Free batch expansion of a compressible fluid
Input(s)
\(S_{2}\): Output Surface Area \(\left(\mathrm{ft}^{2}\right)\)
\(\boldsymbol{P}_{\mathbf{1}}\): Input Pressure \((\mathrm{psi})\)
\(\boldsymbol{\rho}_{1}:\) Density (ppg)
\(\gamma\): Adiabatic Constant (dimensionless)
Output(s)
\(w_{\text {max }}\): Discharge Rate \((\mathrm{lb} / \mathrm{s})\)
Formula(s)
\[
\mathrm{w}_{\max }=\mathrm{S}_{2} *\left(\left(\mathrm{P}_{1} * \rho_{1} * \gamma *\left(\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{\gamma-1}}\right)\right)^{0.5}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 15, Page: 474.