Question: A highly viscous (non-turbulent) fluid fills the gap between two long concentric cylinders of radii a and b > a, respectively. If the outer cylinder

A highly viscous (non-turbulent) fluid fills the gap between two long concentric cylinders of radii a and b > a, respectively. If the outer cylinder is fixed and the inner cylinder moves steadily at axial velocity U, the fluid will move at the axial velocity:
vz = U In (b/r) / In (b/a)
See Fig. 4.2 for a definition of the velocity component vz. Sketch this velocity between the cylinders and comment. Find expressions for the shear stresses at both the inner and outer cylinder surfaces and explain why they are different.

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