QUESTION 1: 30 Marks
a. A vertical cylinder of 0.076 m diameter is mounted concentrically in a drum of 0.08
m internal diameter. Oil fills the space between them to a depth of 0.3m. The torque
required to rotate the cylinder in the drum is 4.5 Nm when the speed of rotation is 7.5
revs/second. Assumingthat the end effects are negligible, determine the dynamic
viscosity of the oil.
(7 Marks)
b.
For the diagram shown in Figure 1, determine the gauge pressure at point A, if h1 = 1300
mm, h2 = 1500 mm, h3 = 1000 mm, andspecific gravity (SG) for Mercury = 13.6, and
SG of the oil = 0.9.
(8 Marks)
c. Water is supported by the surface shown in Figure 2. If atmospheric pressure prevails
on the side AB, determine the magnitude and line of action of the resultant hydrostatic
force on AB per unit length.Take ρw = 103 kg/m3.
(8 Marks)
Figure 1
Figure 2
d. In a vertical pipe carrying water, pressure gauges are inserted at points A and B where
the pipe diameters are 0.15m and 0.075m respectively. Point B is 2.5 m below A and
when the flow rate down the pipe is 0.02 m3/s, the pressure at A is 14715 N/m2
greater than at B. Determine the energy losses in the pipe between A and B.
(7 Marks).
QUESTION 2: 20 Marks
a. The 5m wide rectangular gate shown in Figure 3 is hinged at A. Determine the
hydrostatic resultant force, F, of the water on the gate, and its line of action.
(10 Marks)
b. Water stands in the cylindrical tank as shown in Figure 4 when no rotation occurs. If
the system is rotated about the axis symmetry of the tank, determine the allowable
angular (rotational) velocity (r.p.m) to avoid spilling.
(10 Marks)
Figure 4
Figure 3
QUESTION 3: 20 Marks
a. For the setup shown in Figure 5, determine the resultant force due to water on both
sides of the 1.3 m wide gate AB including its line of action. (10 Marks)
b. Determine if the wooden cylinder of specific gravity, SG = 0.61 will be stable if
placed vertically in oil (SG = 0.85) as shown in the Figure 6.
(10 Marks)
Figure 5
Figure 6
QUESTION 4:
20 Marks
a. For the diagram shown in Figure7, determine the difference in pressure between tanks
A and B if d1 = 340mm, d2 = 150 mm, d3 = 500 mm, d4 = 220mm, d5 = 300mm and α
= 30o. Take ρw = 103 kg/m3, ρm = 13.6 x 103 kg/m3.
(10 Marks)
b.
For the condition shown in Figure 8 (H = 3m and R = 1m), determine the magnitude of the
resultant force acting per meter width (towards the paper) on the spherical surface and its line
of action. Also explain why the line of action passes through the centre O.(10 Marks)
Figure 8
Figure 7
QUESTION 5:
20 Marks
a. For the vertical venture meter shown in Figure 9, determine the discharge, Q, in m3/s,if
the pressure gauges p1 and p2 read 1.6x105 Pa and 1.2x105 Pa respectively.(10 Marks)
b. (i) Describe and differentiate between absolute and gauge pressure.
(ii)Discuss Newton’s law of viscosity and the behaviour of viscosity of gases and liquids
with change in temperature.
(iii) Explain the cause of cavitation and its effects in flow of liquids in pipes under
pressure.
(iv) Explain and show with neat sketches the different types manometers.
(10 Marks)
Figure 9