Flow rate through orifice

Input(s)

$C d$ : Dimensionless Flow Factor (dimensionless)

$\rho_{1}$ : Initial Density $(\mathrm{ppg})$

$\rho_{2}$: Final Density $(\mathrm{ppg})$

$P_{1}$: Initial Pressure $(\mathrm{psi})$

$P_{2}$: Final Pressure (psi)

$\gamma$: Adiabatic Constant (dimensionless)

$S_{o}$ : Output Cross Section $\left(\mathrm{ft}^{2}\right)$

$S_{1}$ : Input Cross Section $\left(\mathrm{ft}^{2}\right)$

Output(s)

w: Flow Rate $\left(\mathrm{ft}^{3} / \mathrm{s}\right)$

Formula(s)

$$ w=C d * \rho_{2} * S_{o} *\left(\frac{2 *\left(\frac{P_{1}}{\rho_{1}}\right) *\left(\frac{\gamma}{\gamma-1}\right) *\left(1-\left(\left(\frac{P_{2}}{P_{1}}\right)^{\frac{\gamma-1}{\gamma}}\right)\right)}{1-\left(\left(\frac{S_{o}}{S_{1}}\right)^{2}\right) *\left(\left(\frac{P_{2}}{P_{1}}\right)^{\frac{2}{\gamma}}\right)}\right)^{0.5} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 15, Page: 472.