iii
NUMERICAL MODELLING STUDY FOR APPLICATION OF HYDRAULIC
STRUCTURES FOR FLOOD CONTROL
SYAHRULNIZAM @ HELMI BIN MD SUKIMIN
A project report submitted in partial fulfilment of
the requirements for the award of the degree of
Master of Engineering (Civil – Hydraulics and Hydrology)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
May 2006
PSZ 19:16 (Pind. 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS‹
JUDUL:
NUMERICAL MODELLING STUDY FOR APPLICATION OF HYDRAULIC
___________________________________________________________________
STRUCTURES FOR FLOOD CONTROL
__________________________________________________________________
SESI PENGAJIAN: ___________________
2005/2006
SYAHRULNIZAM @ HELMI BIN MD SUKIMIN
___________________________________________________________________
(HURUF BESAR)
Saya
mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan
Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:
1.
2.
3.
4.
Tesis adalah hakmilik Universiti Teknologi Malaysia.
Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan
pengajian sahaja.
Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara
institusi pengajian tinggi.
* * Sila tandakan (9)
SULIT
TERHAD
9
(Mengandungi maklumat yang berdarjah keselamatan atau
kepentingan Malaysia seperti yang termaktub di dalam
AKTA RAHSIA RASMI 1972)
(Mengandungi maklumat TERHAD yang telah ditentukan
oleh organisasi/badan di mana penyelidikan dijalankan)
TIDAK TERHAD
Disahkan oleh
________________________________
(TANDATANGAN PENULIS)
________________________________
(TANDATANGAN PENYELIA)
Alamat tetap:
NO. 32, FELCRA BUKIT KEPONG,
____________________________________
PETI SURAT 4, 85300 LABIS, SEGAMAT,
____________________________________
JOHOR.
___________________________________|
5 MAY 2006
Tarikh: ______________________________
CATATAN:
ASSOC. PROF. DR. NORHAN ABD.
RAHMAN
___________________________________
Nama Penyelia
5 MAY 2006
Tarikh: ____________________________
* Potong yang tidak berkenaan.
** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak
berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan
tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.
‹ Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana
secara penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan
penyelidikan, atau Laporan Projek Sarjana Muda (PSM).
ii
I/We* hereby declare that I/we* have read this thesis and in my/our* opinion this
thesis entitled “Numerical Modelling Study for Application of Hydraulic
Structures for Flood Control” is sufficient in terms of scope and quality for the
award of the degree of Master in Engineering (Hydraulic and Hydrology)
Signature
: ………………………………
Assoc. Prof. Dr. Norhan bin Abd. Rahman
Name of Supervisor I : ………………………………
5th May 2006
Date
: ………………………………
Signature
Name of Supervisor II :
………………………………
En. Kamarulazlan bin Mohd. Nasir
………………………………
Data
………………………………
5th May 2006
* Delete as necessary
:
:
iv
“I declare that this project report entitled ‘Numerical Modelling Study for Application
of Hydraulic Structures for Flood Control’ is the result of my own research, except
as in cited references”
Signature
:
Author
:
………………………………
En. Syarulnizam @ Helmi bin Md Sukimin
………………………………
Date
:
5th May 2006
………………………………
v
TO:
MY FAMILY
&
EMILIA
THANKS FOR YOUR PRAYER, ATTENTION
AND SPIRITUAL…….
vi
ACKNOWLEDEMENTS
It is great pleasure to address those people who helped me throughout this
project to enhance my knowledge and practical skills especially in research area. My
deepest and most heartfelt gratitude goes to my supervisor, Assoc. Prof. Dr. Norhan
bin Abd. Rahman and En. Kamarulazlan bin Mohd. Nasir. The continuous guidance
and support from both of them have enabled me to approach work positively.
My gratitude also been extended to all personnel of the Laboratory of
Hydraulics and to all staff especially in the Department of Hydraulics and Hydrology
for their support, cooperation and constructive criticisms during the research period.
Many thanks to Universiti Teknologi Malaysia and generally to Malaysia
Government for giving me chance to pursue my study. Also thanks to Adib, Mohd.
Kamarul Huda, Mohd. Amzari, Hood Tendot, Norasman, Zulkifli, Hakim, Juwita,
Liew Kuet Fah and other classmates for their helped and support.
Finally, I wish to express my special thanks to my beloved parents and family
who gives me spirit, support and encouragement to me in completion this project. I
would also like to thank everyone who has contributed directly or indirectly to this
project. This project would have been impossible without your guidance, advice and
support.
vii
ABSTRACT
Mathematical models have been developed to resolve many problems that are
related to water profile evaluation. The flow through weir can be solved using
numerical methods and computer techniques. Storage in channel and river could be
utilized by installing weir at strategic locations along the river. This approach might
be benefited in flood control to the downstream area, but it could also cause flooding
in the upstream due to the backwater effect. The problem is whether by the
installation of those weirs will produce backwater at the upstream area. By using
numerical equation the effective application of hydraulic structures such as weir can
be determined. The computer program such as FEWMS Fst2dh is numerical program
has ability to simulate the flow in structure hydraulics. The effectiveness of weirs at
the upstream Sungai Plentong can be determined by using FESWMS Fst2dh
modelling that is enable Surface Water Modelling System (SMS) software. The
simulated water surface elevation will be used to identify which areas that are have
problem with backwater. The result observed data shows that the existing weir in the
channel at the upstream of Sungai Plentong can reduce to 80% of the channel water
depth. The simulated of water level results shows that the weir did not producing
significant increase effect of water level due a backwater.
viii
ABSTRAK
Model matematik telah lama dibangunkan untuk menyelesaikan banyak
masalah dalam penentuan profil permukaan air sungai. Kadar alir pada empangan
kecil boleh ditentukan menerusi kaedah berangka dan teknik computer. Pendekatan
ini boleh memberi faedah kepada pengawalan banjir di kawasan hilir tetapi juga
boleh berlaku banjir disebabkan oleh air balik. Dengan menggunakan kaedah
berangka keberkesanan penggunaan empangan kecil di sungai dapat ditentukan.
FESWMS Fst2dh adalah perisian yang berupaya menentukan profil permukaan air
sungai terutamanya pada struktur hidraulik dengan menggunakan pengiraan keadah
berangka. Berdasarkan aras permukaan yang ditentukan oleh Perisian FESWMS
Fst2dh dari Surface Water Modelling System (SMS) sebagai enjin utama dalam
perisian ini kawasan yang akan berlaku air balik dapat dikenalpasti. Daripada data
kedalaman air yang dicerap terhadap hulu Sungai Plentong didapati empangan kecil
di dalamnya dapat mengurangkan kedalaman air sehingga 80 peratus. Selain itu
daripada simulasi yang dilakukan tiada berlaku peningkatan kedalaman air sungai di
sebabkan air balik di belakang empangan kecil tersebut.
CHAPTER I
INTRODUCTION
1.1
INTRODUCTION
Mathematical models have been developed to resolve many problems for
water profile evaluation. A mathematical model consists of a set of differential
equations that are known to govern the flow of surface water. Usually, the
assumptions necessary to solve a mathematical model analytical are fairly restrictive.
To deal with more realistic situations, it is usually necessary to solve the
mathematical model approximately using numerical technique.
Hydraulic structures such as weir in urban stormwater drainage can be use as
detention facilities for reducing flow peak in the channel. Thus can reduce the
frequency and extent of downstream flooding. This facility can also be categorised as
on-line storage which is a facility that intercepts flow directly within a conveyances
system. On-line storage occasionally is provided as an on-site facility, though it is
more often a community or regional facility (Department of Irrigation and Drainage,
2000).
Weir is one of the applications of hydraulic structures in river. Some weirs
have sluice gates or orifices which release water at a level below the top of the weir.
Jabatan Bekalan Air (JBA) commonly used a weir to raise the level of a small river
or stream for water supply. Department of Irrigation and Drainage (DID) normally
used a weir to measure river water level. The channel of river traditionally as a
conveyance but its also can use as a temporary storage. The detain conveyance
2
concept which is the system use to optimise storage in river channel using hydraulic
structures such as weir to decrease flow and water level .
Rivers are valuable natural resources for human life, environment and
national development. There are 150 river systems in this country with 100 of them
in the
Peninsula Malaysia and 50 in Sabah & Sarawak. These river systems consist
of 1800 rivers with a total length of 38,000 km. River conservancy is one of the
responsibility of DID since its inception in the year 1932. After the 1971 major
flood in the country, DID was given the task to carry out flood mitigation programs.
One of the challenge of this department is problem of many river at downstream in
this country is not capable to cater the flow. So, one of the solution for this problem
is to construct hydraulic structures to control the flow in river channel.
1.2
PROBLEM STATEMENT
Land acquisition for the construction detention or retention ponds is not
practical because of the increase of land prices in urban area. The method on this
hydraulic structures system (weir and orifices) is to maximized storage in the channel
so that it can detain flow temporarily. But it may have risks such as backwater, trap
of rubbish and sedimentation. The proper design of weir and orifices system is
required to avoid the problem mentioned above. The design also must consider
maximum overflow, number of orifices and efficiency to reduce depth of flow in
order to come up with the optimum design.
