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European Journal of Applied Sciences – Vol. 10, No. 4
Publication Date: August 25, 2022
DOI:10.14738/aivp.104.12709. Khadka, D. B., & Bhandari, P. (2022). Effects of Bed Materials to Flow Characteristics on Open Channel and Gradually Varied Flow
Simulation Using Genetic Algorithm (GA). European Journal of Applied Sciences, 10(4). 1-20.
Services for Science and Education – United Kingdom
Effects of Bed Materials to Flow Characteristics on Open Channel
and Gradually Varied Flow Simulation Using Genetic Algorithm
(GA)
Dak Bahadur Khadka
Institute of Engineering, Tribhuwan University
Purwanchal Campus Dharan
Prajwal Bhandari
Institute of Engineering, Tribhuwan University
Purwanchal Campus Dharan
ABSTRACT
Determination of accurate roughness coefficient was realized necessary for
hydraulic parameters estimation in open channel flow. For the purpose this study
was planned to carry out on experimental basis in hydraulic laboratory hall of
campus itself. In this study, a combination between experimental and numerical
models study were carried out to investigate the influence of bed roughness on flow
characteristics. Experiments were conducted on six bed materials (Sand, Gravel,
Cement plaster, Grass, Formica and cast iron (original bed of channel)) in three
conditions. Firstly the discharge was varied at same tail water level. Secondly the
depths were varied for same discharge and thirdly the depths were measured for
different discharges for each bed material Results were analyzed and were
graphically presented .The Manning roughness coefficient was estimated for each
bed material using the experimental and discharge optimization technique. The
percentages of errors between the observed and predicted were reported. Since the
channel represents compound case having glass wall and different bed material, the
roughness coefficient of each bed materials were predicted by optimization on
genetic algorithm to the lotter’s modified equation in which the exponent alpha
value varies from 1.28 to 1.76 The shear stress distribution was examined by first
and second approximation theory on smooth rectangular channel on Knight et al
(1984) model. It was compared with the experimental average shear stress and was
found the first approximation theory over estimated to the experimental value
whereas second approximation result was within the average relative error of
1.61% for bed. Side wall/bed stress ration was found of 0.61. Similarly gradually
varied flow was simulated in python using optimal value of roughness coefficient.
Key Words: Estimation of open channel roughness, parameter estimation, optimization
method, GVF profiles.
INTRODUCTION
Background
River hydraulics is complex phenomena in hydrology. The hydraulic parameters of natural
river estimation are a difficult task especially in large river. This parameter depends on
resisting property of the bed materials of river .The large discharge in river causes high velocity
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European Journal of Applied Sciences (EJAS) Vol. 10, Issue 4, August-2022
Services for Science and Education – United Kingdom
in steep terrain and large depth in plain region which controls the resisting property of the river
boundary. The material properties on river bed affects to the flow characteristics.[1] Exact
estimation of the hydraulic parameters of a natural river is useful for river engineering for the
sustainable construction of hydraulic structures like bridge, culvert, dam, spillway, cross
drainage structures. Due to these structures the flow becomes non- uniform at up stream of
structure section that causes high variation on hydraulic parameters of channel which leads to
the effect on the flow rate and energy of water. The gradually varied flow on upstream and
rapidly varied flow on downstream of the reservoir at structure section may cause high
deposition and degradation of soil that control the stability of structures. Reliable and
sustainable structures to be constructed for large projects the effects on hydraulic parameters
of Natural River are to be analyzed on different flow (steady, unsteady, and uniform as well as
non -uniform flow) conditions. The measurement of flow depth and wetted perimeter on
natural large rivers is complex and inconvenient work. Direct measurement of this parameter
is not possible in many cases.[2] The most important parameters to be considered are hydraulic
mean radius, hydraulic depth, water conveyance and section factor in open channel which
depends on roughness of bed and side slope material its type, property and homogeneity. The
roughness of Boundary surface condition that depends on the soil type and its sizes of river
affect the flow discharge of the channel inversely. [1]Seepage loss from river bed causes high
variation on roughness value of river and it uderpredict the real discharge of the river which
may lead to the failure of hydraulic structures. The effect of seepage on hydraulic parameters
is equally significant for stability of structures.[3]. River flow analysis is difficult in bend in case
of meandering channel section.[4] So exact estimation of this roughness value of Natural River
at different flow condition is needed. Many research works have been carried out for roughness
and its effect in natural rivers as well as in artificial channel. However these are not sufficient
to tackle the problems in many conditions. The present technology and tools has made the
study more effective today. We have advanced tools for the study. But the validation of such
tools is compulsory for its validation and reliability. The genetic algorithm is widely used for
the optimization of the river properties analysis which consist computer coding on high level
language.[5] This research work was initiated to investigate the roughness value and its effect
to flow characteristics on open channel at uniform as well non uniform gradually varied flow
conditions for different bed materials experimentally.
