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.