Sphere Drag in Flows of Almost-Free Molecules

Abstract

A kinetic theory of sphere drag in the transition flows, based on the Boltzmann equation for the Maxwellian molecules, is presented. The exact binary collision integral, in the first order Knudsen iteration, is expanded as a function of Hermite polynomials in molecular velocity. The drag of a sphere at free stream temperature with molecular diffuse reflection is calculated. The results agree well with Millikan's measured values over a wide range of Knudsen number (0.5 < λ∕d < 10). It is found that the sphere drag of the almost‐free molecular flows normalized by the corresponding collisionless drag is essentially independent of the speed ratio for the present range of calculations