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 Oseen's linearized equations of motion, confining ourselves to the case when the cylinder is moving midway between the bounding walls. The drag experienced by the cylinder is then calculated to Lamb's approximation. It is shown that at sufficiently small Reynolds numbers, the drag on the cylinder is independent of the Reynolds number, namely, it is of the so-called Stokes type, as was shown by White's experiments on wires falling in viscous liquids between two vertical plates. When the ratio of the distance between the walls to the diameter of the cylinder is greater than 20, our theoretical results coincide fairly well with White's experiments, allowing for some experimental errors.