Nearly Free Flow through an Orifice

In the case of steady flow out of an orifice into an originally evacuated half-space, a method is given for obtaining the first correction to free flow for the net outflow through the orifice for the class of collision functions B(θ, V) cut off or made regular near θ = π/2. An explicit computation is described for hard-sphere molecules and the resultant fractional correction is 1 + 0.145/K where K is the Knudsen number. The coefficient 0.145 is about 30% lower than the current best data for argon.