Definitive equations for the fluid resistance of spheres

Abstract

For calculation of terminal velocities it is convenient to express the Reynolds' number, Re, of a moving sphere as a function of the dimensionless group ψRe2, where ψ is the drag coefficient. The following equations have been fitted by the method of least squares to critically selected data from a number of experimenters: Re = ψRe2/24 -0.00023363(ψRe2)2 + 0.0000020154(ψRe 2)3 - 0.0000000069105(ψRe2)4 for Re<4 or ψRe2<140. This tends to Stokes' law for low values of Re. It is specially suited to calculation of the sedimentation of air-borne particles. The upper limit corresponds to a sphere weighing 1.5 μg. falling in the normal atmosphere, that is, one having a diameter of 142 μ for unit density. logRe=-1.29536+0.986 (logψRe2)-0.046677 (logψRe 2)2+0.0011235 (logψRe2)3 for 3