Two concentric corrugated cylinders are separated by a viscous fluid. When the inner cylinder is rotated, unsteady and steady torque and forces may be generated. Assuming low Reynolds numbers and small amplitude corrugations, the Navier–Stokes equations are solved by perturbations to second order. The torque and forces are dependent on the gap width, the amplitude of corrugations, and especially the number of waves of the corrugations.