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MECHANICAL PROPERTIES OF FLUIDS
Study Material
MECHANICAL PROPERTIES OF FLUIDS
Very Short Answer Questions
Q1. Define average pressure? Mention its units.
Q2. Define relative density of a substance.
Q3. Write down the expression for variation of pressure with depth.
Q4. What is hydrostatic paradox?
Q5. What is Archimedes principle?
Q6. Write down the equation of continuity.
Q7. State Bernoulli's principle?
Q8. State two conditions under which Bernoulli's theorem is applicable.
Q9. What is the principle involved in the carburetor of automobiles?
Q10. What is Magnus effect?
Q11. State coefficient of viscosity and state its units.
Q12. How does viscosity vary with temperature in case of gases and liquids?
Q13. Write the expression for Stoke's law?
Q14. Define eddy flow in the case of a fluids?
Q15. Define surface tension? State its units.
Q16. Why are drops and bubbles spherical in shape?
Q17. Define angle of contact?
Q18. How does surface tension vary with temperature?
Q19. Define critical velocity and give its expression?
Q1. A solid sphere has a radius of 1.5 cm and a mass of 0.038 kg. Calculate the specific gravity of the sphere.
Q2. State Pascal's law. Write its applications.
Q3. Define gauge pressure and explain the measurement of pressure differences using a manometer.
Q4. Explain the principle involved in hydraulic lifts and brakes.
Q5. Differentiate between streamline motion and turbulent motion of a fluid with examples.
Q6. Explain how Bernoulli's principle accounts for the occurrence of a heart attack in human beings.
Q7. Explain the construction and working of a venturimeter.
Q8. What is Reynolds number? Write its significance.
Q9. Explain critical Reynolds number and discuss its significance.
Q10. Explain Stokes' law with an application.
Q11. Define surface tension. Obtain relation between surface tension and surface energy.
Q12. Discuss the role of surface tension in the removal of dirt from clothes using detergents.
Q13. Explain how surface tension can be measured experimentally.
Q14. Define angle of contact. Differentiate between water-wetting agents and water-proofing agents with examples.
Q1. What is dynamic lift? Explain it with two examples?
Q2. State Bernoulli's principle. Obtain its equation and give two applications.
Q3. Define coefficient of viscosity. Explain Stoke's law with the help of terminal velocity.
Q4. Discuss the construction and working of venturi meter with a neat sketch.
Q1. Calculate the work done in blowing a soap bubble of diameter \(0.6\,\mathrm{cm}\) against the surface tension force. (Surface tension of soap solution \(=2.5\times10^{-2}\,\mathrm{N\,m^{-1}}\))
Q2. How high does methyl alcohol rise in a glass tube of diameter \(0.06\,\mathrm{cm}\)? (Surface tension of methyl alcohol \(=0.023\,\mathrm{N\,m^{-1}}\) and density \(=0.8\,\mathrm{g\,cm^{-3}}\). Assume that the angle of contact is zero)
Q3. What should be the radius of a capillary tube if water has to rise to a height of \(6\,\mathrm{cm}\) in it? (Surface tension of water \(=7.2\times10^{-2}\,\mathrm{N\,m^{-1}}\))
Q4. Find the depression of the meniscus in the capillary tube of diameter \(0.4\,\mathrm{mm}\) dipped in a beaker containing mercury. (Density of mercury \(=13.6\times10^3\,\mathrm{kg\,m^{-3}}\) and surface tension of mercury \(=0.49\,\mathrm{N\,m^{-1}}\) and angle of contact \(=135^\circ\))
Q5. If the diameter of a soap bubble is \(10\,\mathrm{mm}\) and its surface tension is \(0.04\,\mathrm{N\,m^{-1}}\), find the excess pressure inside the bubble.
Q6. If work done by an agent to form a bubble of radius \(R\) is \(W\), then how much energy is required to increase its radius to \(2R\)?
Q7. If two soap bubbles of radii \(R_1\) and \(R_2\) (in vacuum) coalesce under isothermal conditions, what is the radius of the new bubble? Take \(T\) as the surface tension of soap solution.
Q8. At a depth of \(1000\,\mathrm{m}\) in an ocean, what is the absolute pressure? What is the gauge pressure? Find the force acting on the window of area \(20\,\mathrm{cm}\times20\,\mathrm{cm}\) of a submarine at this depth, the interior of which is maintained at sea-level atmospheric pressure. (The density of sea water is \(1.03\times10^3\,\mathrm{kg\,m^{-3}}\), \(g=10\,\mathrm{m\,s^{-2}}\).)
Q9. What is the pressure on a swimmer at \(10\,\mathrm{m}\) below the surface of a lake?
Q10. Find the velocity of the blood in the artery when the wider part of the meter has a cross-sectional area equal to that of the artery, the narrower part has an area of \(4\,\mathrm{mm^2}\), and the pressure drop in the artery is \(24\,\mathrm{Pa}\).
