Exp. (6): Flow Over Weirs
Purpose:
o To demonstrate the characteristics of flow over weirs.
o To determine the 'Coefficient of Discharge' for each type of weir.
Introduction:
In open channel hydraulics, weirs are commonly used to either regulate or to
measure the volumetric flow rate. They are of particular use in large scale situations
such as irrigation schemes, canals and rivers. For small scale applications, weirs are
often referred to as notches and invariably are sharp edged and manufactured from
thin plate material.
Apparatus:
Hydraulics Bench incorporates a weir channel. The rectangular notch weir or
(V) vee notch weir to be tested is clamped to the weir carrier in the channel by thumb
nuts.
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Figure 1: Flow over Weirs vee notch weir
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Figure 2: Flow over Weirs rectangular notch weir
Hydraulics Bench
Weir channel
(V) Vee notch weir
Hook & point gauge
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Basket of glass spheres
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Volumetric measuring tank
Rectangular weir
Hook Gauge and Scale
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There are different shapes of weirs that can be used to measure the volumetric
flow rate. These shapes with their dimension are shown in fig 3 below.
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Figure 3: Details of weirs
Theory:
Rectangular Weir:
A rectangular notch is a thin square edged weir plate installed in a weir channel as
shown in figure 4.
Figure 4: Rectangular Notch
Consider the flow in an element of height 𝛿ℎ at a depth h below the surface.
Assuming that the flow is everywhere normal to the plane of the weir and that the
free surface remains horizontal up to the plane of the weir, then
velocity through element √2𝑔ℎ
∴ Theoretical discharge through element 𝑑𝑄 = 𝑣. 𝑑𝐴 = √2𝑔ℎ. 𝑏. 𝑑ℎ
Integrating between h = 0 and h = H
H
H
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Total theoretical discharge 𝑄𝑡ℎ = ∫0 √2gh. B. dh = B√2g ∫0 h2 . dh
2
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So, 𝑄𝑡ℎ = 𝐵√2𝑔𝐻 2
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In practice the flow through the notch will not be parallel and therefore will not be
normal to the plane of the weir. The free surface is not horizontal and viscosity
and surface tension will have an effect. There will be a considerable change in the
shape of the nappe as it passes through the notch with curvature of the stream
lines in both vertical and horizontal planes as indicated in Figure 5, in particular
the width of the nappe is reduced by the contractions at each end.
Figure 5: Shape of a Nappe
The discharge from a rectangular notch will be considerably less.
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Volume
Qact  C d Qth  C d B 2 g H 2 
3
time
𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝑒
𝐶𝑑 =
2
3 𝐵√2𝑔
In British Code:
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Qact  [0.5461  0.2716 H ]( H  0.001) 2
Important Note: This Equation is special for Cussons Hydraulic Bench
(Rectangular Notch B = 10 cm ), For other notches (like Armfield Hydraulic
Bench) refer to original equation in British code.
Vee (Triangular) Notch:
A sharp edged triangular notch with an included angle of θ is shown in Figure 6
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θ
5
Qth = 15 √2g tan (2) H 2
Qact = Cd
Cd =
8
θ 5
√2g tan ( ) H 2
15
2
eintercept
8
θ
2g tan 2
15 √
Figure 6: Triangular or V Notch
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Operation:
1. FLOW
MEASUREMENT
The discharge from the weir may be measured using either the
Rotameter (if fitted) or by using the volumetric measuring tank
and taking the time required to collect a quantity of water. The
time to collect the water is at least 120 seconds to obtain a
sufficiently accurate result.
2. Measuring the
Weir Datum
head-gauge datum or gauge zero, which is defined as the gauge
reading corresponding to the level of the weir crest (rectangular weirs) or
the level of the vertex of the notch (triangular-notch weirs) …..BS ISO
3. Measuring the
Head
1438:2008
The surface of the water as it approaches the weir will fall, this is
particularly noticeable at high rates of discharge caused by high
heads. To obtain an accurate measure of the undisturbed water
level above the crest of the weir it is necessary to place the hook
gauge at a distance at least three times the head.
Experimental Procedure:
1. Place the flow stilling basket of glass spheres into the left end of the weir channel
and attach the hose from the bench regulating valve to the inlet connection into the
stilling basket.
2. Place the specific weir plate which is to be tested first and hold it using the five
thumb nuts. Ensure that the square edge of the weir faces upstream.
3. Start the pump and slowly open the bench regulating valve until the water level
reaches the crest of the weir and measure the water level to determine the datum
level Hzero.
4. Adjust the bench regulating valve to give the first required head level of
approximately 10mm. Measure the flow rate using the volumetric tank or the
rotameter. Observe the shape of the nappe.
5. Increase the flow by opening the bench regulating valve to set up heads above the
datum level in steps of approximately 10mm until the regulating valve is fully
open. At each condition measure the flow rate and observe the shape of the nappe.
6. Close the regulating valve, stop the pump and then replace the weir with the next
weir to be tested. Repeat the test procedure.
Results and Analysis:
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2.
3.
Record the results on a copy of the results sheet. Record any observations of the
shape and type of nappe paying particular attention to whether the nappe was
clinging or sprung clear, and of the end contraction and general change in shape.
Plot a graph of loge (Q) against loge (H) for each weir. Measure the slopes and the
intercepts.
From the intercept calculate the coefficients of discharge and from the slopes of
the graphs confirm that the index is approximately 1.5 for the rectangular weir
and 2.5 for the triangular weirs.
Compare the results with those predicted using the empirical formula for
rectangular weir in British Standard BS3680.
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