3
1.3
IMPORTANT OF THE STUDY
For most of this century, open-channel flow and other hydraulic calculation is
based on 1-D flow approximations. Although 1-D solutions provide accurate analysis
of many problems, the assumptions upon which are based is often strained, therefore
the reliability of the solution is compromised. However, 2-D approximation of flow
in a horizontal plane often yields solutions of sufficient detail for highly complex
hydrodynamic problems. Two dimensional depth average flow solutions have been
found to provide excellent descriptions of flow in open channels and flood plains
where topography has created unusual flow pattern that are difficult to evaluate using
1D flow approximations such as flow at hydraulic structures.
1.4 OBJECTIVES OF THE STUDY
The objectives of the study are as follows:
a) To study an effectiveness of hydraulic structures for flood quantity control.
b) To evaluate flow characteristics for weir and orifices system in open channel.
1.5 SCOPE OF STUDY
To achieve the above objective, this study will focus on:
a) Sungai Plentong, Taman Pelangi Indah, Johor Bahru. (see Figure 1.1). The
location of Sungai Plentong catchment is within Taman Pelangi Indah with
minimum elevation of 39.6m above mean sea level. It is just 16 km from the
city Johor Bahru centre, along Jalan Tebrau. The site is also near to Pasir
4
Gudang Highway and North South Highway and is located in the area
upstream Sungai Plentong (see Figure 1.2). The study will involve weir and
orifices system. The study will concentrate on one weir at the downstream
area. The weir was constructed in 2001. All three weirs were constructed in
same channel (see Figure 1.3). The catchment area involved is about 0.52
km2. The size of existing monsoon drain is 11 m width and 3.3 m heights
(see Figure 1.4). The maximum flow capacity for this channel is 240 m3/s and
the estimate flow rate base on 100 years ARI from catchments area is about
23.4 m3/s.
b) The software used to simulate surface water profile is FESWMS Fst2dh
(numerical model for hydraulic structures) integrated in Surface Water
Modelling System (SMS).
c) Field Work- involved data collection such as flow rate, river water level, river
condition and topography
Figure 1.1: The Location of Study Area
5
Figure 1.2: Location of Site Area at Upstream Sungai Plentong
Figure 1.3: Location of Weir in Upstream Sungai Plentong
Figure 1.4: Detail of Weir Structures
CHAPTER II
LITERATURE REVIEW
2.1
PHYSICAL OF NUMERICAL HYDRAULIC MODELLING
Hydraulic is a branch of engineering that studies the mechanical properties of
fluids and deals with practical application of fluids in motion. There are two
subdivisions in this field, hydrostatics and hydrokinetics. Aspects of both
subdivisions will be discussed as they apply to finite elements modelling.
Hydrostatics is the study of liquids at rest, it specially focuses on the problems of
buoyancy and flotation that create pressure on dams, submerged devices and
hydraulic presses. In contrast, hydrokinetics is the study of liquids in motion and is
concerned with such as friction and turbulence generated in pipes by flowing liquids
and the use of hydraulic pressure in machinery.
2.2
OVERVIEW OF HYDRAULIC THEORY
A basic understanding of the relationship of fundamental physical principles
to water flow is necessary to recognize the type of analysis needed to solve a
particular problem. If water flows in only one direction and there is no need for
detailed velocity description, a one-dimensional (1D) study of a river will probably
be sufficient. On the other hand, if water flows in both longitudinal and transverse
7
directions, or detailed velocity description is needed, a two-dimensional (2D)
solution is probably warranted. Both 1D and 2D solutions can be obtained using
several numerical methods. One method, the finite element method, is the basis for
the calculations carried out in Flo2DH, Hivel2D and RMA2 Software’s Model from
Surfaces Water Modeling System (SMS).
2.2.1
Fundamental Principles
The interactions of matter and energy in a river system composed of water,
solid surfaces and other external forces are complex. However, there are basic
principles of physics that apply to all matter and energy and can be applied in this
circumstance to enable us to quantify and predict the flow of water and it’s on
surrounding structures and the environment. Mass, velocity, acceleration,
momentum, mechanical energy, the definition of a system and its boundaries all play
a role in developing models of river water flow.
2.2.1.1 Mass and Weight
Mass is the measure of body’s resistance to acceleration. Weight is the
product of objects mass and local value of gravitational acceleration. The standard
value for gravitational acceleration is 9.80665 m/s2 on the surface on the earth, but it
varies from a minimum of 9.77 m/s2 to a maximum of 9.83 m/s2. The mass of an
object is constant, but its weight depends on the gravitational pull acting it. Figure
2.1 is shows the relationship between mass and weight.
8
Figure 2.1: Relationship between Mass and Weight
2.2.1.2 Mass in Motion
In the absence of any resistance, a force applied to a mass will cause the mass
to accelerate at a constant rate in the direction of the applied force. A mass of 1kg
acted on by a force of 1N will accelerate at a rate of 1m/s/s if no other forces are
present. To stop the mass, a force needs to be applied in a direction opposite the
direction of motion. Because the direction in which a force is applied determines the
direction of movement, force and acceleration are vector quantities (that is, they are
defined by both a magnitude and a direction). Figure 2.2 is shows the relationship
between mass and acceleration.
9
Figure 2.2: Relationship between Mass and Acceleration
2.2.1.3 Velocity
Velocity is the speed of an object in given direction. Velocity is a vector
quantity, since its direction is important as well as its magnitude. The velocity at any
instant of a particle travelling in a curved path is the direction of the tangent to the
path at the instant considered (see Figure 2.3).
10
Figure 2.3: Direction of Velocity Magnitude
2.2.1.4 Acceleration (The Rate of Change Velocity)
Acceleration is the rate of change of velocity with respect to time. According
to Newton’s 2nd Law of Motion, acceleration is a direct result of the action of forces.
If an object increases its velocity from 1 m/s to 3 m/s in the same direction in a
period of 4 seconds, the average rate of acceleration is 0.5 meters per second. The
equation can be write as:
a=
dV
dt
(2.1)
where,
V = velocity,
t = time
A change in speed can result in slowing downs as well as speeding up. Many
people call a reduction in speed deceleration.
11
2.2.1.5 Momentum
Momentum is the product of a body’s mass and linear velocity, that is
M=mxV
(2.2)
where,
m = mass,
V = velocity.
Momentum is a vector value just like velocity because it has both a magnitude and a
direction. A force needs to be applied to the mass to change its velocity (that is, to
accelerate the mass) and thus the momentum of the body (see Figure 2.4).
Figure 2.4: Illustration of Momentum
2.2.1.5 Mechanical Energy
Mechanical or usable energy is associated with the motion of a mass and its
potential for creating motion. The kinetic energy of the mass shown above equals
one-half the product of its mass times the square of its speed. The potential energy
equals the height of the mass above some horizontal datum times its weight. The
mechanical energy is the sum of the two.
12
All the laws of mechanics are written for a system which is defined as an
arbitrary quantity of mass of fixed identity. Everything external to a system is called
the surroundings. The system is separated from its surrounding by its boundaries (see
Figure 2.5).
Figure 2.5: Illustration of Mechanical Energy.
2.2.2
Momentum Equation
Issac Newton’s Law of Motion, also called the momentum equation, states
that the resultant force acting on a system equals the rate at which the momentum of
the system changes. The mathematically, can write:
dM/dt = d(mV)/dt = F
where,
M = momentum
m = mass
F = force acting on the mass
If the mass is fixed, then
mdV/dt = ma = F
(2.3)
13
2.2.3
One Dimension (1-D) Flow Equations
The 1-D flow equations are based on cross-sectional average velocity and a
water surface elevation that is considered constant along a channel transect. Crosssectional area, which is a function of the water surface elevation and cross section
flow rate, which equals the average velocity times the cross section area are usually
the values are calculated.
2.2.3.1 One Dimension Flow Variables
The 1D flow variables are found by integrating both vertically and then
laterally across the width of a section (see Figure 2.6).
Figure 2.6: One Dimension Flow Variables
B = ∫ H dy
(2.3a)
Q = ∫ U .H dy
(2.3b)
B
B
Where,
Q = Flow rate
B = Cross Section Width
14
2.2.3.2 One Dimension Continuity Equation
The continuity equation for one-dimensional open channel flow is based on
the continuity principle applied to the “system” contained in length of channel
bounded by two transects or cross sections.
∂A ∂Q
+
=0
∂t ∂x
(2.4)
where,
A = area,
Q = Flow rate.
2.2.3.3 1D Momentum Equation
The one-dimensional momentum equation is found by applying the
momentum principle to the system contained in the channel segment.
∂Q ∂ (VQ )
∂zw τb P
+
+ gA
+
=0
∂t
∂x
∂x
ρ
where,
P = Cross Section “Wetted Perimeter”,
τb = Average Bed Shear Stress.
