# 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.

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