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SCHOOL OF COMPUTING, INFORMATION TECHNOLOGY & ENGINEERING
CIVIL ENGINEERING & SURVEYING FIELD
EXAMINATIONS
Module Code: CE 2206
Module Title: HYDRAULICS
Date: Thursday 28th May 2009
Time: 2 hours 15 minutes(plus 10 minutes reading time)
INSTRUCTIONS TO CANDIDATES
Answer THREE out of FIVE questions. All questions carry equal marks.
Only THREE questions will be marked. If you attempt more than THREE questions, please cross out the questions you do not wish to be marked, otherwise the FIRST THREE questions in the order they appear in your answer book will be marked. A data sheet is provided at the end of the paper.
Subject: CE2206 Hydraulics
Q1. A pipeline of length 1000m, diameter 0.15m carries water at 15°C at a rate of
0.03m3/s. The pipeline has an internal surface roughness height of 1.5mm.
(a) A venturi meter with throat diameter 0.1m is used to measure the flow rate Q
through the pipeline. The flow equation for the meter is given by:
i) Explain why it is necessary to include a coefficient of discharge.
ii) Assuming a discharge coefficient of 0.97, determine the value of h that
would result.
iii) Suggest an alternative flow meter and discuss its advantages and
disadvantages when compared with the venturi meter.
(8 marks)
(b) Use the HR Wallingford chart provided to determine the velocity and the head
loss through the pipeline.
(7 marks)
(c) Determine the friction factor, λ, and the flow type by finding the position of this
flow on the Moody diagram. Comment on the relative effects of pipe roughness
and the fluid viscosity on the head loss in this case.
(10 marks)
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where: A1 = area of the pipe A2 = area of the throat CD = coefficient of discharge∆h = piezometric head differenceg = acceleration due to gravity
Subject: CE2206 Hydraulics
Q2. (a) A pump with characteristics given in Table Q2 is used to lift water a vertical
distance of 10m through a pipeline of length 180m and diameter 0.125m.
Assume a constant friction factor of 0.028, and add 10% to the pipe length
to allow for local energy losses. Determine the rate of flow and the power
used by the pump.
(12 marks)
Table Q2
(b) In order to increase the discharge, a second identical pump must be installed.
Investigate whether the second pump should be installed in series or in
parallel with the original pump. For both cases, determine the resulting
discharge, total power required and the energy used per cubic metre, and
comment on the results.
(13 marks)
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Discharge Q (m3/s) 0 0.012 0.018 0.024 0.03 0.036
Head H (m) 20.3 19.2 17.5 15.1 11.1 5.9
Efficiency - 52 67 75 71 47
Subject: CE2206 Hydraulics
Q3. (a) Water flows through a 300 m long rigid pipeline with a velocity of 3.5 m/s.
Ignoring friction losses, calculate the maximum surge pressure that will result
when a valve at the end of this pipeline is closed instantaneously.
(5 marks)
(b) Calculate how quickly in practice the valve in part (a) must be closed for this
to be considered as instantaneous.
(5 marks)
(c) Show from first principles with explanation, that the surge pressure p resulting
from complete slow closure in time interval t of a valve at the end of a pipeline
of length L, is given by:
where is the density of the fluid flowing with velocity V prior to the closure.
(7 marks)
(d) Calculate for the pipeline in part (a) what the surge pressure would be if the
valve was closed in a time interval of 6 seconds. Justify the method selected
for use in the calculation.
(6 marks)
(e) Outline ways in which the surge pressure may be reduced from the values
calculated above.
(2 marks)
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Subject: CE2206 Hydraulics
Q4. (a) A rectangular channel of width 2.4 m has Manning’s n = 0.015 and a
longitudinal slope S = 0.0005. Calculate the velocity and discharge when the
channel flows with a depth of water of 1.2 m.
(5 marks)
(b) A circular pipe of diameter 2.4 m has Manning’s n = 0.015 and a longitudinal
slope S = 0.0005. Calculate the velocity and discharge when the pipe flows
half full of water.
(5 marks)
(c) Compare and explain the similarities and differences in the answers obtained
for parts (a) and (b).
(3 marks)
(d) Sketch a design chart for flow in part full circular pipes, with proportional depth
on the vertical axis, and proportional velocity and proportional discharge on the
same horizontal axis.
(6 marks)
(e) Using the chart sketched in part (d), or otherwise, find the velocity and
discharge in the pipe described in part (b) when the flow in the pipe is one
quarter full by depth.
(6 marks)
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Subject: CE2206 Hydraulics
Q5. (a) Given that flow over a broad crested weir passes through critical depth on the
crest, show that the discharge Q (m3/s) over a weir of width b (m) is given by
the formula:
Q = 1.705 Cd b H3/2
where H is the total energy head relative to the weir crest level.
(10 marks)
(b) A broad crested weir has an upstream water depth of 3.2 m and a crest
height above bed level of 2.0 m as shown in Figure Q5. The width of the weir
is equal to 10 m, and the discharge coefficient may be taken as Cd = 1.0.
Calculate an approximate value for the discharge over the weir, assuming
that the upstream velocity head is negligible. (4 marks)
(c) For the weir described in part (b), refine the answer for the discharge by taking
account of the upstream velocity head in the calculation, giving the answer in
m3/s correct to one decimal place. (7 marks)
(d) Compare the answers for parts (b) and (c) above, and determine the
percentage error that would arise in this case from ignoring the upstream
velocity head in the calculation. (2 marks)
(e) If the channel in which the weir is located has a mild slope with normal depth of
2.5 m, identify the gradually varied flow profile that will apply upstream of the
weir. (2 marks)
Figure Q5
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2.0 m3.2 m
Subject: CE2206 Hydraulics
Hydraulics Data Sheet
Darcy formula
Sudden contraction
Sudden expansion
Colebrook White formula
Manning formula
Wide channel where q is flow rate per unit width of channel
Reynolds number (for non circular sections use 4R in place of D)
Froude number = for a rectangular channel
Hydraulic jump for a rectangular channel
Critical depth for a rectangular channel
Gradually varied flow
Broad crested weir Q = 1.705 Cd b H3/2 (metric units)
Power P = gQH
Surge pressure p = cV for instantaneous closure
Wave celerity
continued
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Subject: CE2206 Hydraulics
Density of water = 1000 kg/m3
Gravity g = 9.81 m/s2
Kinematic viscosity of water = 1.14 x 10-6 m2/s at 15oC
Bulk modulus of water K = 2.1 x 109 N/m2
1000 litres = 1 m3
1 bar = 105 N/m2
Quadratic equation ax2 + bx + c = 0 has solutions
Newton-Raphson method:
If x = a is an approximate solution to f(x) = 0
then generally a better solution is given by
Additional design charts may also be provided if these are specifically required for a numerical solution.
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Subject: CE2206 Hydraulics
Re
ynold
s Num
ber R
e
Friction Factor
0.05
0.0002
0.0001
0.00005
0.0005
0.002
0.001
0.005
0.02
0.01
Relative Roughness k/D