(2.5)
15
2.2.3.4 One Dimension Energy Equation
When flow is steady, an equation representing the conservation of mechanical
energy of the system is solved to find water surface elevations at channel cross
sections (Hadibah Ismail et. al. 1996).
Figure 2.7: One Dimension Energy Equation
2.2.4
Two Dimensional (2D) Flows
The 2D depth-averaged flow modelling takes into account the following
features (see Figure 2.8):
•
Horizontal flow composed of downstream and cross stream flows
•
Vertical components, such as width of river and other factors, such as
structures within the river (piers, weirs, culverts). These components
change the direction and speed of the water flow.
16
Figure 2.8: Downstream and Cross-stream Flows
2.2.4.1 Depth-Average Flow-2D Principles
The hydraulic principles of 2DH flows are an extension of the 1D
approximation. The 2DH approach adds spatial resolution of the flow. Instead of
cross section wide averaged flow, the flow is computed at node points using depthaveraged quantities. Flow properties are defined by flow depth and flow velocity in
the x and y directions.
Equation that describe the flow of water in rivers, floodplains, estuaries and
other surface-water bodies are based on the classical concepts of conservation of
mass and momentum. For many practical surface-water flow applications,
knowledge of the full three-dimensional flow structure is not needed and it is
sufficient to use depth-averaged flow quantities in two perpendicular horizontal
directions. A basic assumption of two-dimensional depth averaged flow
approximations is that vertical accelerations and velocities are negligible. For many
physical situations this is good approximation, except in small areas where vertical
flow may be locally significant (see Figure 2.9).
17
Figure 2.9: Illustration of Depth-Averaged Flow.
2.2.4.2 The Water Column
Equation the govern depth-average flow are obtained by applying the
conservation of mass and momentum laws to a vertical column of water as shown.
The center of the column is located at the point (x,y) and the sides have widths ∆x
and ∆y as shown. Depth at the centre of the column is H (see Figure 2.10).
Figure 2.10: Illustration of Water Column
18
2.2.4.3 Continuity Principle
From Figure 2.11 its show the conservation of mass principle requires that the
rate of change of mass within the water column equal the net flux of mass entering
the column. Solving the continuity equation helps us to determine the rate of flow in
a given direction.
Figure 2.11: Illustration of Continuity Principle
2.2.4.4 Continuity Equation
Substituting depth-average velocities U and V along the water depth H into
the general expression for conservation of mass of the system contained within the
water column yields the partial different equation that applies to appoint in space.
∂H ∂ (UH ) ∂ (VH )
+
+
=0
∂t
∂x
∂y
(2.6)
19
2.2.4.5 Momentum Principle
Applying the momentum principle (Newton’s 2nd law) to the system
contained in the column says that the rate of change of the momentum within the
column minus the rate at which momentum flows into the column plus the rate at
which momentum flows out of the column is equal to the sum of the forces acting on
the column (see Figure 2.12).
Figure 2.12: Illustration of Momentum Principle
2.2.4.6 Forces Acting on Column
Several different forces act on the vertical column of water. These forces
consist of the following:
•
Hydrostatic pressure forces
•
Drag forces at the bottom (bed) and top (surface) of the column
•
Forces on vertical faces caused by the turbulence induced transport of
momentum
•
Gravitational forces
•
Coriolis force by rotation of the earth.
20
The gravitational and Coriolis forces are body forces, that is, they act on the
column throughout and do not require direct contact. The other forces are surface or
traction forces and arise form direct contact of the water column with surrounding
media. Traction forces give rise to shear and normal stress (force per unit area).
2.2.4.7 Momentum Equations
Newton’s 2nd Law of motion tells us that the rate of change of momentum
inside the water column equals the net flux of momentum through the sides of the
column plus all the forces acting on the column. This illustrated by the equation
shown below.
JJG JJG
JG
∂ JJG
+ M column = M in − M out + ∑ F
∂t
(2.7)
2.2.4.8 Hydrostatic Pressure
Pressure is a type of stress that is exerted uniformly in all directions, its
measure is the force exerted per unit area (see Figure 2.13). A hydrostatic pressure
distribution in which the pressure varies linearly with depth will exist if vertical
velocity is small. We will assume a hydrostatic pressure distribution exists in our
two-dimensional depth-averaged (2DH) flow approximation. This assumption might
not be valid for through culverts, pressure flow through submerged bridges, or flow
over weirs or weir-type structures such as highway embankments. These are special
cases that not handled in 2D elements.
21
Figure 2.13: Illustration of Hydrostatic Pressure
2.2.4.9 Bed Shear Stresses
Shear stress at the bottom of the column is caused by frictional resistance to
flow along the bed. Bed shear stress is increased to account for the additional surface
area caused by a sloping bed (see Figure 2.14).
Figure 2.14: Illustration of Bed Shear Stresses
22
2.2.4.10 Wind Shear Stress
The Figure 2.15 is represented the concept of shear stress at the water
surface is caused by friction between the moving air and water. The shear stress
coefficient is a function of wind speed. Directional components of wind shear stress
can be computed.
Figure 2.15: Illustration of Wind Shear Stress
2.2.4.11 Turbulence
Tractive forces on vertical faces of the column are caused by the horizontal
mixing of momentum by turbulent motion. There are four stresses shown acting on
the column that is computed. Turbulence-induced shear stresses result from fast
moving parcels of water mixing with slower moving parcels and vice versa.
Magnitude of the shear stress depends on the velocity gradients and the rate of
mixing. The rate of mixing is described by the kinematics eddy viscosity.
23
2.2.4.12 Momentum Equations
Applying the momentum principle to the system contained within the water
column yields the partial differential equation shown below for flow in the x
direction (vector quantity). A similar equation results for flow in the y direction.
∂ ( HU ) ∂
∂zb
1⎡
∂ ( H τxx ) ∂ ( H τxy ) ⎤
+ ( β uvHUV ) + gH
− ΩHV + ⎢ τbx − τsx −
+
= 0 (2.8)
∂t
∂x
∂x
ρ⎣
∂x
∂y ⎥⎦
2.3
Numerical Hydraulic Modelling Review
The hydraulic behavior of side weirs as a means of limiting flow has been the
subject of many investigations such as those by Hager (1982), Uyumaz and Muslu
(1985), and Borghei et.al. (1999). However a complete analytical solution of
equations governing the flows has not been possible because of the large number of
parameters to be considered. Therefore, a clear understanding of the hydraulic
characteristics of the side weir will be a useful tool for the design engineers. A
numerical approach was applied, and two basic equations were used. One accounts
for the energy along the channel and the other relates flow rate over the weir to that
in the main channel. From the study by Yilmaz Mushu (2001), a theoretical analysis
based on the energy principle for discharge over side weir was presented and its
application was demonstrated using numerical approach. Equation that were
developed were also used to obtain hydraulic characteristics of storm water
overflows as a practical application.
From a study by Unami K. et. al (1997), a numerical model using the finiteelement and finite-volume methods was developed for the resolution of twodimensional free-surface flow equations including air entrainment and applied to
calculation of the flow in a spillway. The model is implemented on an unstructured
triangular mesh where the standard Galerkin scheme and an upwind finite-volume
24
scheme are developed to solve the continuity and the conservative momentum
equations, respectively. A physically realistic solution is obtained that represents a
series of flow state alternations from supercritical to subcritical and as well as the
surface level increase due to the entrained air. The investigations prove that the
model is valid as a primary analysis tool for hydraulic design of spillways.
While numerous steady compound channel flow studies have been
conducted, unsteady compound channel flow has received relatively little attention.
From the study by Alex George Mutasingwa (2000) was presented comparison
between 2-dimensional unsteady flow numerical model and experimental results for
flow variables in a compound meandering channel. The numerical method is based
on a finite volume discretization on a staggered grid with upwind scheme in flux, it
handles drying and wetting process for a flood plain, has the ability to handle
complex geometry and discontinuities, which are the main requirements for
modelling compound channel flows. Comparison between the measured and the
simulated water depth hydrographs showed good agreements, this demonstrate how
useful the model can be for flood prediction in channels. This unsteady flow study
shows additional temporal change of those hydraulic variables and parameters need
to be considered during flood flow. The accuracy of upstream and downstream input
data is very important for unsteady flow computations.
Backwater computation is used to model steady flows in nonuniform
channels. For a given discharge the method is also suitable to simulate slightly
unsteady flows (e.g. water surface profiles for flood waves or even dam break
waves). For sub-critical flows the solution is straightforward, wheres it become more
complicated for transcritical flows (i.e. flows which change from one stated to
another.). In this case the direction of the calculation has to be changed from
upstream to downstream or depending on the Froude number [see e.g. Molinas and
Yang (1985)]. Such a procedure is suitable for well defined hydraulic jumps (e.g. in
abrupt changes of bed slope) but is difficult to handle if the flow conditions oscillate
between sub and supercritical from one cross section to the other. From the study by
Beffa E. (1995), analysis of the discrete equations for steady open-channel flows
shows that the solution of the upstream backwater computations can be Froude
numbers exceeding one. An iterative method is proposed that allows for solution of
25
either the momentum equation or the energy equation up to a limiting Froude
number. The value of the limiting Froude number depends mainly on the friction
losses and the size of the calculation interval, i.e. distance between the cross sections.
