The Pumping Speed of a Circular Aperture in a Diaphragm Across a Circular Tube

Abstract

Measurements are reported of the pumping speed, for molecular flow, of a circular hole located coaxially in a diaphragm across a circular cylindrical tube. A study is specifically made of the conductance between points not immediately adjacent to the diaphragm but separated by an axial distance L. A theoretical derivation of the conductance leads to the expression $$\mathrm{KA}{\left[\frac{{\text{1−A/A}}_0}{C}+\frac{3}{4}\frac{L}{D_0}\frac{A}{A_0}\right]}^{\text{−1}},$$ where A and A₀ are, respectively, the areas of the aperture and tube, D₀ represents the diameter of the tube, K = (RT/2πM)^½, and C is a dimensionless factor which has been evaluated as a function of relative aperture size. C takes on values from C=1 for A small to C=4/3 for A=A₀. The experimental data indicate that the reciprocal of the conductance per unit area of the aperture does vary in an approximately linear fashion with A/A₀, in concordance with the theoretical expression in which the slow variation of the coefficient C is of little effect. It is suggested that knowledge of the pumping speed for the case considered may be of value in measurements of speed at other parts of a kinetic vacuum system.