indicates the gamma value for the
right flood plain
Y3=sqrt(2/lamdafp)*((f/8)^0.25)*(1/(H-h));
%Y3 indicates the gamma value for the left
flood plain
K1=taumc/(ro*g*H*S);
K2=taufp/(ro*g*S*(H-h));
K3=taufp/(ro*g*S*(H-h));
% calculation of secondary current
cgmmamc=ro*g*H*S*(1-K1);
cgmmafp2=ro*g*(H-h)*S*(1-K2);
cgmmafp3=ro*g*(H-h)*S*(1-K3);
% calculation of Beta
betamc=cgmmamc/(ro*g*H*S);
betafp2=cgmmafp2/(ro*g*(H-h)*S);
betafp3=cgmmafp3/(ro*g*(H-h)*S);
% calculation of k
k1=((8*g*S*H)/f)*(1-betamc);
k2=((8*g*S*(H-h))/f)*(1-betafp2);
k3=((8*g*S*(H-h))/f)*(1-betafp3);
%matrix method
[
[
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]
]
Appendix-II
I=A\B;
y=0.45:-0.05:-0.45;
for j=1:2
for i=1:19
ud(i,1)=y(i);
taub(i,1)=y(i);
Q1(i,1)=y(i);
Q2(i,1)=y(i);
for i=1:4
ud(i,2)=(I(3)*exp(Y2*y(i))+I(4)*exp(-Y2*y(i))+k2)^0.5;
taub(i,2)=(f*ro*ud(i,j)^2)/8;
Q1(i,2)=ud(i,2)*area1;
end
for i=5:10
ud(i,2)=(I(1)*exp(Y1*y(i))+I(2)*exp(-Y1*y(i))+k1)^0.5;
taub(i,2)=(f*ro*ud(i,j)^2)/8;
Q2(i,2)=ud(i,2)*area2;
end
for i=11:16
ud(i,2)=(I(1)*exp(-Y1*y(i))+I(2)*exp(Y1*y(i))+k1)^0.5;
taub(i,2)=(f*ro*ud(i,j)^2)/8;
Q2(i,2)=ud(i,2)*area2;
end
for i=16:19
ud(i,2)=(I(6)*exp(-Y3*y(i))+I(5)*exp(Y3*y(i))+k3)^0.5;
taub(i,2)=(f*ro*ud(i,j)^2)/8;
Q1(i,2)=ud(i,2)*area1;
end
end
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Appendix-II
end
ud
taub
plot(y,ud)
hold on
plot(y,taub);
hold off
table1=[y,ud];
table2=[y,taub];
fid1=fopen('depth averaged value.txt','w');
fid2=fopen('boundary shear.txt','w');
fprintf(fid1,' m/s \n');
fprintf(fid1,' %1.5f\n',table1);
fprintf(fid2,' N/m^2 \n');
fprintf(fid2,'%1.5f\n',table2);
fclose(fid1);
fclose(fid2);
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Appendix-II
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