Gas mass rate flow in compressible tube flow

Input(s)

$\mathrm{m}$: Molecular Mass $(\mathrm{g})$

$\kappa$: Boltzmann $\left(\mathrm{W} / \mathrm{cm} \mathrm{K}^{4}\right)$

$\mathrm{T}$: Temperature $(\mathrm{K})$

$\boldsymbol{P}_{\boldsymbol{o}}$: Input Pressure $(\mathrm{psi})$

$\boldsymbol{P}_{\boldsymbol{L}}$: Output Pressure (psi)

R: Radius $(\mathrm{cm})$

L: Length $(\mathrm{cm})$

Output(s)

w: Mass Rate $(\mathrm{g} / \mathrm{cm})$

Formula(s)

$$ \mathrm{w}=\left(\left(\frac{2 * \mathrm{~m}}{\pi * \kappa * \mathrm{~T}}\right)^{0.5}\right) *\left(\frac{4}{3} * \pi *\left(\mathrm{R}^{3}\right)\right) *\left(\frac{\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}}{\mathrm{L}}\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 2, Page: 66.