Simple method for calculating the flow rate in a cylindrical tube of arbitrary length over a whole flow regime

Abstract

Three types of semi-empirical equation for calculating the gas flow rate in a cylindrical tube of arbitrary length-to-diameter ratio are proposed. The solutions of these equations cover all flow regimes from molecular flow to critical flow or subcritical flow via intermediate flow, viscous laminar flow, and turbulent flow. In addition, the calculation procedure is straightforward because it does not require selecting a suitable equation based on the Knudsen number, Reynolds number, and Mach number. Comparing the solutions of the proposed equations with reported results from experiments and computer simulations shows good agreement within about 20%.