problem 1:
a) The pressure inside a droplet of water is 0.04N/cm^{2} greater than the atmospheric pressure. find out the diameter of the droplet. Take surface tension (water with air) = 81N/m.
b) A velocity profile of a flowing fluid over a at plate is parabolic and given by u = ay^{2}+ by + c where a, b and c are constants. The velocity of fluid is 1.4m/s at 15cm from the plate. The plate is the vertex point of the velocity distribution. Find out the velocity gradients and shear stresses at y = 0, 8 and 15 cm respectively. Assume dynamic viscosity as 0.8 Ns/m^{2}
problem 2: A rectangular lamina 3mx1m is held in water at a depth of 1.5m below the free water surface:
a) If the 3m height is vertical, determine the total pressure force on the lamina and depth of centre of pressure.
b) If 1m side lies in the vertical plane at the same depth, then find out the change in total pressure force acting and depth of centre of pressure.
c) Another circular lamina having same area of rectangle is also kept at 1.5m below the free water surface. Find the total pressure force acting on the circular lamina and centre of pressure.
problem 3:
a) prepare the units of the following terms in SI and MKS systems:
- Mass density
- Specific weight
- Surface tension
- Dynamic viscosity
- Kinematic viscosity
b) describe:
i) How certain insects are able to walk on the surface of water?
ii) Why petrol evaporates more readily than water at ordinary temperature?
problem 4: A tank 1.5m x1.5m x1.5m is filled with water upto 0.5m height and remaining is filled with an oil of 0.8 specific gravity:
a) Determine total pressure force on one side of the tank and
b) Position of centre of pressure.
problem 5: Define the following terms:
- Viscosity
- Kinematic viscosity
- Velocity gradient