For the calculation of channel with rough beds and relatively small flow depths a
typical value the limiting Froude number is 1.5. The method is especially useful for
transcritical flows in natural river where the flow oscillates sub and supercritical and
changing direction of calculation would be impracticable.
2.4
Hydraulic Structures of Weir
A weir is a small overflow-type dam commonly used to raise the level of a
small river or stream. Weirs have traditionally been used to create mill ponds in such
places. Water flows over the top of a weir, although some weirs have sluice gates
which release water at a level below the top of the weir. The Photo 2.1 is example of
weir have a sluice gates. The crest of an overflow spillway on a large dam is often
called a weir.
Photo 2.1: The Bridge and Weir Mechanism at Sturminster Newton on the River
Stour, Dorset.
26
Weirs are used in conjunction with locks to render a river navigable. In this
case, the weir is made significantly longer than the width of the river by forming it in
a 'U' shape or running it diagonally. This is done in order to minimize fluctuation in
the depth of the river upstream, with changes in the flow rate of the river.
A weir also gives hydrologists and engineers a simple method of measuring
the rate of fluid flow in small to medium sized streams. Since the geometry of the top
of the weir is known, and all water flows over the weir, the height of water flowing
over the weir will be an indication of the flow.
Photo 2.2: The weir at Coburg Lake in Victoria (Australia) after Heavy
While a weir will typically increase the oxygen content of the water as it
passes over the crest, a weir can have a detrimental effect on the local ecology of a
river system. A weir will artificially reduce the up-stream water velocity which can
lead to an increase in siltation. The weir may pose a barrier to migrating fish. Mill
ponds provide a water mill with the power it requires, using the difference in water
level above and below the weir to provide the necessary energy. A walkway over the
weir is likely to be useful for the removal of floating debris trapped by the weir or for
working staunches and sluices on it as the rate of flow changes. This is sometimes
used as a convenient pedestrian crossing point for the river. The photo 2.2 is example
the effectiveness weir to reduce the water depth of the river.
27
2.4.1
Types of Weir
There are different types of weir, they may be a simple metal plate with a V
notch cut into it or it may be a concrete and steel structure across the bed of a river.
A v-notch weir will give a more accurate indication of low flow rates. The most
common types of weir are the b the sharp-crested weir, broad-crested weir, v-notch
weir, the proportional weir, the circular-crested weir, embankment-crested weir and
nowadays the ogee crest weir.
2.4.1.1 The Sharp-Crested Weir
Typical sharp-crested weirs are illustrated in Figure 2.16. Equation 2.9
provides the discharge relationship for sharp-crested weirs with no end contractions
(illustrated in Figure 2.16(a))
Q = CscwBH1.5
(2.9)
where,
Q
= weir disharge (m3/s)
Cscw
= 1.81 + 0.22 (H/Hc), sharp-crested weir discharge coefficient
B
= weir base width (m)
H
= head above weir crest excluding velocity head (m).
As indicated in Equation 2.9, the value of the coefficient Cscw is known to
vary with the ratio H/Hc (see figure 2.16(c) for definition terms). For values of the
ratio H/Hc less than 0.3, a constant Cscw of 1.84 may be used.
Equation 2.10 provides the discharge equation for sharp-crested weirs with
end contractions (illustrated in Figure 2.16(b). As noted above, a constant Cscw of
1.84 may be used for values of the ratio H/Hc less than 0.3.
Q = Cscw (B – 0.1nH)H1.5
(2.10)
28
where,
n
= number of end contractions
Sharp-crested weirs will be affected by submergence when the tailwater rises
above the weir crest elevation, as shown in Figure 2.16(d), resulting in a reduced
discharge. The discharge equation for a submerged sharp-crested weir is:
Qs = QT [ 1 – (H2/H1)1.5 ]0.385
(2.11)
where,
Qs
= submerged weir discharge (m3/s)
QT
= unsubmerged weir discharge from Equation 2.9 or 2.10 (m3/s)
H1
= upstream head above weir crest (m)
H2
= downstream head above weir crest (m)
Flow over the top edge of riser pipe is typically treated as flow over a sharp-crested
weir with no end contractions. Equation 2.9 should be used for this case.
Figure 2.16: Sharp-Crested Weirs
29
2.4.1.2 The Broad-Crested Weir
The equation typically used for a broad-crested weir is:
Q = CBSWBH1.5
(2.12)
Where,
Q
= weir discharge (m3/s)
CBSW = broad-crested weir coefficient
B
= weir base width (m)
H
= effective head above weir crest (m)
If the upstream edge of a broad-crested weir is so rounded as to prevent contraction
and, if the slope of the crest is as great as the loss of head due to friction, flow will
pass through critical depth yc at the weir crest; a value of 1.7 may be used fro Cbcw.
For sharp corners on the broad-crested weir, a value of 1.44 may be used
(Department of Irrigation and Drainage, 2000).
2.4.1.3 V-Notch Weir
The discharge through a V-notch weir is shown in Figure 2.17 and be
calculated using (Department of Irrigation and Drainage, 2000):
Q = 1.38 tan (θ/2)H2.5
Where,
Q
= weir discharge (m3/s)
θ
= angle of V-notch (degree)
H
= head on apex of V-notch (m)
(2.13)
30
Figure 2.17: V-Notch Weirs
2.4.1.4 Proportional of Weir
Although more complex to design and construct, a proportional weir may
significantly reduce the required storage volume for a given site. The proportional
weir is distinguished from other control devices by having a linear head-discharge
relationship. This relationship is achieved by allowing the discharge area to vary
non-linearly with head. A typical proportional weir is shown in Figure 2.18. Design
equations for proportional weirs are follows (Department of Irrigation and Drainage,
2000):
Q
= 2.74a0.5b [H – a/3]
(2.14)
x/b
= 1 – (0.315) [arctan (y/a)0.5]
(2.15)
Where,
Q
= weir discharge (m3/s)
H
= head above horizontal sill (m)
31
Figure 2.18: Proportional Weir
2.4.1.5 The Circular-Crested Weir
Waters flowing over weirs and spillways are characterised by rapidly varied
flow region near the crest. Advantages of the circular weir shape are the stable
overflow pattern compared to sharp-crested weir, the ease to pass floating debris, the
simplicity of design compared to ogee crested design and the associated lower cost.
Circular-crested weir has larger discharge capacity (for identical upstream head) than
broad-crested weirs and sharp-crested weir (see Figure 2.19).
Related application includes roller gates and inflated flexible membrane dams
(i.e rubber dam). Roller gates (also called cylindrical gates or rolling dams) are
hollow metal cylinders held in place by concrete piers and they can be raised to allow
the flow underneath (e.g. Perikat (1958)). For small overflows it is not economical to
lift the gate and overflow is permitted. Inflated flexible membrane dams are a new
form of weir. They are used to raise the upstream water level by inflating the rubber
membrane placed across a stream or along a weir crest. Small overflow are usually
allowed without dam deflation and the overflow characteristics are somehow similar
32
to those of circular weirs (e.g. Anwar(1967)). These related applications are
nevertheless special areas of interest and need to be researched on their own.
Figure 2.19: (a) Common Circular-crested Weir and (b) Circular-crested Weir with
Sluice Gate. (Chansom et. al (1997)).
2.4.1.6 Embankment Weir
Embankment-shaped weirs are a standard engineering structure of highways,
railroads, dams and dikes. From geotechnical considerations, the embankment slope
is normally 1V:2H ( ± 10%) due to bank stability and seepage control. In this study,
such embankments with a variable crest length of zero (triangular section), is
interesting from the hydraulic point of view and the maximum length of crest used in
this study was equal to the height of the dam. Longer dams have been analyzed
33
previously. For free embankment overflow, the coefficient of discharge determines
the overflow capacity. Sloping embankments have a higher discharge than the
standard broad-crested weir with vertical faces.
Submerged embankments as found in floodplains may perform under various
regimes, including the plunging jet with a surface roller and the surface wave and the
surface jet, both with a bottom recirculation. Currently, the type of flow over an
embankment cannot be predicted. Clearly, tailwater protection, embankment erosion,
and storage considerations depend essentially regimes. In addition, the complete
velocity field for a two-dimensional flow configuration is determined, including
forward and backward flow portions and velocity distributions. The generalized
results exhibit surprises regarding the flow features of embankment dams. (Hermann
et. al. (1997)).
