Tutorial 1 - Chapter 1 Fluid Properties

UNIVERSITI TEKNIKAL MALAYSIA MELAKA
FAKULTI KEJURUTERAAN MEKANIKAL
TUTORIAL 1
CHAPTER 1: FLUID AND ITS PROPERTIES
1. (a) Calculate the weight of a reservoir of oil if it has a mass of 825 kg. [8.093 kN]
3
(b) If the reservoir has a volume of 0.917 m , compute the density, specific weight, and the
3 3
specific gravity of the oil. [900 kg/m ; 8.83 kN/m ; 0.90]
2. A cylindrical can, 150 mm in diameter, is filled to a depth of 100 mm with a fuel oil. The oil has a
3
mass of 1.56 kg. Calculate its density, specific weight, and specific gravity. [883 kg/m ; 8.659
3
kN/m ; 0.883]
3. A plate, 0.5 mm distant from a fixed plate, moves at 0.25 m/s and requires a force per unit area
of 2 Pa to maintain this speed. Determine the viscosity of the substance between the plates.
[0.004 kg/ms]
4. A shaft 80 mm in diameter is being pushed through a bearing sleeve 80.2 mm in diameter and
0.3 m long. The clearance, assumed uniform is flooded with lubricating oil of viscosity 0.1 kg/ms.
(a) If the shaft moves axially at 0.8 m/s, estimate the resistance force exerted by the oil on the
shaft, (b) If the shaft is axially fixed and rotated at 1800 rpm, estimate the resisting torque
exerted by the oil and the power required to rotate the shaft. [60.32 N; 22.74 N; 4.29 kW]
5. A very large thin plate is centred in a gap of width 0.06 m with different oils of unknown
viscosities above and below: one viscosity is twice the other. When the plate is pulled at a
2
velocity of 0.3 m/s the resulting force on 1 m of plate due to the viscous shear on both sides is
29 N. Assuming viscous flow and neglecting all end effects, calculate the viscosities of the oils.
[0.97 kg/ms]
6. A 50-cm x 30-cm x 20-cm block

weighing 150 N is to be moved at a
constant velocity of 0.8 m/s on an
inclined surface with a friction
coefficient of 0.27. (a) Determine the
force, F that needs to be applied in
horizontal direction. (b) If a 0.4-mm-
thick oil film with a dynamic viscosity
of 0.012 Pa.s is applied between the
block and inclined surface, determine
the percent reduction in the required
force.
[105.5 N; 45.8 %] Figure 1.1
7. A thin 20-cm x 20-cm flat plate is pulled

at 1 m/s horizontally through a 3.6-mm-
thick oil layer sandwiched between two
plates, one stationary and the other
moving at a constant velocity of 0.3
m/s, as shown in Figure 1.2. The
dynamic viscosity of oil is 0.027 Pa.s.
Assuming the velocity in each oil layer
to vary linearly,
(a) plot the velocity profile and find the
location where the oil velocity is zero
and
(b) determine the force that needs to Figure 1.2
be applied on the plate to maintain this
motion.
[0.6-mm from the bottom plate; 1.62 N]
8. The belt in Figure 1.3 moves at a steady velocity V = 2.5 m/s and skims the top of a tank of oil
of dynamic viscosity µ = 0.29 kg/ms, as shown. Distance between rollers L = 2 m, width of the
belt b = 60 cm and depth of the oil h = 3 cm. Assuming a linear velocity profile in the oil,
determine (a) the resisting force exerted on the belt by the oil, and (b) the power P required to
drive the belt. (Given, P = Tw) [29 N; 72.5 watt]
Figure 1.3
9. Two square plates (15 mm x 15 mm) are dipped into a fluid of density ρ = 1000 kg/m3 parallel
to each other, as shown in Figure 1.4. If distance between the plates W = 2 mm, determine the
capillary rise h. Given, surface tension σ = 0.073 N/m and contact angle is negligible, i.e. θ = 0º.
[7.44 mm]. Determine the factors that might affect the capillary rise.
Figure 1.4
10. Assume that the surface tension forces act at an angle  relative to the water surface as shown
in Figure 1.5. (a) The mass of the double edge blade is 0.64 x 10-3 kg, and the total length of its
sides is 206 mm. Determine the value of  required to maintain equilibrium between the blade
weight and the resultant surface tension force. (b) The mass of the single-edge blade is 2.61 x
10-3 kg, and the total length of its sides is 154 mm. Explain why this blade sinks. Support your
answer with the necessary calculations. [(a) 24.5]
Figure 1.5

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UNIVERSITI TEKNIKAL MALAYSIA MELAKA

FAKULTI KEJURUTERAAN MEKANIKAL

6. A 50-cm x 30-cm x 20-cm block

7. A thin 20-cm x 20-cm flat plate is pulled

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