When drilling a well at constant angular velocity, the bottom end of the drill pipe

Chapter 5, Problem 5-29

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When drilling a well at constant angular velocity, the bottom end of the drill pipe encounters a torsional resistance \(T_{A}\). 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 \(t_{A}\) at A. Determine the minimum torque \(T_{B}\) that must be supplied by the drive unit to overcome the resisting torques, and compute the maximum shear stress in the pipe. The pipe has an outer radius \(r_{o}\) and an inner radius \(r_{i}\).

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