hydraulics 2009 exam

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.

http://www.uel.ac.uk/index.htm

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)

School of Computing, Information Technology & Engineering

1

where: A1 = area of the pipe A2 = area of the throat CD = coefficient of discharge∆h = piezometric head differenceg = acceleration due to gravity


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)


2

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


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)


3


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)


4


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


5

2.0 m3.2 m


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


6


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.


7


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

hydraulics 2009 exam

Documents