The Molecular and the Frictional Flow of Gases in Tubes

Abstract

I N 1866 O. E. Meyer 1 integrated approximately the equations for the flow of a viscous gas through a circular capillary tube, obtaining the following equation in which F is the volume of gas passing per second, measured at pressure p t R is the radius, L the length of the tube, £ the slip coefficient, p x the entrance, p % the exit pressure, rj the coefficient of viscosity.He also showed 2 that £ is equal to the mean free path of the molecule.This varies inversely as the pressure, which, of course, is not the same throughout the tube ; an average value of £ may be used, computed from the kinetic theory equations for pressure and viscosity, and the two measured end pressures.A not very satisfactory derivation of the value of £ was given by E. Warburg, 3 a better one by A. Bestelmeyer, 4 who showed that the proper pressure to use is the arithmetical mean of the entrance and exit pressures.Using this value of the mean pressure and the kinetic theory relations, O. E. Meyers equation reduces to in which p x denotes the density of the gas at a pressure of 1 dyne per square centimeter and the temperature of the tube.The numerical factor 7t</3/2 has the value 2.72.M. Knudsen, 5 of Copenhagen, has recently published a theoretical and experimental study of the flow of gases through capillary tubes, with pressures ranging from ordinary to one or two thousandths of 1 O.