When drilling a well at constant angular velocity, the bottom end of the drill pipe encounters a torsional resistance ta. also, soil along the sides of the pipe creates a distributed frictional torque along its length, varying uniformly from zero at the surface b to ta at a. determine the minimum torque tb that must be applied by the drive unit to overcome the resisting torques, and calculate the maximum shear stress in the pipe. the pipe has an outer radius ro and an inner radius ri.