Wall effects on cylinder drag at low Reynolds number

Abstract

Measurements were made of the terminal velocity of a slender circular cylinder moving transverse to its axis at low Reynolds number in a fluid bounded by a rectangular container. The measurements are compared to theoretical results in four limiting cases: (1) a cylinder of infinite length in an unbounded fluid, (2) a cylinder of finite length (but large length to diameter ratio) in an unbounded fluid, a cylinder of finite length moving midway between infinite plane parallel boundaries when (3) the boundary influence is strong, and (4) when the boundary influence is weak. The effects of other boundaries are shown to be small. Empirical correction terms are presented and the practical limitations of the theoretical solutions are discussed. The most important result is that when the boundary influence is strong, there is an unexpectedly large correction term due to the finite length of the cylinder. In these experiments the Reynolds number based on cylinder length ranges from 8.1 to 0.065 and the ratio of sidewall boundary separation to cylinder length ranges from 18 to 0.022.