Flow of a Rarefied Gas through a Cylindrical Tube

Abstract

The problem of Poiseuille flow through a cylindrical tube previously solved numerically by Cercignani is attacked analytically. The integral equation for the velocity as a function of radius is cast into a convenient form and its solution is obtained in limiting cases. For large Knudsen number a solution is obtained by Neumann series. For small Knudsen number the problem is transformed to a singular integral equation and an asymptotically valid solution is derived. It is found that first order slip effects are the same as in the case of flat plates but that the second order slip effect is only approximately half as large. Finally, the results of a variational calculation of the volume flow rate are given and compared with other results.