Physics · Textbook solutions

Mechanical Properties of Fluids

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 44 questions

2. Mechanical Properties of Fluids — worked examples

13 q

Solved Examples

Worked · 13
  1. Solved Ex.2.1
    Two different liquids of density ρ1\rho_1 and ρ2\rho_2 exert the same pressure at a certain point. What will be the ratio of the heights of the respective liquid columns?
  2. Solved Ex.2.2
    A swimmer is swimming in a swimming pool at 6 m below the surface of the water. Calculate the pressure on the swimmer due to water above. (Density of water =1000= 1000 kg/m3^3, g=9.8g = 9.8 m/s2^2)
  3. Solved Ex.2.3
    A hydraulic brake system of a car of mass 1000 kg having speed of 50 km/h, has a cylindrical piston of radius of 0.5 cm. The slave cylinder has a radius of 2.5 cm. If a constant force of 100 N is applied on the brake what distance the car will travel before coming to stop?
  4. Solved Ex.2.4
    A beaker of radius 10 cm is filled with water. Calculate the force of surface tension on any diametrical line on its surface. Surface tension of water is 0.075 N/m.
  5. Solved Ex.2.5
    Calculate the work done in blowing a soap bubble to a radius of 1 cm. The surface tension of soap solution is 2.5×10−22.5 \times 10^{-2} N/m.
  6. Solved Ex.2.6
    What should be the diameter of a water drop so that the excess pressure inside it is 80 N/m2^2? (Surface tension of water =7.27×10−2= 7.27 \times 10^{-2} N/m)
  7. Solved Ex.2.7
    A capillary tube of radius 5×10−45 \times 10^{-4} m is immersed in a beaker filled with mercury. The mercury level inside the tube is found to be 8×10−38 \times 10^{-3} m below the level of reservoir. Determine the angle of contact between mercury and glass. Surface tension of mercury is 0.465 N/m and its density is 13.6×10313.6 \times 10^{3} kg/m3^3. (g=9.8g = 9.8 m/s2^2)
  8. Solved Ex.2.8
    A steel ball with radius 0.3 mm is falling with velocity of 2 m/s at a time tt, through a tube filled with glycerin, having coefficient of viscosity 0.833 N s/m2^2. Determine viscous force acting on the steel ball at that time.
  9. Solved Ex.2.9
    A spherical drop of oil falls at a constant speed of 4 cm/s in steady air. Calculate the radius of the drop. The density of the oil is 0.9 g/cm3^3, density of air is 0.0013 g/cm3^3 and the coefficient of viscosity of air is 1.8×10−41.8 \times 10^{-4} poise, (g=980g = 980 cm/s2^2)
  10. Solved Ex.2.10
    As shown in the given figure, a piston of cross sectional area 2 cm2^2 pushes the liquid out of a tube whose area at the outlet is 40 mm2^2. The piston is pushed at a rate of 2 cm/s. Determine the speed at which the fluid leaves the tube.
  11. Solved Ex.2.11
    The given figure shows a streamline flow of a non-viscous liquid having density 1000 kg/m3^3. The cross sectional area at point A is 2 cm2^2 and at point B is 1 cm2^2. The speed of liquid at the point A is 5 cm/s. Both points A and B are at the same horizontal level. Calculate the difference in pressure at A and B.
  12. Solved Ex.2.12
    Doors of a dam are 20 m below the surface of water in the dam. If one door is opened, what will be the speed of the water that flows out of the door? (g=9.8g = 9.8 m/s2^2), specific gravity of mercury =(ρHg/ρw)=13.6= (\rho_{Hg}/\rho_w) = 13.6
  13. Solved Ex.2.13
    Water flows through a tube as shown in the given figure. Find the difference in mercury level, if the speed of flow of water at point A is 2 m/s and at point B is 5 m/s. (g=9.8g = 9.8 m/s2^2, specific gravity of mercury =13.6= 13.6)

