Hydraulics 2006 Exam

8/6/2019 Hydraulics 2006 Exam

1/6

SCHOOL OF COMPUTING & TECHNOLOGY

CIVIL ENGINEERING

EXAMINATIONS

Module Code: CE 2206

Module Title: Hydraulics

Date: 25th May 2006

Time: 9.30 12.40 hours

INSTRUCTIONS TO CANDIDATES

Answer anyFOUR out ofSIX questions.Only FOUR will be marked.

If you attempt more than FOUR questions, please cross outthe questions you do not want to be marked, otherwise thefirst FOUR questions in the order they appear in youranswer book will be marked.

All questions carry equal marks.


2/6

Subject: CE2206 Hydraulics

1. (a) Figure Q1 below shows a broad crested weir in a 0.100 m wide horizontal openchannel. When the water depth y was 0.276 m, the discharge of water was measuredto be 0.0079 m3/s. Use this information to calculate the value of the dischargecoefficient Cd in the broad crested weir formula (given in the data sheet) in the followingtwo ways:

(i) assuming that the upstream velocity head is negligible and may be ignored

(ii) including the upstream velocity head in the calculation of the total head H

[10 marks]

(b) Use each of the Cd values from part (a) to calculate the upstream depth to thenearest millimetre, when the measured flow rate Q is 0.035 m3/s. Compare these tworesults and comment on the merits of the two methods (i) and (ii).

[15 marks]

Figure Q1

2. (a) Show from first principles that the surge pressure p resulting from slow closureof a valve on a pipeline of length L in which water flows with velocity V, is given by

t

VLp

=

Hence calculate the surge pressure when a valve is closed in t of 5 seconds, at the

end of a 100 mm diameter pipeline of length 200 m, in which the initial flow of water was10 litres/second.

[13 marks]

(b) For the pipeline in part (a) with the same initial flow rate, calculate the limitingvalue of the time t taken to close the valve, for the closure to be regarded asinstantaneous. Calculate the value of the surge pressure resulting from thisinstantaneous closure, briefly stating any assumptions made.

[12 marks]

School of Computing & Technology - May 2006 2

0.145 my


3/6


3. (a) For a pipeline of length 100 m, diameter 0.150 m, and with a Darcy friction factorthat may be assumed to have a constant value = 0.026, express the friction head losshfas a function of the flow rate Q. Local energy losses may be ignored.

[3 marks]

(b) The pipeline described in part (a) is connected to a pump whose characteristicsare given in Table Q3 below, and is used to supply water to a reservoir which is 10 mhigher than the source of the water. Determine the rate of flow, and the power used bythe pump.

[10 marks]

(c) To obtain greater output from the arrangement described above in part (b), thefollowing two options are to be considered

(i)connect a second identical pump in parallel with the original pump, bothconnected to the original pipeline.

(ii) add a second identical pipeline in parallel with the original pipeline, bothconnected to the one original pump.

In each case find the rate of flow, and the power used, and hence compare the twooptions.

[13 marks]

Flow Q (m3/s) 0 0.01 0.02 0.03 0.04 0.05Head H (m) 15.0 14.5 13.5 12.0 10.0 7.0Efficiency - 0.29 0.54 0.72 0.80 0.70

Pump dataTable Q3



4/6


4. Water flows at a rate of 5.2 m3/s in a channel of width 4.0 m which contains a sluicegate. The depth of water upstream of the sluice gate is y0. Supercritical flow at depth y1= 0.205 m emerges from beneath the sluice gate, and then after a very short distanceforms a hydraulic jump to reach the depth y2 of the subcritical flow in the channeldownstream.

(a) Sketch (not necessarily to scale) a longitudinal section of the flow at the sluicegate and the hydraulic jump, indicating the numbered points 0, 1 and 2 as used inthe subscripts above for depths, and showing the total energy head line. Alsoshow the numbered points on a sketch of the specific energy curve.

[9 marks]

(b) Calculate the depth y2 downstream of the hydraulic jump. Hence calculate theenergy head dissipated by the hydraulic jump.

[8 marks]

(c) Calculate the water depth y0 immediately upstream of the sluice gate, assumingthat no energy is lost between section 0 and section 1.

[8 marks]

5. (a) A rectangular channel has a bed width of 8 m and a bed slope of 0.001. The

Mannings roughness coefficient n = 0.020, and the flow rate in the channel is10 m3/s. Calculate the following:

(i) critical depth

(ii) normal depth (correct to two significant figures)

(iii) determine whether the flow is subcritical or supercritical

[12 marks]

(b) Explain what is meant by the term gradually varied flow, and describe theclassification system for gradually varied flow profiles. Give two different examples of wheresuch profiles may be encountered, and describe a situation where it is useful to carry outcalculations using the gradually varied flow equation.

[13 marks]



5/6


6. (a) Using the data in Figure Q6, complete the values in the empty cells in Table Q6below, for uniform flow in a circular pipe with fixed constant values of Manning's n andslope S.

d/D

(radians)

A/Afull P/Pfull R/Rfull V/Vfull Q/Qfull

1 2 1 1 1 1 1

0.75 4/3

0.5

0.25 2/3

0 0 0 0 0 0 0

Table Q6

=2

sin

A

A

full

=2P

P

full

Figure Q6[8 marks]

(b) Use your results from part (a) to plot (on graph paper) a design chart for flow inpart full circular pipes, that links the proportional depth (d/D) on the y axis toboth the proportional velocity (V/Vfull) and the proportional discharge (Q/Qfull) onthe x axis.

[7 marks]

(c) Calculate from Manning's formula the full pipe values of velocity and dischargein a 0.300 m diameter gravity pipeline at a slope of 0.003, assuming a

Manning's n value of 0.013. [4 marks]

(d) Use the chart produced in part (b) to determine the velocity and flow rate in thepipe described in part (c) when it flows part full with a proportional depth of 0.4.

[6 marks]


(radians)

d


6/6


Hydraulics Data Sheet

Density of water = 1000 kg/m3, Kinematic viscosity of water = 1.14 x 10-6 m2/s at 15oC,

Bulk modulus of water K = 2.1 x 109 N/m2,

Gravity g = 9.81 m/s2, 1000 litres = 1 m3, 1 bar = 105 N/m2

Darcy formulagD2

LVh

2

f

=

Colebrook White formula

+=

Re

51.2

D7.3

klog2

1 s

Manning formula2/13/2 SR

n

1V =

Reynolds number =VD

Re(use 4R in place of D for non circular sections)

Froude numberBgA

VFr = =

gy

Vfor a rectangular channel

Hydraulic jump

++= 2

11

2 Fr8112

1

y

yfor a rectangular channel

Critical depth 32

cg

qy = for a rectangular channel

Gradually varied flow2

fo

Fr1

SS

dx

dy

=

Broad crested weir Q = 1.705 Cd b H3/2 (metric units)

Power P = gQH

Surge pressure p = cV for instantaneous closure

Wave celerity= Kc

Quadratic equation ax2 + bx + c = 0 has solutionsa2

ac4bbx

2 =

Newton-Raphson method: if x = a is an approximate solution to f(x) = 0

then generally a better solution is given by( )( )afaf

ax

=


Documents

Hydraulics 2006 Exam