1. (a) what is meant by a streamline in fluid flow?
(b) What is the difference between laminar and turbulent flow?
(c) Draw a graph to show the change in velocity of a spherical ball bearing falling through a viscous fluid.
2. Oil having a viscosity of 0.3 Pa s and a density of 900 kg m-3 is pumped from one large open tank into another through a smooth steel pipe 1 km long and 15 cm in internal diameter. The outlet point is 30 cm above the inlet point.
Calculate the pump pressure needed to maintain a flow rate of 0.05 m3 s-1.
3. Two capillary tubes AB and BC are joined end to end at B. AB is 16 cm long with a bore 0.4 cm in diameter and BC is 4 cm long with a bore 0.2 cm in diameter. The composite tube is held horizontally with the end A connected to a reservoir giving a constant pressure head of 3 cm of water above the open end. Calculate the pressure differences between A and B and between B and C.
4. A reservoir containing water is attached to a vertical capillary tube 50 cm long with a bore 0.8 mm diameter. The water level in the reservoir is maintained at a height of 20 cm above the top end of the tube and it is found that water flows out at 8 ml per minute. Density of water = 1000 kgm-3.
Calculate the viscosity of water from this data.
5. Calculate the terminal velocities of the following raindrops falling through air:
(a) one with a diameter of 0.3 cm,
(b) one with a diameter of 0.01 mm.
Take the density of water to be 1000 kg m-3 and the viscosity of air to be 1.8x10-5 Pas. The buoyancy effect of the air may be ignored.)
6. An explosion occurs at an altitude of 1000 m where there is a constant horizontal wind speed of 10 ms-1. It is estimated that the smallest particles produced by the explosion have a diameter of 0.01 mm and a density of 2000 kg m-3. Calculate
(a) the time taken for the smallest particles to fall to the ground,
(b) the horizontal distance travelled from the point of the explosion.
Assume the viscosity and density of the air to be uniform over the distances considered. (Viscosity of air 1.8 x 10-5 Pas; density of air 1.2 kg m-3)
7. Calculate the viscous drag on a drop of oil of 0.1 mm radius falling through air at its terminal velocity. (Viscosity of air = 1.8 x 10-5 Pas; density of oil = 850 kg m-3)
8. Discuss the following statements:
(a) Large ball bearings fall through glycerol faster than do smaller ones of the same material.
(b) The acceleration of a sphere falling through a fluid varies with the distance that it has fallen in the fluid.
(c) The size of the vessel through which an object falls also affects its motion.
(d) The viscosity of a liquid could be used to measure temperature.
9. Powdered chalk (density 2800 kg m-3) is vigorously shaken up in a bottle containing 15 cm depth of water. It is found that it is half an hour before all the chalk has finally settled to the bottom of the bottle. If the coefficient of viscosity of water is 1.1 x10-3 Pas, find the diameter of the smallest particles (assumed spherical) of the chalk.
How would your answer differ if the suspension had been placed in a centrifuge to give an acceleration ten times that of gravity?
10. Compare the speed at which a steel ball (density 7800 kg m-3) of radius 2 mm will fall through treacle, with that at which an air bubble (density 1.3 kg m-3) of radius 1 mm will rise through the same liquid. (Take the density of treacle to be 1600 kg m-3.)
11. Two spherical raindrops of equal size are falling through air at a velocity of 0.08 ms-1. If the drops join together forming a large spherical drop, what will be the new terminal velocity?
12. Explain the shapes of the bulbous bows on nuclear submarines.