This paper presents the solution to the problem of determining the velocity field and the moment necessary to sustain the motion of a viscous incompressible fluid between two concentric infinite cylinders, rotating with constant but different angular velocities, when the radii of the cylinders vary axially. The solution is obtained for cases when the equations of slow motion govern the problem. The roughness of each cylinder is assumed small compared to the smooth radius; the roughness need not be small compared to the spacing between the cylinders. Results are explicitly obtained for the case of sinusoidal roughness.

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