Gas mass rate flow in compressible tube flow

Input(s)

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

κ\kappa: Boltzmann (W/cmK4)\left(\mathrm{W} / \mathrm{cm} \mathrm{K}^{4}\right)

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

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

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

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

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

Output(s)

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

Formula(s)

w=((2 mπκ T)0.5)(43π(R3))(PoPLL)\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.


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