Exercises of Mechanical Properties of Fluids
1) Multiple Choice Questions
i) A hydraulic lift is designed to lift heavy objects of maximum mass 2000 kg. The area of cross section of piston carrying the load is 2.25 x 10-2 m2. What is the maximum pressure the smaller piston would have to bear?
(A) 8711 x 106 N/m2
(B) 5862 x 107 N/m2
(C) 4869 x 105 N/m2
(D) 3271 x 104 N/m2
ii) Two capillary tubes of radii 0.3 cm and 6 cm are dipped in the same liquid. The ratio of heights through which the liquid will rise in the tubes is
(A) 1:2
(B) 2:1
(C) 1:4
(D) 4:1
iii) The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly
(A) 0.9 x 10-3 J
(B) 0.4 x 10-3J
(C) 0.7 x 10-3 J
(D) 0.5 x 10-3 J
iv) Two hail stones with radii in the ratio of 1:4 fall from a great height through the atmosphere. Then the ratio of their terminal velocities is
(A) 1:2
(B) 1:12
(C) 1:16
(D) 1:8
v) In Bernoulli’s theorem, which of the following is conserved?
(A) linear momentum
(A) angular momentum
(A) mass
(A) energy
2) Answer in brief.
i) Why is the surface tension of paints and lubricating oils kept low?
ii) How much amount of work is done in forming a soap bubble of radius r?
iii) What is the basis of the Bernoulli’s principle?
iv) Why is a low density liquid used as a manometric liquid in a physics laboratory?
v) What is an incompressible fluid?
3. Why two or more mercury drops form a single drop when brought in contact with each other?
4. Why does velocity increase when water flowing in broader pipe enters a narrow pipe?
5. Why does the speed of a liquid increase and its pressure decrease when a liquid passes through constriction in a horizontal pipe?
6. Derive an expression of excess pressure inside a liquid drop.
7. Obtain an expression for conservation of mass starting from the equation of mass starting from the equation of continuity.
8. Explain the capillary action.
9. Derive an expression for capillary rise for a liquid having a concave meniscus.
10. Find the pressure 200 m below the surface of the ocean if pressure on the free surface of liquid is one atmosphere.
(Density of sea water = 1060 kg/m3)
[Ans. 21.789 x 105N/m2]
11. In a hydraulic lift, the input piston had surface area 30 cm2 and the output piston has surface area of 1500 cm2. If a force of 25 N is applied to the input piston, calculate weight on output piston.
[Ans. 1250 N]
12. Calculate the viscous force acting on a rain drop of diameter 1 mm, falling with a uniform velocity 2 m/s through The coefficient of viscosity of air is 1.8 x 10-5 Ns/m2.
[Ans. 3.393 x 10-7 N]
13. A horizontal force of 1 N is required to move a metal plate of area 10-2 m2 with a velocity of 2 x 10-2 m/s, when it rests on a layer of oil 1.5 x 10-3 m thick. Find the coefficient of viscosity of oil.
[Ans. 7.5 Ns/m2]
14. With what terminal velocity will an air bubble 0.4 mm in diameter rise in a liquid of viscosity 0.1 Ns/m2 and specific gravity 0.9? Density of air is 1.29 kg/m3.
[Ans. – 0.782 x 10-3 m/s, The negative sign indicates that the bubble rises up]
15. The speed of water is 2m/s through a pipe of internal diameter 10 cm. What should be the internal diameter of nozzle of the pipe if the speed of water at nozzle is 4 m/s?[Ans. 7.07 x 10-2 m]
16. With what velocity does water flow out of an orifice in a tank with gauge pressure 4 x 105 N/m2 before the flow starts? Density of water = 1000 kg/m3.
[Ans. 28.28 m/s]
17. The pressure of water inside the closed pipe is 3 x 105 N/m2. This pressure reduces to 2 x 105 N/m2 on opening thevalue of the pipe. Calculate the speed of water flowing through the pipe. (Density of water = 1000 kg/m3).
[Ans. 14.14 m/s]
18. Calculate the rise of water inside a clean glass capillary tube of radius 1 mm, when immersed in water of surface tension 7 x 10-2 N/m. The angle of contact between water and glass is zero, density of water = 1000 kg/m3, g = 9.8 m/s2.
[Ans. 0.142 m]
19. An air bubble of radius 0.2 mm is situated just below the water surface. Calculate the gauge pressure. Surface tension of water = 7.2 x 10-2 N/m.
[Ans. 7.2 x 10-2 N/m2]
20. Twenty seven droplets of water, each of radius 0.1 mm coalesce into a single Find the change in surface energy. Surface tension of water is 0.072 N/m.
[Ans. 1.628 x 10-3 J]
21. A drop of mercury of radius 0.2 cm is broken into 8 droplets of the same size. Find the work done if the surface tension of mercury is 435.5 dyne/cm.
[Ans. 2.18 x 10-5J]
22. How much work is required to form a bubble of 2 cm radius from the soap solution having surface tension 0.07 N/m.
[Ans. 0.703 x 10-3J]
23. A rectangular wire frame of size2 cm x 2 cm, is dipped in a soap solution and taken out. A soap film is formed, if the size of the film is changed to 3 cm x 3 cm, calculate the work done in the process. The surface tension of soap film is 3 x 10-2 N/m.
[Ans. 3 x 10-5 J]