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University of Leeds

Department of Civil Engineering

Level 2 Fluid Mechanics Laboratory Class

Critical Depth Flumes

Objective

The objective of this set of experiments is to demonstrate that when flow is made to pass

through the critical depth a stable and reliable relationship exists which can be used to

determine the flow in the channel. In order to create critical depth within the flow a structure

has to be built in the channel. In this experiment three types of structure will be used, a broad

crested weir, a Venturi flume and a simplified Crump weir.

Theory

The generalised equation for critical depth flumes will be derived in the lecture course, it can

be written as

Q 1.71Cd

B(E1

h)3 / 2

where Q is the flow in m3/s

1712

3

2

3. is

g in SI units

Cdis a coefficient of discharge which should lie in the range 0.9 < C d < 1.0

B is the width of the channel at the point where the depth is critical

h is the height of the bed of the flume above the channel bed at the point where the

flow is critical

E1is the specific energy immediately upstream of the flume, this is defined as theenergy per unit weight of fluid using the bed of the channel as datum hence it has

the dimensions of length and can be written as

E yv

1 1

1

2

2g

where y1is the depth of flow immediately upstream of the flume

v1is the mean velocity of flow immediately upstream of the flume

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2. Crump Weir

Repeat the above experiment with the Crump weir.

y1 Q E1-h (E1-h)3/2

(m) (m3/sec) (m)

Width of weir (B) = ______________(m)

Height of weir (h) = _____________(m)

3. The Venturi Flume

The Venturi flume achieves the same effect as the weirs but by restricting the width instead ofraising the bed level.

Place the two halves of the Venturi flume into the channel and hold it in position with the

stretcher screw but be careful not fasten it too tightly otherwise you will split the sides of

the flume. In this case the value of the height, h, in our generalised formula is zero however

B has a value which is the width of the throat of the Venturi meter. Repeat the experiment

with this flume.

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y1 Q E1 E13/2

(m) (m3/sec) (m)

Width of flume (B) =______________(m)

Graphs

Plot the following graphs for each flume:-

1. Q against (E1- h)3/2hence determine a value for Cd

2. log Q against log (E1- h) hence determine both Cdand the power to which (E1- h)

is raised. All the data for this graph will be far away from the origin; you should

choose a scale so that the plot makes full use of the paper and then determine the

intercept by similar triangles. If you choose scales so that the origin is on the paperthen the determination of the intercept will be grossly in error.

After considering the results you should be able to answer the following questions

how well does the equation relating flow to depth upstream of the

flume describe what actually happens

how well does the concept of a constant Cdmodel the energy loss

whether or not critical depth actually occurs within the length of the

flumes

the effect of errors in the measurement of upstream depth on the

computed value of the flow

how effective the flumes are at very low flows

how resistant the flumes are to flooding

what can you say about the validity of the governing equation when flooding

occurs

If these flumes were being used to measure flow in a real river or water/sewage treatment

works then what additional design considerations would you anticipate having to take into

account?I.M. Goodwill.

January, 2004.

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