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 ψRe
2, 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 = ψRe
2/24 -0.00023363(ψRe
2)2 + 0.0000020154(ψRe
2)3 - 0.0000000069105(ψRe
2)4 for Re<4 or
ψRe
2<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 (logψRe
2)-0.046677 (logψRe
2)2+0.0011235 (logψRe
2)3 for 3<Re<10,000 or
100<ψRe
2<4.5.107.
Correction for slip in gases should be applied to Stokes' law by the following
expression, based on the best results available:
1 + l/a[1.257 +
0.400exp(-1.10a/l)],
where the mean free path l is given by η/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)]
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