Nearly Free Molecular Flow Through an Orifice

The problem of the flow through an orifice is a very interesting one in fluid mechanics, as it promises to be one of the few configurations which can be investigated over virtually the whole range of possible motions. For this reason, Liepmann(1) has recently made measurements of the mass flow through an orifice at what are practically infinite pressure rations, through a range of Knudsen numbers covering the transition from continuum to free molecule flow. The mass flow rate per unit area in the Knudsen limit (i.e., at high K = λ1/R where λ1 is the mean free path at upstream infinity and R is the radius of the hole) is well known from kinetic theory to be m = 1/4p1c1 where p1 is the density and c1 the mean molecular speed at upstream infinity. The purpose of this note is to estimate the effect on m of a Knudsen number K that is not so large.