2.4.1.7 Aeration of Weir
While a weir will typically increase the oxygen content of the water as it
passes over the crest, a weir can have a detrimental effect on the local ecology of a
river system. A weir will artificially reduce the up-stream water velocity which can
lead to an increase in siltation. Labyrinth weirs are hose for which the weir crest is
not straight in platform. The increased crest length of labyrinth weirs gives them
clear advantage of reducing upstream levels for a particularly discharge (or
conversely increasing discharge for a given head) over low head ranges. Taylor
(1968) and Hay and Taylor (1970) carried out experiments and demonstrated the
advantage of these weirs in insituation where channel widths are limited. Cassidy
(1983) showed how these weirs can be used to effectively increase the length of a
dam spillway crest.
34
2.5
Orifices
For a single circular orifice, illustrated in Figure 2.20(a), the orifice flow can
be determined using Equation 2.16.
Q = Cd A0 2 gH 0
(2.16)
Where,
Q
= the orifice flow rate (m3/s)
Cd
= orifice discharge coefficient (0.40 – 0.62)
A0
= area of orifice (m2)
Do
= orifice diametre (m)
Ho
= effective head on the orifice measured from the centre of the
opening (m)
g
= acceleration due to gravity (9.81 m/s2)
If the orifice discharges as a free outfall, the effective head is measured from
the centreline of the orifice to the upstream water surface elevation. If the orifice
discharge is submerged, the effective head is the difference between the upstream
and downstream water surface levels. This latter condition is shown in Figure
2.20(b). For square-edged uniform orifice entrance conditions, a discharge
coefficient of 0.6 should be used for Dd < 50mm or 0.62 for Dd ≥ 50mm. For ragged
edged orifices, such as those resulting from the use of an acetylene torch to cut
orifice openings in corrugated pipe, a value of 0.4 should be used.
Pipe outlets smaller than 0.3m diameter may be analysed as a submerged
orifice as long Ho/Do is greater than as a discharge pipe with headwater and tailwater
effects taken into account, not just as an orifice. Flow through multiple orifices (see
Figure 20.20(c) can be computed by summing the flow through individual orifices.
For multiple orifices of the same size and under the influence of the same effective
35
head, the total flow can be determined by multiplying the discharge for a single
orifice by the number of openings (Department of Irrigation and Drainage, 2000).
Figure 2.20(a): Free Fall
Figure 2.20(b): Single (Submerged)
36
Figure 20.20(c): Multiple
CHAPTER III
METHODOLOGY OF STUDY
3.1
GENERAL
In this section, the numerical model with computer program will be described
and discussed. The methodology of this study is designed to achieve the objectives of
the study based on the prescribed on the scope of work. A continuous literature
review had been carried out until report writing stage so that improvement can be
made during research period. Figure 3.1 is shows the methodology for this study.
3.2
NUMERICAL MODEL
The numerical model will be applied at real field work. There is plenty of
software that has been produced for hydraulic structures application. It can in be two
dimensional models or three dimensional models. For this study one numerical
model will be used based on FESWMS for a prediction flow at hydraulic structures.
38
Start
Site Area
Sg. Plentong, Taman Pelangi Indah
Data Collection
Flowrate, Average Depth, Rainfall Data
Numerical Modelling
FESWMS Flo2dh (one/two orifices)
Network Design
Model Debugging
Model Calibration & Validation
(MAPE Method)
1)
2)
3)
4)
Model Application (Subcritical)
Unsubmerge Flow with Two Orifices as Weir
Unsubmerge Flow with One Orifices as Weir (3 Examples)
Submerge Flow with Two Orifices
Submerge Flow with One Orifices (2 Examples)
Result & Discussion
Location of Orifices for Different
Examples in Model Application
Conclusion
Figure 3.1: Flow Chart of Methodology
39
3.2.1
Background of FESWMS FST2DH Software’s
The Depth-averaged Flow and Sediment Transport Model (FESWMS Fst2dh)
is a computer program that simulates movement of water and no cohesive sediment
in rivers, estuaries, and coastal waters. FESWMS Fst2dh applies the finite element
method to solve steady state or time-dependent systems of equations that describe
two-dimensional depth averaged surface water flow and transport of no cohesive
sediment by surface waters. FESWMS Fst2dh also can use to simulate flows in
surface-water bodies where vertical velocities and accelerations are small in
comparison to those in horizontal directions. Special emphasis has been placed on
modeling highway river crossings where complex hydraulic conditions exist, because
conventional analyses based on one-dimensional flow calculations often cannot
provide the needed level of solution detail.
3.2.1.1 Overview of the Finite Element Method and Equation Solution
The finite element method is a numerical procedure for solving differential
equations encountered in problems of physics and engineering. Continuous quantities
are approximated by sets of variables at discrete points that form networks or meshes
because the finite element method can be adapted to problems of great complexity
and unusual geometry, it is an extremely powerful tool in the solution of problems in
heat transfer, fluid mechanics, and mechanical systems. Furthermore, availability of
fast and inexpensive computers allows problems that are intractable using analytic or
mechanical methods to be solved straightforwardly by the finite element method. A
large amount of literature on the subject has already emerged. Lee and Froehlich
(1986) provide an extensive, although not up-to-date, review of literature on finite
element solutions of the equations of two-dimensional depth-averaged surface-water
flow.
40
FESWMS Fst2dh uses the Galerkin finite element method to solve the
governing system of differential equations. Solutions begin by dividing the physical
region of interest into subregions, which are called elements. Two-dimensional
elements can be either triangular or quadrilateral in shape, and are defined by node
points placed along their boundaries and interiors. Lists of nodes connected to
elements are easily recorded for identification and use. Dependent variables are
approximated within elements using values defined at element node points along
with sets of interpolation functions (also called shape, basis, or trial functions).
Mixed interpolation is used in FST2DH to help stabilize the numerical solution (that
is, quadratic functions are used to interpolate unit flow rates based on solution values
at all the nodes of an element, and linear functions are used to interpolate water
depths based on solution values at only vertex nodes.)
The method of weighted residuals is applied to the governing differential
equations to form a set of equations for each element. Approximations of the
dependent variables are then substituted into the governing equations, which
generally are not satisfied exactly, to form residuals. The residuals are made to
vanish, in an average sense, when they are multiplied by weighting functions and
integrated with respect to the solution domain. Weighting functions are chosen to be
the same as the interpolation functions. By requiring summations of weighted
residuals to equal zero, the finite element equations take on integral forms.
Coefficients of the equations are integrated numerically, and all of the element
(local) equations are assembled to obtain the complete (global) system of equations.
The global set of algebraic equations is solved simultaneously in FST2DH using
Gaussian elimination.
3.2.1.2 Two-Dimensional Depth-averaged Flow Equations
Depth-averaged velocity components in the horizontal x and y coordinate
directions, respectively, are defined as follows:
41
1
U=
H
zw
∫ udz
zb
1
V=
H
zw
∫ vdz
(3.1)
zb
where,
H
= water depth,
Z
= vertical direction,
Zb
= bed elevation,
Zw
= zb + H = water surface elevation,
U
= horizontal velocity in the x direction at a point along the vertical
coordinate,
v
= horizontal velocity in the y direction at a point along the vertical
coordinate.
The coordinate system and variables are illustrated in Figure 3.2, and depth averaged
velocity is shows in Figure 3.3.
Figure 3.2: Depth-averaged velocities are mean horizontal velocities in the x and y
directions
42
Figure 3.3: Three-dimensional coordinate system and variables
Equations describing depth-averaged surface-water flow are found by
integrating the three-dimensional mass and momentum transport equations with
respect to the vertical coordinate from the bed to the water surface, considering
vertical velocities and accelerations to be negligible. The vertically-integrated mass
transport equation or continuity equation is
∂zw ∂q1 ∂q2
+
+
= qm
∂t
∂x ∂y
(3.2)
where,
q1 = UH = unit flow rate in the x direction,
q2 = VH = unit flow rate in the y direction,
qm = mass inflow rate (positive) or outflow rate (negative) per unit area.
Water mass density ρ is considered constant throughout the modeled region.
Equations describing momentum transport in the x and y directions, respectively, are
as follows:
⎞ ∂ ⎛ qq ⎞
∂z H ∂pa
∂q1 ∂ ⎛ q12 1
+ ⎜ β + gH 2 ⎟ + ⎜ β 1 2 ⎟ + gH b +
− Ωq2
∂t ∂x ⎝ H 2
∂x ρ ∂x
⎠ ∂y ⎝ H ⎠
(3.3)
∂ ( H τ xx ) ∂ ( H τ xy ) ⎤
1⎡
+ ⎢ τbx − τ sx −
−
⎥=0
ρ⎣
∂x
∂y ⎦
and
43
⎞ ∂ ⎛ qq ⎞
∂z H ∂pa
∂q2 ∂ ⎛ q12 1
+ ⎜ β + gH 2 ⎟ + ⎜ β 1 2 ⎟ + gH b +
− Ωq1
∂t ∂y ⎝ H 2
∂y ρ ∂y
⎠ ∂x ⎝ H ⎠
∂ ( H τ yx ) ∂ ( H τ yy ) ⎤
1⎡
+ ⎢ τby − τ sy −
−
⎥=0
ρ⎣
∂x
∂y ⎦
(3.4)
where β = isotropic momentum flux correction coefficient that accounts for the
variation of velocity in the vertical direction, g = gravitational acceleration, ρ = water
mass density, pa = atmospheric pressure at the water surface, Ώ = Coriolis parameter,
τbx and τby = bed shear stresses acting in the x and y directions, respectively, τsx and τsy
= surface shear stresses acting in the x and y directions, respectively and τxx, τxy, τyx
and τyy = shear stresses caused by turbulence where, for example, τxy is the shear
stress acting in the x direction on a plane that is perpendicular to the y direction.