OBJECTIVE
The aims of the research are to have better understanding on the flow characteristics in non- mobile bed compound straight rectangular channels having different bed materials. The study
has been carried out to achieve the following objectives:
(I)To characterize and quantify the flow characteristics in the compound straight channels on
different bed materials.
(II)To distinguish the effects of bed roughness on flow characteristics and to establish the
relationship of bed roughness with the flow properties for each bed material.
(III) To analyze shear stress Distribution on bed and side wall of rectangular channel.
(IV)To simulate and evaluate the roughness values of the channel on non-uniform gradually
varied flow in python on straight rigid boundary channel.
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Khadka, D. B., & Bhandari, P. (2022). Effects of Bed Materials to Flow Characteristics on Open Channel and Gradually Varied Flow Simulation Using
Genetic Algorithm (GA). European Journal of Applied Sciences, 10(4). 1-20.
URL: http://dx.doi.org/10.14738/aivp.104.12709
LITERATURE REVIEW
Theories and controlled Equations on uniform flow in open channel
In open channel flow analysis the computation of flow characteristics in prismatic channel is
easier as the flow is steady and uniform along the channel length. But if the channel geometries
change it causes the flow non uniform which leads to the changes in flow properties. Channel
roughness value is more significant for the flow rate control in compound channel having
different material on bed and side wall. The computation of composite roughness in compound
channel is necessary for the flow characteristics analysis. In case of Natural River the flow
characteristics computation is more complex as the measurement of its geometric parameters
is difficult for large rivers[7]. Optimization technique is one of the best alternatives for the
analysis on compound artificial channel as well as natural rivers. For this the governing theories
and equation for the flow analysis is to be well understood. In case of uniform flow condition
where discharge remains constant Manning’s and Chezy’s equations are mostly used. For the
river flow measurement area velocity method is most common.[8] The manning’s equation for
open channel flow is given as:
� = !
" ��#/%√�� (1)
Where Q is flow rate, n is manning’s roughness value of the boundary surface. A is the wetted
section area , R is the hydraulic mean depth also called hydraulic Radius which is the ratio of
wetted section to the wetted perimeter and So is the longitudinal bed slope of the channel. In
this equation the roughness value is the function of flow properties flow depth, velocity,
Reynolds number, Froude number and Darcy friction factor of channel. For the same material
the computation of roughness value can be obtained by the manning’s equation directly. But in
case of compound channel as shown figure 1 below the composite roughness is to be computed.
For this there are different mathematical models given as[5]:
1. Cox (1973)
�& = ∑("! )!)
) (2)
2. Yen (2002)
�& = ∑("+,+)
, (3)
3. Horton (1933)
�& = *
!
, ∑(��-��)0
.
(4)
4. Pavlovskii Method (1930)
�& = 1∑ (,/"/#) $
%
, (5)
5. Colebatch Method (1940)
�& = 2
∑ 0)$"$%.'1 $
%
) 3
#/%
(6)
6. Lotter’s Method (1930)
�& = ,2'/)
∑ 3
*$+$'/)
,$ 4 $
%
(7)
7. Krishnamurthy and Christensen Method (1970)
�& = ��� 6
∑ 0,$5$
$6""$1 $
%
∑ 0,$ 5$%.'1 $
%
7 (8)