MOI UNIVERSITY
SCHOOL OF ENGINEERING
DEPARTMENT OF MECHANICAL & PRODUCTION ENGINEERING
MPE 232 FLUID MECHANICS – TUTORIAL QUESTIONS I
PROPERTIES OF FLUID; FLUID STATICS
1. A hydrogen-filled balloon is to expand to a sphere 20 m diameter at a height of
30 km where the absolute pressure is 1100 Pa and the temperature −40 ◦C. If
there is to be no stress in the fabric of the balloon what volume of hydrogen must
be added at ground level where the absolute pressure is 101.3 kPa and the
temperature 15 ◦C?
[56.2 m3]
2. Calculate the density of air when the absolute pressure and the temperature are
respectively 140 kPa and 50 ◦C and R = 287 J · kg−1 ·K−1.
[1.51 kg ·m−3]
3. Eight kilometres below the surface of the ocean the pressure is 81.7 MPa.
Determine the density of sea-water at this depth if the density at the surface is
1025 kg ·m−3 and the average bulk modulus of elasticity is 2.34 GPa.
[1061 kg ·m−3]
4. The space between two large flat and parallel walls 25 mm apart is filled with a
liquid of dynamic viscosity 0.7 Pa · s. Within this space a thin flat plate 250 mm
× 250 mm is towed at a velocity of 150 mm· s−1 at a distance of 6 mm from one
wall, the plate and its movement being parallel to the walls. Assuming linear
variations of velocity between the plate and the walls, determine the force exerted
by the liquid on the plate.
[1.439 N]
5. A uniform film of oil 0.13 mm thick separates two discs, each of 200 mm diameter,
mounted co-axially. Ignoring edge effects, calculate the torque necessary to
rotate one disc relative to the other at a speed of 44 rad · s−1 (7 rev/s) if the oil
has a dynamic viscosity of 0.14 Pa · s.
[7.44 N·m]
6. What is the approximate capillary rise of water in contact with air (surface tension
0.073 N·m−1) in a clean glass tube 5 mm in diameter?
[5.95 mm]
7. What is the approximate capillary rise of mercury (relative density 13.56,
interfacial tension 0.377 N·m−1, angle of contact approximately 140◦) in contact
with water in a clean glass tube 6 mm in diameter? (Note: As the mercury moves
it displaces water, the density of which is not negligible.)
[−1.563 mm]
8. Calculate the pressure in the ocean at a depth of 2000 m assuming that salt water
is (a) incompressible with a constant density of 1002 kg m−3, (b) compressible
with a bulk modulus of 2.05 GN m−2 and a density at the surface of 1002 kg
m−3.
[(a) 19.66 MN m−2, (b) 19.75 MN m−2]
9. What will be (a) the gauge pressure, (b) the absolute pressure of water at a depth
of 12 m below the free surface? Assume the density of water to be 1000 kg m−3
and the atmospheric pressure 101 kN m−2.
Page 1 of 3
SCHOOL OF ENGINEERING
DEPARTMENT OF MECHANICAL & PRODUCTION ENGINEERING
MPE 232 FLUID MECHANICS – TUTORIAL QUESTIONS I
PROPERTIES OF FLUID; FLUID STATICS
1. A hydrogen-filled balloon is to expand to a sphere 20 m diameter at a height of
30 km where the absolute pressure is 1100 Pa and the temperature −40 ◦C. If
there is to be no stress in the fabric of the balloon what volume of hydrogen must
be added at ground level where the absolute pressure is 101.3 kPa and the
temperature 15 ◦C?
[56.2 m3]
2. Calculate the density of air when the absolute pressure and the temperature are
respectively 140 kPa and 50 ◦C and R = 287 J · kg−1 ·K−1.
[1.51 kg ·m−3]
3. Eight kilometres below the surface of the ocean the pressure is 81.7 MPa.
Determine the density of sea-water at this depth if the density at the surface is
1025 kg ·m−3 and the average bulk modulus of elasticity is 2.34 GPa.
[1061 kg ·m−3]
4. The space between two large flat and parallel walls 25 mm apart is filled with a
liquid of dynamic viscosity 0.7 Pa · s. Within this space a thin flat plate 250 mm
× 250 mm is towed at a velocity of 150 mm· s−1 at a distance of 6 mm from one
wall, the plate and its movement being parallel to the walls. Assuming linear
variations of velocity between the plate and the walls, determine the force exerted
by the liquid on the plate.
[1.439 N]
5. A uniform film of oil 0.13 mm thick separates two discs, each of 200 mm diameter,
mounted co-axially. Ignoring edge effects, calculate the torque necessary to
rotate one disc relative to the other at a speed of 44 rad · s−1 (7 rev/s) if the oil
has a dynamic viscosity of 0.14 Pa · s.
[7.44 N·m]
6. What is the approximate capillary rise of water in contact with air (surface tension
0.073 N·m−1) in a clean glass tube 5 mm in diameter?
[5.95 mm]
7. What is the approximate capillary rise of mercury (relative density 13.56,
interfacial tension 0.377 N·m−1, angle of contact approximately 140◦) in contact
with water in a clean glass tube 6 mm in diameter? (Note: As the mercury moves
it displaces water, the density of which is not negligible.)
[−1.563 mm]
8. Calculate the pressure in the ocean at a depth of 2000 m assuming that salt water
is (a) incompressible with a constant density of 1002 kg m−3, (b) compressible
with a bulk modulus of 2.05 GN m−2 and a density at the surface of 1002 kg
m−3.
[(a) 19.66 MN m−2, (b) 19.75 MN m−2]
9. What will be (a) the gauge pressure, (b) the absolute pressure of water at a depth
of 12 m below the free surface? Assume the density of water to be 1000 kg m−3
and the atmospheric pressure 101 kN m−2.
Page 1 of 3
