Sample Question Paper for 9210-103
Graduate Diploma in Civil Engineering
Hydraulics and hydrology
Duration: three hours
You should have the
following for this examination
• one answer book
• non-programmable calculator
• pens, pencils, ruler
General instructions
• This paper consists of nine questions over two sections A and B.
• Answer five questions, any three questions from Section A and any two questions
from Section B.
• All questions have equal marks. The maximum marks for each section within a
question are shown.
• Use normal graph paper and Semi-logarithmic graph paper for Questions 2 and 8 respectively.
© The City and Guilds of London Institute
Section A
1
2
a
Explain with suitable diagrams, the difference between laminar and turbulent
flow in a circular pipe.
(4 marks)
b
Derive a formula for the loss of head due to friction in a pipeline in terms of the
velocity head and friction coefficient f assuming that the flow is turbulent,
stating any assumptions made.
(4 marks)
c
Two free-surface reservoirs whose difference of free-surface level is 13.5 m are
connected by a pipe ABC, whose highest point B is 1.5 m below the level in the
upper reservoir A. The portion AB has a diameter of 20 cm and portion BC a
diameter of 15 cm, the friction coefficient f (f=Ȝ/4) for each being 0.005. The
total length of the pipe is 3000 m. Calculate the maximum allowable length of
the portion AB if the pressure head at B must not be lower than 3 m below
atmospheric pressure. Minor head losses in the pipe line may be neglected.
.
(12 marks)
a
Explain the function of the following components in centrifugal pumps.
i
Guide vanes
ii
Volute casing
iii
Foot valve
b
What details should be specified in ordering a centrifugal pump for a given
purpose?
(3 marks)
c
Describe with suitable diagrams how a centrifugal pump should be tested to
determine the characteristic curves indicating what is meant by 'characteristic
curves'.
(3 marks)
d
A centrifugal pump tested in the laboratory at a speed of 1000 rev/min gave the
following relationship between total head and discharge:
Discharge (m3/min) 0.0
Total head (m)
22.5
3
(3 marks)
4.5
22.2
9.0
21.6
13.5
19.5
18.0
14.1
22.5
0.0
This pump operating at 1000 rev/min is connected to 300 mm diameter suction
and delivery pipes of total length 69 m and the discharge to atmosphere is at a
level of 15 m above sump level. The entrance loss is equivalent to an additional
6m of pipe and the friction coefficient f for the pipe is 0.006. Calculate the
discharge in m3 /min. Use attached worksheet WSQ2.
(11 marks)
a
Describe the factors to be considered in designing an open channel to convey
water and how the magnitude and other relevant details for these factors
should be determined.
(5 marks)
b
It is required to design an open channel of rectangular cross-section to carry 15
m3/s of water. The channel is to be designed on the economic section criterion.
The bed roughness coefficient (Manning) is 0.015. The bed slope is to be 1/1500.
Derive the necessary details for this channel stating the assumptions made.
(12 marks)
c
Explain why it is necessary to restrict the maximum and minimum velocities of
flow in the channel.
(3 marks)
2
4
a
Indicating any assumptions made, show that when the outflow from a freesurface reservoir is regulated by a rectangular sluice, the maximum discharge
occurs when the sluice opening is about two thirds (2/3) of the reservoir
elevation above the bottom of the sluice opening.
b
A rectangular sluice of width 3.0 m regulates the discharge from a free-surface
reservoir. The reservoir elevation is 15.0 m above the bottom of the sluice and
the vertical opening of the sluice is 0.5 m. The tail water depth in the channel
downstream, which is horizontal, is rectangular and also of width 3.0 m, is 4.5
m.
(5 marks)
i
Determine whether or not the sluice is drowned.
(4 marks)
ii
Calculate the discharge through the sluice neglecting frictional and
contraction effects.
(5 marks)
iii
If the tail water depth is reduced to 3.5 m, show that a hydraulic
jump will be formed and calculate the initial depth of the jump and
the power lost in the jump expressed in kw.
(6 marks)
The equation connecting initial depth d1 and sequent depth d2 of a hydraulic
jump in a rectangular channel on a level bed may be assumed as:
d2 = {d12/4 + (2q2/gd1)}1/2 - d1/2
where q is the discharge per unit width.
5
a
Explain the following, as applied to hydraulic model analysis:
i
Geometric, kinematic and dynamic similarity
ii
Distorted models of rivers
iii
Scale effect.
(3 marks)
b
The hydraulic model of a river estuary is constructed with a vertical scale of 1:50
and a horizontal scale of 1:1000. The tidal period in the estuary is 12.4 hours.
Calculate the tidal period that should be set up in the model.
c
Explain why it is necessary to have different scales horizontally and vertically.
(3 marks)
d
In the above model, a velocity was measured as 0.25 m/s. Calculate the
corresponding prototype velocity.
