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The University of Nottingham Malaysia Campus

DEPARTMENT OF CIVIL ENGINEERING

A LEVEL 3 MODULE, AUTUMN SEMESTER 2010-2011 HYDRAULICS 3

Time allowed TWO Hours

Candidates may complete the front cover of their answer book and sign their desk card but

must NOT write anything else until the start of the examination period is announced

Answer FOUR questions

This module has 20% coursework assessment

All questions and parts of questions carry marks as indicated in brackets.

Only silent, self contained calculators with a Single-Line or Dual-Line Display are permitted in

this examination.

Dictionaries are not allowed with one exception. Those whose first language is not English

may use a standard translation dictionary to translate between that language and English provided that neither language is the subject of this examination. Subject specific translation

dictionaries are not permitted.

No electronic devices capable of storing and retrieving text, including electronic dictionaries,

may be used.

DO NOT turn examination paper over until instructed to do so

ADDITIONAL MATERIAL: None

INFORMATION FOR INVIGILATORS: None

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Use gravitational acceleration g = 9.81 m/s2; density of water = 1000 kg/m3; density of

sediment s = 2650 kg/m3; kinematic viscosity of water = 1.0 x 10-6 m2/s; atmospheric pressure (Patm) = 101 kPa.

1. (a) Figure Q1a shows a pipeline of length L connected from the bottom of a constant-level, upstream reservoir to a valve located at the downstream end. Initially, the

valve is closed. If h = 20 m, L = 500 m, d = 2 m, = 0.01 and Km = 0.5, calculate

the steady state velocity (V0) and the time taken to reach 90% of V0. You may use the relation:

(5 marks)

vv

vv

gh

Lvt

0

00 ln2

Figure Q1a

(b) Figure Q1b shows a pipeline connecting the upstream Reservoir 1 to the

downstream Reservoir 2.

Figure Q1b

T.W.L = Top water level M.W.L = Minimum water level G.L = Ground level

A1 = Cross-sectional area of Reservoir 1 (= 1000 m2) A2 = Cross-sectional area of Reservoir 2 (= 500 m2)

H = Head difference between Reservoirs 1 and 2

z = Difference in elevation between the base of Reservoirs 1 and 2 L = Length of pipeline connecting Reservoirs 1 and 2 (= 1000 m)

D = Diameter of pipeline connecting Reservoirs 1 and 2 (= 2 m) V = Velocity of flow through pipeline connecting Reservoirs 1 and 2

Continued on next page H23H13-E1

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At time t = 0, the water level in Reservoir 1 stands at T.W.L of 80 m and water

level at Reservoir 2 stands at M.W.L of 42 m. If = 0.01 and Km = 0.5, calculate the time for storage in Reservoir 2 to reach 4000 m3.

(10 marks)

(c) Refer to Figure Q1a. The valve at the downstream end of the pipeline is initially

opened. The valve is then adjusted such that it can give a uniform deceleration of the water in the pipe. Given, length of pipeline L = 1000 m, diameter = 1 m,

reservoir water depth h = 10 m, = 0.01, g = 9.81 m/s2. Assume incompressible

liquid, rigid pipeline and ignore minor losses. Maximum allowable surge pressure is 91 Pa:

i) What is the minimum time required to close the valve?

(3 marks)

ii) If the operating procedure required that the valve must be completely closed

in 2 seconds, what is the maximum allowable discharge from the pipeline?

(2 marks)

2. (a) A control valve is installed at the downstream end of a 2 km long pipeline of

diameter d = 500 mm. Initially, water flows through the pipeline with mean

velocity 1.0 m/s. Assume frictionless pipeline. You may use the relation:

Kc for rigid pipeline and

KEdc

1 for elastic pipeline and;

pK

Take K = 2.11 x 109 N/m2 for water and E = 2 x 1011 N/m2 for steel.

i) If steel pipeline with wall thickness 20 mm is used, calculate the magnitude of surge pressure and the corresponding density increase generated by sudden and complete closure of the downstream control valve.

(5 marks)

ii) Calculate the maximum allowable discharge if the surge pressure following

instantaneous shut down is limited to 1000 kN/m2. (4 marks)

iii) If the surge pressure following instantaneous shut down is limited to 1000

kN/m2, calculate if we can increase the discharge by replacing the steel

pipeline using concrete pipeline of the same diameter. (6 marks)

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(b) A pipeline has a control valve at the upstream end and a reservoir at the downstream end. At time t = 0, the control valve is instantaneously closed,

reducing the flow velocity V to zero.

i) Will the pressure rise or fall at the valve and by how much?

