Question 1
(a) Explain the major differences between a fluid and a solid. [4]
(b) Show that for three dimensional incompressible flow the continuity equation is given
by
vx+ vy+ vz = 0
x y z [16]
Question 2
(a) Water flows through a pipe diameter AB 1.2m at 3m/s and then passes
through a pipe BC that is 1.5m in diameter. At C the pipe forks, branch
CD is 0.8m in diameter and carries one third of the flow in
AB. The velocity in branch CE is 2.5m/s
Find:
i) The volume rate of flow in AB [2]
ii) The velocity in BC [3]
iii) The velocity in CD [2]
iv) The diameter of CE [3]
(b) Derive from first principles Bernoulli’s equation for frictionless and
incompressible flow through a pipe. Explain the terms involved. [10]
Question 3
Show that in a fully developed laminar flow a pipe of radius r and
length L, the velocity profile and the flow rate are given by:
R 2 p r
2
u 1
4 x R
p D 4
Q
128L
Page 2 of 4
Copyright: National University of Science and Technology, 2014
TIE 2202
Question 4
(a) Water flows through a pipe line which contracts from 400 diameters at A to
300 mm diameter at B and then forks, one branch being 150 mm diameter discharging
at C and the other branch 200mm diameter discharging at D. If the velocity at A is
1.8m/s and the velocity at D is 3.6 m/s. What will be the discharge at C and D and the
velocities at B and C? [12]
(b) A centrifugal pump has an impeller with dimensions r1=75mm, r2=150mm,
b1=50mm, b2=30mm, 1=2=30. For a discharge of 70 litres per second and without
shock entry to vanes, calculate
b) The speed
c) The head, and
d) The power.
Neglect losses (1=90) take the speed as 1450 r.p.m. [8]
Question 5
Water flows at U=1m/s part a flat plate with L=1m in the flow direction. The boundary layer
is tripped so that it becomes turbulent at the leading edge.
Evaluate i) the disturbance thickness [4]
ii) The displacement thickness [4]
iii) The wall shear stress at the location X= L [4]
vi. Compare with the values that would be found if laminar flow [8]
could be maintained to the same position. Assume a 1/7 power law for
turbulent velocity profile [20]
(a) A vertical venture-meter measures the flow of oil of specific gravity 0.82
and has an entrance of 125mm diameter and a throat of 50mm diam. There
are pressure gauges at the entrance and at the throat, which is 300mm above
the entrance,if the coefficient for the meter is 0.97. Find the flow rate in m3/s
when the pressure difference is 27.5 KN/m2. [10]
(b) Show that Stodola's slip factor
Sin 2
SF 1
V f2
z[1 Cot 2
U2
For impeller pumps [10]
Page 3 of 4
Copyright: National University of Science and Technology, 2014
TIE 2202
Question 7
Hot water is to be pumped by means of high pressure from a large reactor at ground-level,
through a heat exchanger to an open tank of the second floor. The inlet to the open tank is
14m above the ground floor. The tubes are made of cast iron.
Calculate: The needed pressure in the rector to pump 30 tones of water in
10 mins. [20]
Data: Tube length 20 m
Diameter 200 mm
Hot water viscosity 10-3 Ns/m2
Density 1050 kg/m3
Friction losses the coefficient of friction losses K (p = Ku2/2g)
90 bend 0.7
sharp inlet 0.45
valve 4
heat exchanger 16
Take f as = 0.006
The water level in the reactor can be regarded as constant.
Tank
High Pressure
heat
exchange
14m
Reactor
4m
End of Exam
Page 4 of 4
Copyright: National University of Science and Technology, 2014
TIE 2202
