# Compressible Fluid Flow

This web application calculates flow of a single phase compressible fluid through a pipe for a given pressure drop.

Pipe Data

Fluid Data

Result

Fluid mass flowrate is calculated by iteratively solving following equation in Imperial units.

\displaystyle \displaystyle W_{s} = \sqrt{\left[\frac{144gA^{2}\rho_{1}}{\left(f\frac{L}{D}+2\ln\frac{P_{1}}{P_{2}}\right)}\right]\left[\frac{P_1^2-P_2^2}{P_{1}}\right]}

where, f is Darcy's friction factor, L is pipe length (ft), D is pipe diameter (ft), ρ is fluid density (lb/ft³), A is pipe cross-sectional area (ft²), g is constant 32.174 ft/sec², P is pressure in psi and Ws is gas flow (lbm/sec). Subscript 1 denotes conditions at pipe inlet and 2 denotes at pipe outlet.

Sonic Velocity

The maximum possible velocity of a compressible fluid in a pipe is called sonic velocity.

\displaystyle \displaystyle V_{s} = 68.1\sqrt{\left(\frac{Cp}{Cv}\right)\frac{P}{\rho}}

where, Cp/Cv is gas specific heat ratio, P is pressure in psi, ρ is density in lb/ft³ and Vs is sonic velocity in feet/sec.

Mach Number

The Mach number is the velocity of the gas divided by the sonic velocity in gas.

\displaystyle \displaystyle Ma = \frac{V}{V_{s}}

where V is gas velocity in pipe and Vs is the sonic velocity.

Erosional Velocity

Erosional velocity is maximum allowable gas velocity in a pipeline, as gas velocity increases, vibration and noise increases. Erosional velocity can be estimated as following.

\displaystyle \displaystyle V_{Max} = \frac{100}{\sqrt{\rho}}

where ρ is gas density in lb/ft³ and Vmax is erosional velocity in ft/sec.

Reference

- Compressible fluid flow at cheguide.com