THE UNIVERSITY OF ZAMBIA
SCHOOL OF ENGINEERING
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
2017 ACADEMIC YEAR
FINAL EXAMINATIONS
CEE 3311 – FLUID MECHANICS
INSTRUCTIONS
1. Attempt any FIVE questions.
2. All questions carry equal marks (20%). Marks for sub-questions are indicated at the end of each subquestion.
3. If you fail to answer part of a question, assume a value and use it in the subsequent calculations
4. Make sure the computer number is clearly indicated on all the booklets together with the questions
attempted.
TIME: THREE (3) HOURS
CLOSED BOOK TEST
Question 1
a) Name the terms in the Bernoulli Equation
𝑉12 𝑝1
𝑉22 𝑝2
+
+ ℎ1 =
+
+ ℎ2
2𝑔 𝜌𝑔
2𝑔 𝜌𝑔

𝑝1
is
𝜌𝑔
the static pressure head

𝑉12
is
2𝑔
the dynamic pressure

𝑝
𝜌𝑔

𝑉2
2𝑔
+ ℎ is the piezometric head
𝑝
+ 𝜌𝑔 is the total pressure head or stagnation pressure head
 The sum of all 3 terms is the total head or energy head
(2 marks)
b) Briefly explain what would happen when a ship on the Zambezi River enters the Indian Ocean whose
water has a specific gravity of 1.2.
It will be lifted up and the depth below the water will reduce due to a larger buoyant force for a smaller
depth
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c) How does one choose a control volume?
It is usually chosen as a region that fluid flows into and out of.
d) The control surface may be in motion through space relative to an absolute frame of reference. In what
situation is this acceptable?
This is acceptable provided the motion is limited to constant-velocity translation
e) Briefly explain what happens to the buoyant force when a floating body is lowered slightly into the
water.
Buoyant force increases and the larger buoyant force returns the object to its original position
f)
Briefly explain the difference in the Reynolds Number between groundwater flow and fully turbulent pipe
flow
It is very small in groundwater flow while it is very high in fully turbulent pipe flow
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Question 2
a) State 2 properties of a perfect gas.
Molecules of a perfect gas:

Would behave like tiny, perfectly elastic spheres in random motion

Would influence each other only at collision

Form a volume which would be negligible in comparison with the volume in which they moved
b) Why does surface tension manifest itself only in liquids at an interface, usually a liquid-gas interface.
Because it is a property that results from the attractive forces between molecules.
c) Name the type of acceleration which takes place when a pipeline changes its diameter from 30cm to 20
cm.
Convective acceleration
d) What circumstance (s) reduces the Energy Equation to a form identical with the Bernoulli Equation?
If
•
the losses are negligible
•
there is no shaft work
•
the flow is incompressible
e) . Why is the control volume approach also called the Eulerian approach
The control volume approach is also called the Eulerian approach, in contrast to the Lagrangian approach;
control volume does not move
f)
State when flow work is done.
It is done when the pressure forces acting on the boundaries move, in our case when 𝑝1 𝐴1 and 𝑝2 𝐴2 at the
end sections move through ∆s1 and ∆s2, respectively.
(2 marks)
Question 3
a) State the three basic relations that must be satisfied in any pipe network.
b) Briefly discuss how age of a pipe affects the friction factor.
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(3 marks)
With age a pipe will corrode and become fouled, changing both the roughness and the pipe diameter,
with a resulting increase in the friction factor.
(3 marks)
c) A rectangular channel 9m wide carries 7.6m3/s when flowing 1.0m deep.
i.
What is the specific energy?
ii.
Is the flow subcritical or critical??
(8 marks)
Question 4
Given that, in Figure below, pipe 1 is 1,800m of 45cm diameter, pipe 2 is 450m of 30cm diameter, and pipe
3 is 1,350m of 20cm diameter, all galvanised iron. The elevations of the water surfaces in reservoirs A and
C are 75m and 48m, respectively, and the discharge Q2 of 60°F water into reservoir B is xx m3/s. Find the
surface elevation of reservoir B using two trials.
(20 marks)
Question 5
a) Give the reason for referring open channel flow as gravity flow.
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b)
c)
d)
e)
The flow in such a channel is caused not by some external head, but rather only by the gravity
component along the slope of the channel. Thus open-channel flow is often referred to as free-surface
flow or gravity flow.
State two applications of the hydraulic jump
 Scour protection
 Where velocity of fluid has to be reduced
(4 marks)
Using the equations below, prove that the streamlines and equipotential lines are everywhere
perpendicular to each other.
𝑑𝜑 = −𝑣𝑑𝑥 + 𝑢𝑑𝑦
𝑑∅ = −𝑢𝑑𝑥 + 𝑣𝑑𝑦
Along a streamline, ψ = constant, so dψ = 0, and from the first equation (14.14) we get dy/dx = v/u.
Along an equipotential line, ϕ = constant, so dϕ = 0, and from the second equation (14.20) we get dy/dx
= -u/v. Geometrically, this tells us that the streamlines and equipotential lines are orthogonal, or
everywhere perpendicular to each other. As a result, the stream function and the velocity potential are
known as conjugate functions.
(5 marks)
A piece of wood of specific gravity 0.651 is 80mm square and 1.5m long. How many newtons of lead
weighing 110kN/m3 must be fastened at one end of the stick so that it will float upright with 0.3m out of
water?.
(8 marks)
Question 6
Water flows through a horizontal pipe bend and exits into the atmosphere. The bend reduces diameter from 8cm to
4cm. The flow rate is 0.01m3/s. Calculate the force in each of the rods holding the pipe bend in position. Neglect
body forces and viscous effects.
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(20 marks)
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Question 7
a) distinguish between drag and lift in external flows.
Drag is parallel to the motion while lift is perpendicular to it.
(2 marks)
b) What is the usual definition of the thickness of the boundary layer?
The thickness δ of the boundary layer is usually defined as the distance from the boundary to the point
where the velocity is 99% of the undisturbed velocity, i.e., to where u = 0.99U.
(4 marks)
c) A pipe carrying oil of specific gravity 0.877 changes in size from 150mm at section E to 450mm at
section R. Section E is 3.66m lower than R, and the pressures are 91.0kPa and 60.3kPa, respectively.
If the discharge is 0.146m3/s, determine
i.
the lost head
ii.
the direction of flow?
(14 marks)
USEFUL HINT
Re 
vD

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END OF EXAMINATION
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