Note on the Drag on a Circular Cylinder moving with Low Speeds in a Viscous Liquid between Two Parallel Walls

Abstract

The steady slow motion of a circular cylinder in a viscous liquid bounded by two parallel plane walls is discussed on the basis of Stokes’ equations of motion, confining ourselves to the case when the cylinder is moving midway between the bounding walls. A second approximation for the drag experienced by the cylinder is then calculated and compared with White’s experiments. But the disagreement existing between the first approximation obtained recently by the present writer on the basis of Oseen’s linearized equations of motion and White’s empirical formula, when the values of the ratio (distance between the walls/diameter of the cylinder) are smaller than 20, has hardly been removed. As far as higher order terms are neglected, the second approximation is in perfect agreement with the first approximation.