# Definitive equations for the fluid resistance of spheres

**C. N. Davies**

CiteWeb id: 19450000061

CiteWeb score: 222

DOI: 10.1088/0959-5309/57/4/301

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(ψRe2)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 (logψRe2)2+**0**.0011235 (logψRe2)3 for 3**0**.499σc. This conveniently transforms to the following for the sedimentation of particles in air at pressure p cm. mercury 1 + l/pa[6.32.10-4 + 2.01.10-4exp(-2190ap)]

**Definitive equations for the fluid resistance of spheres**" is placed in the Top 100 in 1945.

C. N. Davies,

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