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.