Exercises

31 q

Choose the correct option

Practice · 5
  1. Multiple Choice Questions
    Ex Q.1 (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 2.25×10−22.25 \times 10^{-2} m2^2. What is the maximum pressure the piston would have to bear?
    1. A.
      0.8711×1060.8711 \times 10^{6} N/m2^2
    2. B.
      0.5862×1070.5862 \times 10^{7} N/m2^2
    3. C.
      0.4869×1050.4869 \times 10^{5} N/m2^2
    4. D.
      0.3271×1040.3271 \times 10^{4} N/m2^2
  2. Ex Q.1 (ii)
    Two capillary tubes of radii 0.3 cm and 0.6 cm are dipped in the same liquid. The ratio of heights through which the liquid will rise in the tubes is
    1. A.
      1 : 2
    2. B.
      2 : 1
    3. C.
      1 : 4
    4. D.
      4 : 1
  3. Ex Q.1 (iii)
    The energy stored in a soap bubble of diameter 6 cm and T=0.04T = 0.04 N/m is nearly
    1. A.
      0.9×10−30.9 \times 10^{-3} J
    2. B.
      0.4×10−30.4 \times 10^{-3} J
    3. C.
      0.7×10−30.7 \times 10^{-3} J
    4. D.
      0.5×10−30.5 \times 10^{-3} J
  4. Ex Q.1 (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
    1. A.
      1 : 2
    2. B.
      1 : 12
    3. C.
      1 : 16
    4. D.
      1 : 8
  5. Ex Q.1 (v)
    In Bernoulli's theorem, which of the following is conserved?
    1. A.
      linear momentum
    2. B.
      angular momentum
    3. C.
      mass
    4. D.
      energy

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (i)
    Why is the surface tension of paints and lubricating oils kept low?
  2. Ex Q.2 (ii)
    How much amount of work is done in forming a soap bubble of radius rr?
  3. Ex Q.2 (iii)
    What is the basis of the Bernoulli's principle?
  4. Ex Q.2 (iv)
    Why is a low density liquid used as a manometric liquid in a physics laboratory?
  5. Ex Q.2 (v)
    What is an incompressible fluid?

Solve the following

Practice · 21
  1. Ex Q.3
    Why two or more mercury drops form a single drop when brought in contact with each other?
  2. Ex Q.4
    Why does velocity increase when water flowing in broader pipe enters a narrow pipe?
  3. Ex Q.5
    Why does the speed of a liquid increase and its pressure decrease when a liquid passes through constriction in a horizontal pipe?
  4. Ex Q.6
    Derive an expression of excess pressure inside a liquid drop.
  5. Ex Q.7
    Obtain an expression for conservation of mass starting from the equation of continuity.
  6. Ex Q.8
    Explain the capillary action.
  7. Ex Q.9
    Derive an expression for capillary rise for a liquid having a concave meniscus.
  8. Ex Q.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= 1060 kg/m3^3)
  9. Ex Q.11
    In a hydraulic lift, the input piston had surface area 30 cm2^2 and the output piston has surface area of 1500 cm2^2. If a force of 25 N is applied to the input piston, calculate weight on output piston.
  10. Ex Q.12
    Calculate the viscous force acting on a rain drop of diameter 1 mm, falling with a uniform velocity 2 m/s through air. The coefficient of viscosity of air is 1.8×10−51.8 \times 10^{-5} Ns/m2^2.
  11. Ex Q.13
    A horizontal force of 1 N is required to move a metal plate of area 10−210^{-2} m2^2 with a velocity of 2×10−22 \times 10^{-2} m/s, when it rests on a layer of oil 1.5×10−31.5 \times 10^{-3} m thick. Find the coefficient of viscosity of oil.
  12. Ex Q.14
    With what terminal velocity will an air bubble 0.4 mm in diameter rise in a liquid of viscosity 0.1 Ns/m2^2 and specific gravity 0.9? Density of air is 1.29 kg/m3^3.
  13. Ex Q.15
    The speed of water is 2 m/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?
  14. Ex Q.16
    With what velocity does water flow out of an orifice in a tank with gauge pressure 4×1054 \times 10^{5} N/m2^2 before the flow starts? Density of water =1000= 1000 kg/m3^3.
  15. Ex Q.17
    The pressure of water inside the closed pipe is 3×1053 \times 10^{5} N/m2^2. This pressure reduces to 2×1052 \times 10^{5} N/m2^2 on opening the valve of the pipe. Calculate the speed of water flowing through the pipe. (Density of water =1000= 1000 kg/m3^3).
  16. Ex Q.18
    Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7×10−27 \times 10^{-2} N/m. The angle of contact between water and glass is zero, density of water =1000= 1000 kg/m3^3, g=9.8g = 9.8 m/s2^2.
  17. Ex Q.19
    An air bubble of radius 0.2 mm is situated just below the water surface. Calculate the gauge pressure. Surface tension of water =7.2×10−2= 7.2 \times 10^{-2} N/m.
  18. Ex Q.20
    Twenty seven droplets of water, each of radius 0.1 mm coalesce into a single drop. Find the change in surface energy. Surface tension of water is 0.072 N/m.
  19. Ex Q.21
    A drop of mercury of radius 0.2 cm is broken into 8 identical droplets. Find the work done if the surface tension of mercury is 435.5 dyne/cm.
  20. Ex Q.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.
  21. Ex Q.23
    A rectangular wire frame of size 2 cm ×\times 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 ×\times 3 cm, calculate the work done in the process. The surface tension of soap film is 3×10−23 \times 10^{-2} N/m.