(4 marks)
3
(10 marks)
See next page
6
a
b
Explain the following in the context of open-channel flow:
i
Critical depth
ii
Alternate depth
iii
Critical slope
iv
Conjugate depth
v
Normal depth
(5 marks)
In gradually varied flow, show that the slope of the water surface is given by:
(5 marks)
d(d)/dL = [S0-Sf] / [1- (Q2B/(gA3)]
where So = bed slope ; Sf = friction slope; Q = Discharge ; B = width at free
surface, and A = cross-sectional area below the free surface.
c
A weir of sill height 3.0 m completely spans a channel of width 6.0 m. The
discharge equation for the weir is Q = 1.5 L H3/2 in SI units. The bed slope of the
channel is 0.0015 and Manning coefficient is 0.025. The head over the weir is
1.75 m.
i
Show that the normal depth is approximately 1.99 m.
(5 marks)
ii
Determine the critical depth and the location upstream of the weir
at which the depth of flow is 4.70 m. Use one step in the finitedifference method of analysis
(5 marks)
4
Section B
7
a
Explain one practical purpose of carrying out the routing of a flood through a
reservoir. Indicate which data is required for such an exercise and the information
that can be obtained from the process.
b
The following data relate to a reservoir to be used for a joint hydro-power and
irrigation project:
Elevation (m)
Contour area 106 (m2)
298.0
1.250
298.5
1.280
299.0
1.320
299.5
1.360
300.0
1.388
(6 marks)
300.5
1.428
The reservoir has a spillway with a sill of length 3.5 m at elevation 299.0 m. The
discharge equation for the spillway is given as:
Q = 2.68 L H3/2 in SI units.
There is a power outlet of circular cross-section and diameter 0.4 m with its centre
at elevation 282.0 m and an irrigation outlet also of circular section and diameter
0.30 m with its centre at elevation 287.5 m The discharge equation for each outlet
may be taken as :
Q = Cd A [2gH]1/2 in SI units
where, A = area of outlet, H = head above the centre of the outlet (for fully open
condition). Cd for both outlets may be taken as 0.85.
At a certain instant when both outlets are fully open, a flood represented by the
following hydrograph enters the reservoir.
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Time (hrs)
0
0.5
Flood
discharge 16.2 32.4 84.2 97.2 85.8 69.7 51.8 35.6 25.9
(m3/s)
At time = 1.0 hr, from the commencement of the entry of the flood into the
reservoir, the reservoir water surface elevation is 299.75 m. Assuming that the
increase in water surface elevation during the time interval from 1.0 hr to 1.5 hr
from commencement of entry of flood into the reservoir is įh, write down
equations in terms of įh to determine:
i
the mean discharge during the time step from 1.0 hr to 1.5 hr
reckoned from the commencement of the entry of flood into the
reservoir.
(7 marks)
ii
the reservoir elevation at time 1.5 hr from the commencement of
the entry of flood into the reservoir.
(7 marks)
5
See next page
8
a
b
Explain what is meant by the following terms:
i
Return period of a flood
ii
Annual series of flood flows
iii
Partial duration series of flood flows
iv
Frequency factor K in flood probability analysis
(4 marks)
The Gumbel flood probability relationship is given by:
QT = Qav+Ĳ(0.78 y - 0.45)
where, QT= peak flood discharge with a return period of Tr years,
y = -loge[-loge(1-1/Tr)], Ĳ = standard deviation, and
Qav = mean peak flood discharge.
The following data refer to the annual peak flood for a river measured at a gauging
station.
Year
1970
Peak flood m3/s1325
1971
1525
1972
1420
1973
1075
1974
1625
1975
1590
1976
995
1977
1475
1978
1505
1979
1680
Using this set of data, calculate the value of the flood with a return period of 100
years using:
i
The Gumbel relationship as given above
(8 marks)
ii
A semi-logarithmic plot assuming a suitable formula for probability.
Use attached worksheet WSQ8.
(8 marks)
Indicate any assumptions made.
6
9
a
Using a clearly labelled sketch describe the following items related to ground
water:
Confined aquifer, unconfined aquifer, piezometric level, water table, artesian
well, flowing well, underground spring, surface spring, base flow, surface runoff,
groundwater recharge, saturated zone, unsaturated zone.
b
The equation representing groundwater flow in an unconfined aquifer with a
horizontal impermeable base and of length L, with uniform recharge per unit
area q (LT-1) between two constant head boundaries H0 and H1 may be assumed
as:
(10 marks)
h2 = H02- [(H02-H12)/L] x + [(q x/K)] [(L-x)]
where h = height of water table above the impermeable base at a horizontal
distance x from the boundary of constant head H0 and K is the coefficient of
permeability.
Two parallel streams with a horizontal separation of 0.5 km lie on a horizontal
base of impermeable clay. Between the two streams there is a strip of land of
width 0.5 km and uniform thickness lying on the horizontal base of impermeable
clay. The coefficient of permeability of the soil of this strip of land is 8.0 m/day.
The constant heads in the two streams are 2.5 m and 1.5 m above the base.
Calculate the maximum height of water table above the impermeable base
when there is a steady recharge of 3.0 mm/day.
7
(10 marks)