Abstract
A simple approximation is developed for the molecular flow of gas through a cylindrical tube. The pressure distribution along the wall of the tube is derived and is shown to be a good approximation to the short-tube formula of Clausing. Using these results, the problem of measuring the speed of a pump at the end of a tube is examined. If the pressure gauge is located a distance of one tube radius from the pump, then the intrinsic speed is directly measured in the plane of the gauge. To determine the capture coefficient of an open-ended tube whose inner surface has a uniform sticking coefficient, we employ a differential equation which reproduces the Monte Carlo results of Smith and Lewin with an error of less than 5%. For tubes of infinite length the capture coefficient is given by k = 2(σ1/2)/(1 + σ1/2), where σ is the sticking coefficient of the inner-tube surface. We repeat the calculation for tubes which have the exit end closed by a surface of the same sticking factor.