3.2.2
Numerical Model Application
Basic steps to conduct a hydraulic problem in numerical model are introduced
in this section. The pre and post processing are very important. The finite element
meshes or cross section entities along with associated boundary conditions necessary
for analysis are needed to be created and save to model-specific files. The postprocessing is needed to view solution data such as flow velocity and steady water
depth. Generally procedures can divide into a few steps as listed below:
1.
Data collection for model input parameters.
2.
Draw geometry of model in plan view.
3.
Grid generation and mesh editing.
4.
Apply boundary conditions and initial condition.
5.
Adjust the model control such as number of iteration steps and steps
and roughness coefficient.
6.
Run the model. If necessary, repeat the run after refine the mesh grid.
7.
Examine the solution for reasonableness.
44
3.2.3
Data Collection for Model Input Parameters
Data collection such as geometry of channel, roughness coefficient
(Manning’s n), water depth at boundary and slope are required as input parameters.
For geometry and slope of the channel, it can be obtained from Department of
Irrigation and Drainage. The manning’s n was obtained by trial and error by
matching the computed water depth in the river. Figure 3.4 and Figure 3.5 are shows
the input data for orifices (assume small culvert) and weir. For variables types inlet
control flow coefficients of culvert see Appendix A.
Figure 3.4: Input Data for Orifices (assume small culvert)
45
Figure 3.5: Input Data for Weir
3.2.3
Data Input for the Geometry of Model
The geometry of channel was input into model as point coordinate in function
of x and y, which are referred to longitudinal and lateral direction respectively.
Meanwhile coordinate z represents the bed level form datum for each point. The
SMS was provided facilitated Autocad Drawing (.dxf) for reference to setup
geometry of the model. Although, initially, make sure the scale of the Autocad
drawing is correct.
46
3.2.4
Boundary Conditions
Model equations constitute a hyperbolic initial boundary value problem. The
required boundary conditions are determined using characteristics method and
assigned by selecting a specific node or node string. For this study, surface water
elevations at upstream and downstream are used for boundary condition (See Figure
3.6).
Figure 3.6: FESWMS Nodestring Boundary Condition
47
3.2.5
Run Model
During this process, the results for each element are displayed. These results
include velocity magnitude, water surface elevation, water depth, flow rate and
Froude Number. Flow rate and Froude Number need use data calculator for get the
output. Post-processing is needed to view the results.
3.2.6
Results Examination
Results from model were examined for reasonableness. To do this, postprocessing step was needed to open results in graphic or table mode. For this reason,
software named Surface Water Modelling System 9.0 (SMS) was used. Results are
presented in contour or vector mode for easy view. For calibration of the model the
MAPE (mean absolute percentage error) method was used. The equation is showed
below.
MAPE =
1 ⎡ h0 − hs ⎤
⎢
⎥ × 100%
n ⎣ h0 ⎦
(3.5)
where,
h0
= actual observed water level value
hs
= model simulated water level value
The analysis will be considered very accurate when the MAPE is in the range of 5%
to 10%.
CHAPTER IV
RESULTS AND ANALYSIS
4.1
GENERAL
As stated previously, this study involves filed site data collection and model
simulation. For every test case, results from both sources are presented together for
comparison purpose. Input parameters for each simulation are provided and results
from both sources were analysed.
In addition, the simulation was based on three separate storm events recorded
during the study. The data simulation at site gathered on 12 December 2005, 8
January 2006 and 9 January 2006. Since the weir and orifices structures system is not
available in Surface Water Modelling System (SMS), the structures system will be
modified as weir and small culvert system.
4.2
MODELLING PROCEDURE
To create a model conception, SMS includes the Map module. In this study,
AUTOCAD (Figure 4.1) feature objects are used to define the model being used.
There are four main types of feature objects:
•
Nodes – These can be by themselves or can define the end points of arcs.
49
•
Vertices – These define interior points on arc.
•
Arcs – These are the building blocks of polygons. Boundary conditions can
be assigned as attributes of an arc.
•
Polygons – These define areas for which certain attributes will apply.
Polygons attribute control element formation and material types for regions
of the mesh.
In SMS, there are three types of element such as 6-node element (triangle
shape), 8-node quadrilateral and 9-node quadrilateral. However this studies only 6node triangle and 8-node quadrilateral elements were used. The elements created
manually (select each corner node or drag a box around the corners) and
superimposed in SMS from the AUTOCAD drawing. Before that, the AUTOCAD
file must be scaled in 1:1m (Figure 4.2).
To execute SMS model using FESWMS, is needed to assign boundary
conditions. Boundary conditions can be assigned to arcs or point, but for this study
are assigned as points. Feature points may be assigned velocity or head values. For
this modelling study, water surface elevation (wse) was used for upstream boundary
condition (B/C) and its also used for downstream boundary condition across at the
bottom (Figure 4.3).
Figure 4.1: Site Topography Plan in AUTOCAD (dxf. Format)
50
51
Figure 4.2: Elements in SMS Model
26.634
Boundary Condition
at Downstream
Boundary Condition
at Upstream
25.770
Location of
Weir and Orifices
Figure 4.3: Location of Boundary Condition.
52
4.3
DATA COLLECTION
Data collection is an important stage of the study. For this study, all
information and data required such as size of channel, slope and topography are
provided by the Department of Irrigation and Drainage (DID) whilst water surface
depth are taken from observation on site. There are four position at site was taken for
water surface depth. The position is shown at Figure 4.4, Photo 4.1(a), Photo 4.1(b),
Photo 4.1(c) and Photo (d).
Figure 4.4: Water Level Recorded at Position A, B, C and D
Photo 4.1(a): Water Level Recorded at Position A
53
Photo 4.1(b): Water Level Recorded at Position B
Photo 4.1(c): Water Level Recorded at Position C
54
Photo 4.1(d): Water Level Recorded at Position D
There were three storm events recorded during the period of the study which
was considered significant. The events are 12 December 2005, 8 January 2006 and 9
January 2006. The data on 8 January 2006 is chosen for calibration whilst the data on
12 December 2005 and 9 January 2006 for validation model. Table 4.1 is shows the
data recorded on 8 January 2006 and Figure 4.5 is shows the water profiles on that
day in different time. Table 4.2 is describes about data recorded on 12 December
2005 and Figure 4.6 is shows the water profile on that day in different time. The last
data on 9 January is shows at Table 4.3 and the water surface depth profile is
illustrates on Figure 4.7.
Table 4.1: Water Level Recorded on the 8 January 2006
Position
Data 1
Data 2
Data 3
Data 4
Data 5
Data 6
Data 7
A
B
C
D
Time
10:45
10:45
10:45
10:45
Level(mm)
Time
250
10.55
350
10.55
450
10.55
50
10.55
Level(mm)
Time
350
11.00
500
11.00
700
11.00
70
11.00
Level(mm)
Time
550
11:10
600
11:10
800
11:10
100
11:10
Level(mm)
Time
800
11:20
900
11:20
940
11:20
Level(mm)
830
920
950
140
11:20
150
11:35
11:35
11:35
11:35
550
700
800
100
11:50
11:50
11:50
11:50
550
600
750
70
Time
Level(mm)
Time
Level(mm)
Surface Water Depth (m)
55
1000
Data 1(10:45)
Data 2 (10:55)
800
Data 3 (11:00)
600
Data 4 (11:10)
400
Data 5 (11:20)
Data 6 (11:35)
200
Data 7 (11:50)
0
0
20
40
60
80
100
120
Distance(m)
Figure 4.5: Surface Water Depth Profile on 8 January 2006 in Different Time
Table 4.2: Water level recorded on 12 December 2005
Data 8
Data 9
Data 10
Data 11
Data 12
Data 13
Position
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
A
13:05
200
13:10
200
13:20
150
13:25
50
13:35
40
13:45
25
B
13:05
550
13:10
450
13:20
500
13:25
350
13:35
250
13:45
100
C
13:05
500
13:10
550
13:20
500
13:25
400
13:35
300
13:45
200
D
13:05
110
13:10
110
13:20
100
13:25
50
13:35
50
13:45
30
56
Surface Water Depth (m)
600
Data 8 (13:05)
500
Data 9 (13:10)
400
Data 10 (13:20)
300
Data 11 (13:25)
200
Data 12 (13:35)
100
Data 13 (13:45)
0
0
20
40
60
80
100
120
Distance(m )
Figure 4.6: Surface Water Depth Profile on 12 December 2006 in Different Time
Table 4.3: Water Level Recorded on 9 January 2006
Data 14
Data 15
Data 16
Data 17
Data 18
Position
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
Time
Level(mm)
A
14:35
400
14:45
450
14:55
530
15:00
500
15:10
400
B
14:35
500
14:45
550
14:55
600
15:00
550
15:10
530
C
14:35
550
14:45
650
14:55
750
15:00
600
15:10
560
D
14:35
50
14:45
120
14:55
130
15:00
70
15:10
50
Surface Water Depth (m)
600
500
Data 14 (14:35)
400
Data 15 (14:45)
Data 16 (14:55)
300
Data 17 (15:00)
200
Data 18 (15:10)
100
0
0
20
40
60
80
100
120
Distance(m)
Figure 4.7: Surface Water Depth Profile on 9 January 2006 in Different Time
57
4.4
MODEL SIMULATION ON 8 JANUARY 2006 FOR CALIBRATION
AND ANALYSIS
There are seven data recorded during this day. The data recorded consists of
level various location along upstream Sungai Plentong. As stated before, there are 4
points level depth along the river was mesured (Table 4.1). The manning’s n was
obtained by trial and error by matching the computed water depth in the river. The
Data 4, Data 5 and Data 6 were chosen for simulation on this event.
