長い一様断面パイプの分子流コンダクタンスの解析と考え方

Abstract

The old problem on the molecular flow conductance in a long conduit pipe with a uniform cross sections was analyzed by using a concept of gas diffusion process in a uniform medium. This problem was first treated by Knudsen giving a famous approximate expression for the molecular flow conductance and, after a year, Smoluchowski has given a rigorous expression by summing up motions of individual molecules. In this report, a trial was made to understand molecular flow in a conduit pipe as one of the diffusion processes. It turned out that the well known expression of diffusion coefficient (D=1/3·υλ) did not apply to the problem. A careful consideration has given a more rigorous expression of diffusion coefficient, i.e.D=1/2·υ (l cos θ) 2/lwhere l and l2 are the average and average square of free paths of gas molecules and θ is the angle between l and molecular density gradient. By using the above expression, one can treat the molecular flow as an diffusion process and can obtain the regorous expression of molecular flow conductance.