A Model for Drag Forces in the Crevice of Piston Gages in the Viscous and Molecular Flow Regimes
James W. Schmidt, Charles D. Ehrlich, S A. Tison
A model for drag forces in the crevice of pneumatic piston gages is presented. The model uses an interpolation function for momentum transfer between the piston and the cylinder mediated by the gas flowing in the crevice. The interpolation function bridges the gap between the molecular-flow and viscous-flow regimes, and is then used to develop and expression for the effective area of a piston gage. The deviation of the effective area of this model from the viscous flow result is:(formula)for a floating-piston design, and(formula)for a floating cylinder design, where Aeff is the effective area, h is the crevice width, R0 is the radius of the piston, R1 is the radius of the cylinder, Β2 and Β3 are constants that depend on the molecular weight and bulk viscosity of the gas and P0 and P1 are the absolute pressures above and below the piston. Model results are compared with published measurements of the effective area of several piston gages in which relative changes as large as 30 x 10-6 (30 ppm) were observed when different pressurizing gases were used.