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.