A viscous fluid is contained between two long concentric cylinders. The geometry of the system is such that the flow between the cylinders is approximately the same as the laminar flow between two infinite parallel plates.

(a) Determine an expression for the torque required to rotate the outer cylinder with an angular velocity \(\omega\). The inner cylinder is fixed. Express your answer in terms of the geometry of the system, the viscosity of the fluid, and the angular velocity.

(b) For a small, rectangular element located at the fixed wall, determine an expression for the rate of angular deformation of this element. (See Fig. P6.10.)

Fig. P6.10

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D D' A' A (b) (a) B