FACULTE DE DEVELOPPEMENT DURABLE ET D’INGENIERIE
DEPARTEMENT DE GENIE CIVIL
1ère année en BSc (Hons) Civil Engineering
Année : 2021-2022
TP : WEIRS
Name of groupe : Class : FT GC 1
Ratolonjanahary Kevin Allan Stevens Module : HYD 2
Razafindrakoto Brenda Inès Submitted to Mr J. Ramma
Villars Swan Shane Alvinio On 22/07/2022
Distribution of task
Name Task Signature
Ratolonjanahary Kevin Research
Allan Stevens
Razafindrakoto Brenda Inès Research and writing
Villars Swan Shane Alvinio Research
Contents
Introduction ................................................................................................................................ 1
1. Aim and Objectif ............................................................................................................... 2
2. Theory .............................................................................................................................. 2
a. Depending on the geometry of the section ........................................................................ 2
b. Depending on the type of flow ........................................................................................ 4
3. Experimental ..................................................................................................................... 6
4. Application in Génie civil ................................................................................................... 7
Conclusion .................................................................................................................................. 9
Référence .................................................................................................................................. 10
liste of figures
Figure 1: Rectangular weir ..................................................................................................... 3
Figure 2: Triangular weir .......................................................................................................... 3
Figure 3: Trapezoidal weir ...................................................................................................... 4
Figure 4: Narrow-crested weir ............................................................................................... 4
Figure 5: Broad-crested weir.................................................................................................. 5
Figure 6: Sharp-crested weir .................................................................................................. 6
Figure 7: Ogee weir ................................................................................................................ 6
Figure 8: Submerged or drowned weir ................................................................................ 7
Figure 9: thin-walled weir test ................................................................................................ 7
Figure 10: Dewatered slick at thin-walled weir ................................................................... 8
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Introduction
The weir is an element very frequently used in the field of hydraulics, which conveys
water courses or water basins. This alternative to the practical work will allow us to visualize
the generalities of the weir and its usefulness, that is why our group is going to evoke more in
details on the subject below.
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1. Aim and Objectif
A weir is a structure placed generally perpendicular to the flow in a canal, the liquid
flows by forming a free stream downstream of this structure. The purpose of its use is to regulate
the current that passes through the channels while calculating its flow and recording it
continuously.
2. Theory
Water flow can be influenced by the following main criteria:
• The geometry of the weir in the direction of flow : thin wall, thick wall, overflow crest
geometry.
• The geometry of the section : rectangular, triangular, trapezoidal
• The orientation of the weir in relation to the direction of the current in the water body or the
upstream watercourse.
• The type of flow : flooded, dewatered or adherent.
To measure the flow rate, the weir must be accompanied by a secondary element called
a water level meter, which is a device for measuring the water level immediately upstream.
a. Depending on the geometry of the section
There are 3 types of weir according to the geometry of the section by which we can
calculate the flow in the case of a free surface flow:
- Rectangular weir :
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•
Figure 1:
Rectangular weir
For a rectangular shape, the flow through it is represented by the following formula.
The total discharge :
2 3
𝑄𝑟𝑒𝑐 = ⋅ 𝐶𝑑1 ⋅ 𝐿 ⋅ √(2. 𝑔. 𝐻2 )
3
- Triangular weir :
Figure 2: Triangular weir
Water flow and height above the weir are related as shown in the following formula.
The total discharge :
8 𝑡𝑎𝑛𝜃 5
𝑄𝑡𝑟𝑖 = ⋅ 𝐶𝑑2 ⋅ ⋅ √2𝑔 ⋅ 𝐻2
15 2
- Trapezoidal weir :
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Figure 3: Trapezoidal weir
To calculate the flow rate through this type of weir, the load of the rectangular shape
and the two triangular shapes can be calculated, then the total flow rate will be the sum of the
latter :
𝑄𝑡𝑟𝑎𝑝 = 𝑄𝑟𝑒𝑐𝑡 + 𝑄𝑡𝑟𝑖
2 3 8 𝑡𝑎𝑛𝜃 5
𝑄 ⋅ 𝐶𝑑1 ⋅ 𝐿 ⋅ √2𝑔 ⋅ 𝐻2 + ⋅ 𝐶𝑑2 ⋅ ⋅ √2𝑔 ⋅ 𝐻2
3 15 2
b. Depending on the type of flow
There are also different types of weir depending on the flow mode.
- Narrow-crested weirs : When the value of twice the width of the crest is less than the
height of water above the crest, the weir is said to be a narrow-crested weir. However,
the narrow crested weir is hydraulically similar to a rectangular weir, so the flow
formula is the same.
