The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F , which delivers 12 kW of power to the shaft while it is turning at 62 rev/s . Gears A, B, and C remove 3 kW, 4 kW, and 5 kW respectively. The shaft is free to turn in its support bearings D and E.

(a) Determine the absolute maximum shear stress developed in the shaft.

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)