4.4.1
Model Simulation on Data 4
The initial dry bed condition was applied in this model. However, there is
tolerance for the element tolerance drying or wetting. For this model simulation the
tolerance is about 0.15m. The mesh element is presented in Figure 4.2 with
maximum aspect ratio of 0.5.
Photo 4.2: Flow Pattern at the Site on Data 4
58
Results from numerical model on data 4 are presented in Figure 4.9, Figure
4.10, Figure 4.11, Figure 4.12, Figure 4.13 and Figure 4.14. Figure 4.9 shows the
results numerical model for depth of the river. Through this investigation, the higher
depth on this river is at back of weir. The highest depth is about 0.88m which not
includes dry depth flow. However, the results of velocity is opposite from the results
of the water depth. Figure 4.10 shows the higher velocity was at in front of weir
especially at location on two orifices. Figure 4.11 shows the different flow rate
pattern at the back of weir and in front of weir. The maximum flow rate for this event
is 1.19m3/s and it’s located at the both orifices. The velocity is 0.282 m/s and the
maximum Froude Number is 0.343 (Figure 4.12). Since the Froude Number is
smaller than 1, the hydraulic jump is not happen at front of weir and all the flow
along the river was subcritical. Animation can also incorporate vector plots to show
the changing flow patterns combine with scalar quantity such as velocity magnitude.
Figure 4.13 shows the vector. The conclusion can be made from that figure which is
backwater not happen at this channel especially at the back of weir on this event. The
Figure 4.14 shows one frame of the flow trace of model. It shows the flow patterns
separating through the orifices opening in the weir. On this visualisation also shows
all the flow water goes through the orifices and backwater is not occurred. For the
comparison on this model simulation, Photo 4.2 is represented in real flow patterns at
the site.
Table 4.4: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (wse)
B/C (wse)
Average
26.634
25.770
11.00
n
0.021
Slope
(Various)
Depend on Site
59
Figure 4.10: Water Velocity on Data 4
60
Figure 4.11: Flow Rate on Data 4
61
Figure 4.12: Froude Number on Data 4
62
63
Figure 4.13: Vector and Velocity Focus on the Weir on Data 4.
Figure 4.14: Visualization of Flow Patterns on Data 4
64
4.4.2
Model Simulation on Data 5
To model on this data, the features criteria on computer model still the same
compare from data 4. Although, the boundary condition is different and water level
are different. Table 4.5 is describes the input parameter for this model.
Table 4.5: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (wse)
B/C (wse)
Average
26.384
25.730
11.00
n
0.021
Slope
(Various)
Depend on
Site
Results from numerical model based on data 5 are presented in Figure 4.15,
Figure 4.16, Figure 4.17, Figure 4.18, Figure 4.19 and Figure 4.20. Figure 4.15
shows results the numerical model for depth of the river. Through this analysis it’s
showed the higher depth on this river is at back of weir. The highest depth is about
0.83m which not includes dry depth flow. However, the results of velocity it’s
opposite from the results of the depth. Figure 4.16 shows the higher velocity was in
front of weir especially at location on two orifices and its similar compare the Data 4.
Figure 4.17 shows the different flow rate pattern at the back of weir and in front of
weir. The maximum of flow rate at this event is 0.542 m3/s and it’s located at the
orifices which is represented a blue colour. The maximum velocity is 0.100 m/s and
the maximum Froude Number is 0.09 (Figure 4.18). Since the Froude Number is
smaller than 1, the hydraulic jump is not happen in front of weir and all the flow
along the river was subcritical. Animation can also incorporate vector plots to show
the changing flow patterns combine with scalar quantity such as velocity magnitude.
Figure 4.19 shows the vector and the conclusion can be made from that figure which
is backwater not happen at this channel especially at the back of weir on this event.
Figure 4.20 shows one frame of the flow trace of the model. It shows the flow
patterns separating to go through the orifices opening in the weir. On this
visualisation also was showed all the flow water goes through the orifices and
backwater is not occurred.
Figure 4.15: Water Depth on Data 5
65
Figure 4.16: Water Velocity on Data 5
66
Figure 4.17: Flow rate on Data 5
67
Figure 4.18: Froude Number on Data 5
68
69
Figure 4.19: Vector and Velocity Focus on the Weir
Figure 4.20: Visualization of Flow Patterns on Data 5
70
4.4.3 Model Simulation on Data 6
As Data 5, for model on this data, the features criteria on computer model
still the same compare from data 4. Although, the boundary condition is different and
water level are different. Table 4.6 is describes the input parameter for this model.
Table 4.6: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (wse)
B/C (wse)
Average
26.664
25.780
11.00
n
0.021
Slope
(Various)
Depend on
Site
Results from numerical model event 3 based on are presented in Figure 4.21,
Figure 4.22, Figure 4.23, Figure 4.24, Figure 4.25 and Figure 4.26. Figure 4.21
shows the results numerical model for the depth of the river. Through this analysis
it’s showed the higher depth on this river is at back of weir. The highest depth is
about 1.00m which not includes dry depth flow. However, the results are similar
compare to another event. The results of velocity is opposite from the results of the
depth. Figure 4.22 shows the higher velocity was at front of weir especially at
location on two orifices. Figure 4.23 shows the different flow rate pattern at the back
of weir and in front of weir. The maximum of flow rate on this event is 1.28 m3/s and
it’s located at inside both of orifices which is represented a blue colour. The
maximum velocity is 0.159 m/s and the maximum Froude Number is 0.178 as shown
on Figure 4.24. Since the Froude Number is smaller than 1, the hydraulic jump was
not happen in front of weir and all the flow along the river was subcritical.
Animation can also incorporate vector plots to show the changing flow patterns
combine with scalar quantity such as velocity magnitude. Figure 4.25 shows the
vector and the conclusion can be made from that figure which is backwater not
happen at this channel especially at the back of weir on this event. Figure 4.26 shows
one frame of the flow trace of model. It shows the flow patterns separating to go
through the orifices opening in the weir. On this visualisation is shown all the flow
water goes through the orifices and backwater is not occurs.
Figure 4.21: Surface Water Depth on Data 6
71
Figure 4.22: Water Velocity on Data 6
72
Figure 4.23: Flow rate on Data 6
73
Figure 4.24: Froude Number on Data 6
74
75
Figure 4.25: Vector and Velocity Focus on the Weir
Figure 4.26: Visualization of Flow Patterns on Data 6
76
4.5
CALIBRATION RESULTS
An important of any computer model is the verification of results. Surface
water modelling is no exception. Before using a surface water model to predict
results, the model should be tested for accuracy. Calibration is the process of altering
model parameters until the computed solution matches observed field within an
acceptable tolerance. Calibration is an important step before simulation model in the
channel for different flow rate and level. By using the three data recorded, the
calibration work can be done. The Data 4, Data 5 and Data 6 will be used for
calibration. The value need to be determined for calibration purpose is the bottom
roughness, n (manning). After determining the value of bottom roughness, n the
simulation prediction of the flow for different depth can be estimated.
Table 4.7: Calibration Results
U/S
D/S
Data wse (m) wse (m)
n
MAPE, %
Level Depth (m)
Level Depth (m)
Observation at Site
From Modeling
Position B Position C Position B Position C Position B Position C
4
26.634 25.770
0.021
0.90
0.94
0.88
1.03
9.57
2.22
5
26.664 25.780
0.021
0.70
0.80
0.71
0.83
3.75
1.43
6
26.384 25.730
0.021
0.92
0.95
0.88
1.03
8.42
4.35
From the Table 4.7, the level depth observation on site was showed in
different data. According to this table, the different depth between the numerical
model and site observation depth is less than 10%. Average different at position B is
7.25% and at position C is 2.67%. By using this manning roughness, n, the prediction
of flow and level of this channel for Data 4, Data 5 and Data 6 before, is accepted.