(3 marks)

ii) Assume frictionless system, plot the pressure variation with respect to

midpoint between the valve and the reservoir during the period 0 ≤ t ≤ 4Tp (where t = 0 is the time of valve closure).

(2 marks)

3. The following data relate to a wide rectangular turbulent river: Average width = 20 m

Normal flow depth = 2 m Manning’s n = 0.030

Slope = 1 m per 2 km D50 = 2 mm

(a) Under normal flow conditions:

i) Calculate the flow discharge in the river.

(2 marks)

ii) What is bed shear stress and what are its units? (3 marks)

iii) Calculate the largest particle size that can be transported as bed load. (5 marks)

iv) Calculate the mass bed load sediment transport rate for this river using the Shields sediment transport formula:

(5 marks)

msm

gD

qSq

s

crit

s

s //10

3

50

2

02

(b) The river is designed to convey the 100 years return period flood discharge (Q100).

If Q100 = 70 m3/s, determine if a gravel layer of size 500 mm is sufficient to

stabilise the river bed for Q100.

(5 marks)

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4. The following data relate to a wide rectangular turbulent river:

Average width = 20 m Normal flow depth = 2.5 m Slope = 1 m per 2 km

D50 = 0.105 mm Location 1 sediment transport rate = 0.0020 m3/s/m Location 2 sediment transport rate

(2 km downstream of Location 1) = 0.0100 m3/s/m Cr = 1.5 kg/m3 at height 1 m above the bed

Discharge = 60 m3/s K = 0.4

The Rouse formula and power law profile can be used to present the suspended mass sediment transport in a river.

The Rouse formula:

z

a

y

ay

a

y

yy

C

C

0

0

The power law profile:

z

rr

y

yCC

where KU

z*

,

1

18

2

sgd

(a) Give two factors affecting fall velocity of sediment particle? (2 marks)

(b) Based on the above data for the river:

i) Determine whether erosion or deposition is occurring in the river and calculate its rate between the two locations.

(3 marks)

ii) Calculate the suspended mass sediment transport rate for the whole river

using the power law profile.

(8 marks)

(c) At the downstream, the river has an elevation of 220.00 m and surface water

elevation of 225.00 m. The mean particle size is 0.15 mm and the shear stress at

the channel bed is 0.75 N/m2. A sample of suspended load taken at half depth of flow showed a concentration of 500 mg/L. Use the Rouse equation to determine the elevation when the relative concentration equal to 0.1.

(7 marks)

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5. (a) The supply pipeline of a hydro-electric scheme is 1 m diameter. An open surge tank

of diameter 3 m is installed along the pipeline at 200 m from the reservoir. The steady full flow to the turbine is 2.5 m3/s. Ignore friction. You can use the relations:

ag

ALT 2 and

ag

AL

A

Qz

i) Calculate the period of oscillation for the surge tank.

(1 mark)

ii) Determine the time for maximum rise of water level in the surge tank. (2 marks)

iii) The reservoir water level is maintained at 180 m above M.S.L. (mean sea level). If a 2 m freeboard is required, what is the minimum finished level at the top of surge tank?

(2 marks)

(b) Refer to Figure Q5b. The inertia of the pump motor in this pipeline is very small so

that he pump stops instantly upon power failure at time t = 0. A mechanical ratchet

does not allow reverse pump rotation. The initial flow velocity in the pipeline is 1 m/s and the wave speed is 1100 m/s. Determine the amount by which the pipeline would have to be lowered so that the hydraulic grade line at the summit does not

fall below the centreline of the pipeline during the transient-state conditions. Assume frictionless system.

(5 marks)

Figure Q5b

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(c) Seditran River is rectangular channel section with width = 20 m, depth = 2.5 m and bed slope = 0.05%. The average discharge = 60 m3/s with median sediment =

0.3 mm. The Seditran Reservoir with capacity 30 x 106 m3 is located at the downstream of Seditran River.

The Ackers-White’s equation:

m

gr

gr

n

t

A

FC

V

U

qd

yq

1*0

Where

nn

grdy

V

dg

UF

1

0

*

/10log32 and

31

2

gdd gr and 1

s

Coefficients for Ackers-White’s equation:

Coefficient Fine and transitional

( 600.1 grd )

Coarse

( 60grd )

n grdlog56.000.1 00.0

m grd83.667.1 17.0

grA grd23.014.0

C 46.3log98.0log79.2log2 grgr ddC 025.0

i) Determine the total sediment transport rate for Seditran River by Ackers-

White’s equation.

(8 marks)

ii) From your total load calculations, determine the life expectancy of the Seditran Reservoir fed by Seditran River.

(2 marks)

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