Q11. Find the coefficient of viscosity of oil at \(20^\circ\mathrm{C}\), if the terminal velocity of a copper ball of radius \(2.0\,\mathrm{mm}\) falling through it is \(6.5\,\mathrm{cm\,s^{-1}}\). Density of oil is \(1.5\times10^3\,\mathrm{kg\,m^{-3}}\) and density of copper is \(8.9\times10^3\,\mathrm{kg\,m^{-3}}\).
Q1. A solid sphere has a radius of \(2\,\mathrm{cm}\) and a mass of \(0.0050\,\mathrm{kg}\). Calculate the specific gravity or relative density of a sphere.
Q2. The two thigh bones (femurs), each of cross-sectional area \(10\,\mathrm{cm^2}\) support the upper part of a human body of mass \(40\,\mathrm{kg}\). Estimate the average pressure sustained by the femurs.
Q3. What is the pressure on a swimmer at \(10\,\mathrm{m}\) below the surface of a lake?
Q4. The density of the atmosphere at sea level is \(1.29\,\mathrm{kg\,m^{-3}}\). Assume that it does not change with altitude. Then how high would the atmosphere extend?
Q5. At a depth of \(1000\,\mathrm{m}\) in an ocean (a) What is the absolute pressure? (b) What is the gauge pressure? (c) Find the force acting on the window of area \(20\,\mathrm{cm}\times20\,\mathrm{cm}\) of a submarine at this depth, the interior of which is maintained at sea-level atmospheric pressure. (The density of sea water is \(1.03\times10^3\,\mathrm{kg\,m^{-3}}\), \(g=10\,\mathrm{m\,s^{-2}}\).)
Q6. Two syringes of different cross sections \(A_1,A_2\) and lengths \(L_1,L_2\) (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are \(1.0\,\mathrm{cm}\) and \(3.0\,\mathrm{cm}\) respectively. (a) Find the force exerted on the larger piston when a force of \(10\,\mathrm{N}\) is applied to the smaller piston. (b) If the smaller piston is pushed in through \(6.0\,\mathrm{cm}\), how much does the larger piston move out?
Q7. In a car lift compressed air exerts a force \(F_1\) on a small piston having a radius of \(5.0\,\mathrm{cm}\). This pressure is transmitted to a second piston of radius \(15\,\mathrm{cm}\). If the mass of the car to be lifted is \(1350\,\mathrm{kg}\), calculate \(F_1\). What is the pressure necessary to accomplish this task? \((g=9.8\,\mathrm{m\,s^{-2}})\)
Q8. Blood velocity: The flow of blood in a large artery of an anaesthetised dog is diverted through a Venturi meter. The wider part of the meter has a cross-sectional area equal to that of the artery. A is \(8\,\mathrm{mm^2}\). The narrower part has an area \(a=4\,\mathrm{mm^2}\). The pressure drop in the artery is \(24\,\mathrm{Pa}\). What is the speed of the blood in the artery?
Q9. A fully loaded Boeing aircraft has a mass of \(3.3\times10^5\,\mathrm{kg}\). Its total wing area is \(500\,\mathrm{m^2}\). It is in level flight with a speed of \(960\,\mathrm{km\,h^{-1}}\). (a) Estimate the pressure difference between the lower and upper surfaces of the wings (b) Estimate the fractional increase in the speed of the air on the upper surface relative to the lower surface. [The density of air is \(\rho=1.2\,\mathrm{kg\,m^{-3}}\)]
Q10. A metal block of area \(0.10\,\mathrm{m^2}\) is connected to a \(0.010\,\mathrm{kg}\) mass via a string that passes over an ideal pulley. A liquid with a film thickness of \(0.30\,\mathrm{mm}\) is placed between the block and the table. When released, the block moves to the right with a constant speed of \(0.085\,\mathrm{m\,s^{-1}}\). Find the coefficient of viscosity of the liquid.
Q11. The terminal velocity of a copper ball of radius \(2.0\,\mathrm{mm}\) falling through a tank of oil at \(20^\circ\mathrm{C}\) is \(6.5\,\mathrm{cm\,s^{-1}}\). Compute the viscosity of the oil at \(20^\circ\mathrm{C}\). Density of oil is \(1.5\times10^3\,\mathrm{kg\,m^{-3}}\), density of copper is \(8.9\times10^3\,\mathrm{kg\,m^{-3}}\).
Q12. (a) The flow rate of water from a tap of diameter \(1.25\,\mathrm{cm}\) is \(0.48\,\mathrm{L\,min^{-1}}\). The coefficient of viscosity of water is \(10^{-3}\,\mathrm{Pa\,s}\). (b) After sometime the flow rate is increased to \(3\,\mathrm{L\,min^{-1}}\). Characterise the flow for both the flow rates.
Q13. The lower end of a capillary tube of diameter \(2.00\,\mathrm{mm}\) is dipped \(8.00\,\mathrm{cm}\) below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at the temperature of the experiment is \(7.30\times10^{-2}\,\mathrm{N\,m^{-1}}\), \(1\) atmospheric pressure \(=1.01\times10^5\,\mathrm{Pa}\), density of water \(=1000\,\mathrm{kg\,m^{-3}}\), \(g=9.80\,\mathrm{m\,s^{-2}}\). Also calculate the excess pressure.