Find the solution to the below numericals in the pdf:

1. For a laminar flow of an oil having dynamic viscosity = 1.766 pas in a 0.3 meter diameter pipe. The velocity distribution is parabolic with a maximum point velocity 3m/s at the centre of the pipe. Calculate the shear stress at 90 mm from the pipe wall.

2. An oil of viscosity 0.1Ns/m² and relative density 0.9 is flowing through a circular pipe of diameter 50 mm and of length 300 m. The rate of flow of fluid through the pipe is 3.5 litres/s. Find the pressure drop in a length of 300 m.

3. What power is required per kilometre of a line to overcome the viscous resistance to the flow of glycerine through a horizontal pipe of diameter 100 mm at the rate of 10 litres/s? Take dynamic viscosity = 8 poise and kinematic viscosity = 6 stokes.

4. There is a horizontal crack 40 mm wide and 2.5 mm deep in a wall of thickness 100 mm. Water leaks through the crack. Find the rate of leakage of water through the crack if the difference of pressure between the two ends of the crack is 0.02943 N/cm². Take the viscosity of water equal to 0.01 poise.

5. An oil of viscosity 0.02 Ns/m² flows between two stationary parallel plats which are 1 m wide and maintained 10 mm apart. The velocity midway between the plates is 2 m/s. Calculate the average velocity, discharge and the pressure gradient along flow.