Mechanical Properties of Fluids

Liquids and gases are called fluids because they can flow, and they do not have a fixed shape. They support ships, carry blood through our bodies and lift aeroplanes. This chapter begins with pressure, the normal force per unit area, and shows that the pressure in a liquid increases with depth as P = Pa + rho g h, regardless of the shape of the container. Atmospheric pressure is measured with a mercury barometer, and gauge pressure is the difference between the absolute and atmospheric pressures. Pascal's law states that pressure applied to an enclosed fluid is transmitted equally in all directions, and it explains the hydraulic lift and hydraulic brakes. You will study streamline flow and the equation of continuity, A1v1 = A2v2, and Bernoulli's principle, which applies energy conservation to flowing fluids and explains Torricelli's law and dynamic lift. The chapter then covers viscosity, Stokes' law and terminal velocity. It ends with surface tension, surface energy, the angle of contact, the excess pressure inside drops and bubbles, and capillary rise.

Detailed Worksheet: Mechanical Properties of Fluids Section A - Definitions (10 marks) 1. State Pascal's law. (2 marks) 2. Define viscosity and write the SI unit of the coefficient of viscosity. (2 marks) 3. Why is the angle of contact of mercury with glass obtuse? (2 marks) 4. Find the pressure due to a 10 m column of water. Take g = 9.8 m/s^2. (2 marks) 5. Why do small drops of liquid take a spherical shape? (2 marks) Section B - Calculations and Applications (15 marks) 6. In a hydraulic lift, a force of 50 N is applied on a small piston of area 10 cm^2. Find the force on the large piston of area 1000 cm^2. (3 marks) 7. Water flows through a pipe whose area narrows from 4 cm^2 to 1 cm^2. If the speed in the wide part is 2 m/s, find the speed in the narrow part. (3 marks) 8. Find the speed of efflux of water from a small hole 5 m below the water surface in an open tank. (3 marks) 9. Find the excess pressure inside a water drop of radius 1 mm and inside a soap bubble of radius 5 mm. Take the surface tension of water as 0.073 N/m and of soap solution as 0.025 N/m. (3 marks) 10. Show that 76 cm of mercury corresponds to a pressure of about 1.013 x 10^5 Pa. Take the density of mercury as 13600 kg/m^3. (3 marks) Section C - Diagrams (10 marks) 11. Draw a labelled diagram of a hydraulic lift and explain its working. (4 marks) 12. Draw streamlines for the flow of a liquid through a tube of varying cross-section. (3 marks) 13. Draw diagrams showing the angle of contact for water on glass and mercury on glass. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. State and derive Bernoulli's principle for the streamline flow of an ideal fluid. (5 marks) 15. State Stokes' law and derive the expression for the terminal velocity of a sphere falling through a viscous fluid. (5 marks) 16. Derive the expression for the rise of a liquid in a capillary tube. Find the rise of water in a tube of radius 0.5 mm, taking S = 0.073 N/m and angle of contact zero. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Take g = 9.8 m/s^2, the density of water as 1000 kg/m^3 and atmospheric pressure as 1.013 x 10^5 Pa.