Figure 4: Narrow-crested weir
2 3
𝑄 ⋅ 𝐶𝑑1 ⋅ 𝐿 ⋅ √2𝑔 ⋅ 𝐻2
3
With Q = Discharge over the weir
Cd = Coefficient of discharge
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L = Length of the weir
H = Height of water level above the crest of the weir.
- Broad-crested weirs : when twice the width of the crest is greater than the height of
water above the crest, it is said to be a wide crested weir. The flow formula is as follows
:Figure 5: Broad-crested weir
3
2
𝑄 = 1.71 ⋅ 𝐶𝑑 ⋅ 𝐿 ⋅ 𝐻2 or 𝑄 ⋅ 𝐶𝑑1 ⋅ 𝐿 ⋅ √(2. 𝑔)(𝐻 − ℎ)
3
With H = Head of water on the upstream side of the weir (i.e., at A)
h = Head of water on the downstream side of the weir (i.e., at B)
v = Velocity of the water on the downstreamside of the weir (i.e., at B)
Cd = Coefficient of discharge
L = Length of the weir.
- Sharp-crested weirs : It is a weir with a pointed crest whose thickness is kept less than
half the height of water on the weir. The flow formula is the same as for the rectangular
weir.
Figure 6: Sharp-crested weir
3
2
𝑄 ⋅ 𝐶𝑑1 ⋅ 𝐿 ⋅ √2𝑔 ⋅ 𝐻2
3
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With Cd = Coefficient of discharge
L = Length of sharp-crested weir
- Ogee weirs : the crest of a weir rises slightly from the point A which is the crest of the
weir with a pointed crest, and after reaching the maximum elevation of 0.115 H, where
H is the height of water above point A, falls in a parabolic form. The flow formula is
the same as that of the rectangle.
- Figure 7: Ogee weir
2 3
𝑄 ⋅ 𝐶𝑑1 ⋅ 𝐿 ⋅ √2𝑔 ⋅ 𝐻2
3
With Cd = Co-efficient of discharge
L= Length of an ogee weir
- Submerged or drowned weirs : it is a weir that has a downstream water level above the
upper surface of the weir. Then the total flow is calculated by dividing the water level,
considering the flow on the upper part as free flow under a water load equal to (H1-H2)
and the discharge on the lower part as submerged discharge under a load of H2.
Figure 8: Submerged or
drowned weir
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The flow rate at the top is
𝑄 2 3
1=3⋅𝐶𝑑1 ⋅𝐿⋅√2𝑔⋅(𝐻1−𝐻2)2
And the one at the bottom is
𝑄2=𝐶
𝑑1 ⋅𝐿⋅√2𝑔⋅(𝐻1−𝐻2)
Hence the total flow is : 𝑄 = 𝑄1 + 𝑄2
3. Experimental
On the experimental side, the above relationships are demonstrated by the experiment
where the height and flow of water are measured by a dial indicator using a hydraulic bench.
Figure 9: thin-walled weir test
With :
1-Test channel of HM 150
2- Rehbock weir
3- weir blade
4- water gauge
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Figure 10: Dewatered slick at thin-walled weir
With :
1: thin-walled weir
2: weir blade
3: lowering
V: flow velocity, ho height
W : weir height
4. Application in Génie civil
In the field of civil engineering, the weir plays very specific roles.
- The weir regulates the upstream flow so that it does not cause a rise in water
level that is incompatible with the absorption capacity of the mills or sluices
receiving this water, by keeping the water level constant. It then spreads out the
flood by sending an overflow of water towards a discharge arm.
- It also makes it possible to keep a minimum height of water upstream of a reach,
while maintaining a significant height of water in the river upstream, which also
made it possible to use frost stones for the inverts, the foundations and the lower,
immersed part of the bank masonry.
- The weir can also be used to cause a leakage flow by diverting the river when it
needs to be dammed temporarily to dry it out downstream so that work can be
carried out, such as repairing a riffle or a sluice gate, a wall or a water wheel
support.
- Some are designed as fishways.
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So we can say that the weir acts as a flowmeter by providing us with a relationship
between the flow and the upstream water depth while minimising the sources of uncertainty
that could negate this relationship.
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Conclusion
In short, it can be said that the principles of a weir are generally to provide a constant
flow of water for a particular purpose. This gives us an in-depth view of the use of this element
in civil engineering, as well as a practical explanation of the theory.
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Référence
• https://fr.m.wikipedia.org/wiki/D%C3%A9versoir
• Dr Guemou Travaux pratiques MDF
• https://www.gunt.de/fr/produits/deversoirs-a-paroi-mince-pour-hm-
150/070.15003/hm150-03/glct-1:pa-149:pr-550
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