During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate the energy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blast wave radius R, air density rho, and time t. Arrange these variables into a single dimensionless group, which we may term the blast wave number.

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa. s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)