77
4.6
MODEL VALIDATION
Validation is one of the requirements for modelling. For this study, the
validations are involved 2 days data. All the data are shown on Table 4.2 and table
4.3, but only two data is chosen from each day for model validation. The results for
validation are shown on Table 4.8.
Table 4.8: Validation Results
U/S
D/S
Data wse (m) wse (m)
n
MAPE, %
Level Depth (m)
Level Depth (m)
Observation at Site
From Modeling
Position B Position C Position B Position C Position B Position C
9
26.034 25.740
0.021
0.45
0.55
0.445
0.535
1.11
2.73
11
25.994 25.730
0.021
0.35
0.40
0.33
0.41
5.71
2.5
15
26.284 25.750
0.021
0.55
0.65
0.55
0.65
0
0
16
26.364 25.76
0.021
0.60
0.75
0.59
0.71
1.67
1.67
According to the MAPE method the analysis will be consider accurate when
the error between range of 5% to 10 %. Average different at position B is 2.12% and
at position C is 1.72% which are both are less than 10%. So, the model is accepted.
4.7
MODEL EXAMPLES
After completion of the calibration and validation process, the water surface
profile for varying water surface depth can be calculated. Table 4.9 is example input
parameter for unsubmerged orifices.
78
Table 4.9: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (WSE)
B/C (WSE)
Average
26.434
25.770
11.00
n
0.021
Slope
(Various)
Depend on Site
Case 1: Unsubmerge Flow with Two Orifices
Case 1 is represented flow in channel which is not submerging the orifices.
So, the analysis flow through the orifices is as weir. From the numerical model, the
Froude Number in Case 1 for all location is not greater than 1 which means the flow
is subcritical condition. In this subcritical condition, the backwater and hydraulic
jump are not happen for this case. The summarised result for Case 1 is shown on
Figure 4.27.
Figure 4.27: Results Summary for Case 1
79
Case 2: Unsubmerge Flow with One Orifices at the left Channel from the
Downstream view.
Figure 4.28: Results Summary for Case 2
Figure 4.29: Maelstrom Happen front of Weir for Case 2
80
Case 3: Unsubmerge Flow with One Orifice at the Right Channel from The
Downstream View.
Figure 4.30: Results Summary for Case 3
Actually for Case 2 and Case 3, there is same condition of the structures of
orifices which is only use one orifices but have a different place. The summarised
results are shown on Figure 4.28 and Figure 4.30. The flow pattern on Case 2 is
shown on Figure 4.29. The Case 2 and 3 it’s very interesting because the maelstrom
is happened in front of weir. From these results the conclusion can be make which is
the backwater is not happened on both case because the velocity very slow and the
Froude Number is less than 1. From the Froude Number on both case is represented
the flow is subcritical condition.
For the case four (overflow), the boundary condition at the upstream
elevation must be highest from node elevation. The input parameter was given Table
4.10 below.
Table 4.10: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (WSE)
B/C (WSE)
Average
28.000
25.900
11.00
n
0.021
Slope
(Various)
Depend on Site
81
Case 4: Submerge Flow Weir with Two Orifices
Figure 4.31: Results Summary for Case 4
Case 5: Submerge Flow Weir with One Orifices
Figure 4.32: Results Summary for Case 5
The condition of flow for Case 4 (see Figure 4.31) and Case 5 (see Figure
4.32) is submerged flow. Although from the numerical result the maximum Froude
Number on both case is only 0.27 and still less than 1 which mean subcritical
condition. For subcritical condition the backwater definitely will not happen.
82
The example model before which are Case 2, Case 3 and Case 5 was used
one orifice that is located at left or the right of the weir. The example Case 6 is
different compare the case before because the orifice is located at the middle of weir.
Table 4.11 is input parameter for unsubmerge flow and Table 4.12 is input for
submerge flow.
Table 4.11: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (WSE)
B/C (WSE)
Average
26.434
25.770
11.00
n
0.021
Case 6: Unsubmerge Flow with one Orifices as weir
Figure 4.33: Results Summary for Case 6
Slope
(Various)
Depend on Site
83
Figure 4.34: Visualisation Flow Pattern on Case 6
Table 4.12: Input Parameter for Numerical Model
Upstream(m)
Downstream (m)
B (m)
B/C (WSE)
B/C (WSE)
Average
28.000
25.900
11.00
n
0.021
Case 7: Submerge Flow with one Orifices at a Middle of Weir
Figure 4.35: Results Summary for Case 7
Slope
(Various)
Depend on Site
84
The Case 6 and Case 7 is very good examples because the orifices is located
at the middle of the channel. From the analysis by numerical model the results on
Froude Number will be concentrated. The Froude Number for this both case is less
than 1 which is 0.12 and 0.17. So the condition for this case is subcritical and nor
backwater is produced on both cases. The summarised results for both cases are
shown on Figure 4.33 and Figure 4.35.
4.8
DIFFERENT OF WATER DEPTH
The main purpose of the installation of weir with orifices system in this
channel is to reduce the water depth. Table 4.11 is shows the different between depth
position A and position D. From the analysis, most of the different are above 80%. It
shows how effective the hydraulic structures (weir and orifices system) in this
channel.
Table 4.13: Different In Percent, % between Position A and Position D
Data
1
2
3
4
8
9
14
15
16
Level (mm)
Level (mm)
Position A
Position B
250
350
550
800
200
150
40
45
53
50
70
100
140
110
100
5
7
9
% Different
80.0
80.0
81.8
82.5
45.0
33.3
87.5
84.4
83.0
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
5.1
CONCLUSIONS
As a conclusion, the existing weir in this channel will provide 80%
effectiveness to decrease the water depth on the channel. Although it can give the
different results if the flow rate is very low but it’s not significance since the design
is consider for 100 years return period. The high effectiveness to decrease the depth
for this channel is because of high capacity of water can detain. This is because the
cross section for this channel is very high and the slope is gently so this channel has
high capacity storage. One another reason the contribution of the effectiveness for
this weir to reducing water depth is the installation series of weir on this channel. As
mention before there are three weirs on this channel.
One of the benefits on this system is can maximize the storage of the channel.
Sometimes the area of land is not enough or too high of the prices to acquire for
construction detention or retention pond. So, this system is one of the alternatives for
the designer to solve that problem. The system is still same the conventional pond
which is to reduced the peak flow because this system is facilitated to intercept flow
directly within in conveyance system. The system is call on-line storage.
86
Three data were conducted in calibration and four data in validation to obtain
a complete set data for model simulation. In comparison with these observation data
results, determination of roughness becomes the main problem. In order to determine
the most optimum orifices on the weir, a comparison for the number of the orifices
on the weir is conducted. From the numerical results two types weir was modelled
which are weir with one orifices and weir with two orifices. Both of them not
produce backwater. But for weir with one orifices is better design because its can
detain more capacity of water.
There are seven cases was modelled using numerical model. From all cases,
Case 5 is actually the highest of the Fruode Number which is 0.27. The flow is
subcritical condition. The risk of backwater and hydraulic jump still low according
the value of Froude Number. Since for Case 5 is using single orifices, so for the
optimum design on this channel, the number of orifices is suitable only one orifice.
5.2
RECOMMENDATION
As recommendation, it is proposed that the weir with orifices system
geometry is changed weir with rectangular orifices if the system will install to
another channel (see Figure 5.1). There is a lot of sedimentation at the back of
existing weir. If the weir with rectangular system used may be able to reduce the
sedimentation because of the more opening at the bottom on this system for flow.
The designer also can increase the steep of the channel because it can
increase the flow and can reduce the sedimentation. One of the reason sedimentation
is very height at the back of weir because the slope very gently and flow is very slow
and some of them not mowing because of the problem of slope. The slope of channel
must not too steep because can produce a backwater. To find the suitable slope and
optimum design for weir and orifices system the numerical model such as FESWMS
Flot2dh can be used.
87
Figure 5.1: Example Weir with Rectangular Orifices System
The weir and orifices system actually also suitable for purpose in the location
which area the rubbish is a lot in the channel. The designer can put the temporary
screen on the orifices so that the orifices can be function as rubbish trap (see Figure
5.2). For the certain time, the rubbish must be removed manually from channel to
avoid flooding. The maintenance must continue so that risk of flooding can decrease.
Sometimes the capacity of the channel is not enough to cater flow because a
lot of development happens in catchments area. As results the channel has become
sensitive to increased rates and volumes of flow discharges. The problem has become
even more aggravated by frequent intense rainfalls and the physiological nature of
basins. If the installation of the weir with orifices system is not enough to reduce the
flow, the designer can design addition retention pond beside the weir so that can
increase the capacity of volume water to detain so that can reduces the peak flow.
Figure 5.3 shows examples concept design for this method.
88
Figure 5.2: Example Weir with Rectangular Orifices Screen System
Figure 5.3: Example Weir with Rectangular Orifices and Retention Pond