A Novel Adiabatic Pipe Flow Equation for Ideal Gases

Abstract

Compressible flow involves variation in the density with changes in pressure and temperature along the pipe length. This article revisits the conventional adiabatic pipe flow equation and finds a fundamental drawback in this equation. The corrected adiabatic pipe flow equation has fixed the fundamental error in the conventional adiabatic pipe flow equation where the average density estimation for the conventional adiabatic equation is lower than the lower bound of the average density based on isothermal temperature. However, both the conventional adiabatic equation and the corrected adiabatic equation result in an over prediction of mass flux due to a deficiency in the average density definition. The over prediction of mass flux is not significant if the pressure drop is less than 40%; however, the pressure drop is usually greater than 40% of the inlet pressure for most pressure relief system applications. The authors offer a novel adiabatic pipe flow equation based on insights presented in this work. The novel adiabatic pipe flow equation is the most suitable solution for the pressure relief system applications as well as any other common application since it better represents the nature of adiabatic flow in a pipe. The experimental data previously published is compared with the predictions to validate the new adiabatic pipe flow model.