The drag of cylinders in fluids at slow speeds

Abstract

Experiments with wires falling sideways in viscous fluids are described. At very slow speeds the resistance is found to be independent of the density of the fluid when the fluid is finite in extent. In such purely viscous motion the boundary distance controls the pattern and Reynolds’s number is without significance. At higher speeds the resistance becomes independent of this distance and agrees with Lamb’s solution for a cylinder in an infinite fluid. At still higher speeds the experiments close the gap between the upper limit of validity of Lamb’s approximations and the lower end of the wind-tunnel experimental range. The present experiments include Reynolds’s numbers ranging from 10 -5 to 10 +2 : at low speed the influence of distant boundaries is unexpectedly great, and Lamb’s formula is much more restricted in scope than usually thought; when the Reynolds number is 10 -4 the presence of boundaries 500 diameters away multiplies the drag two-fold.