Compressible flow in a horizontal circular tube

Input(s)

$\boldsymbol{p}_{\mathbf{0}}$: Pressure at Initial Point $(\mathrm{Pa})$

$\boldsymbol{p}_{\boldsymbol{L}}$: Pressure at Point $\mathrm{L}(\mathrm{Pa})$

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

$\mu$: Viscosity $(\mathrm{kg} /(\mathrm{ms}))$

L: Length (m)

$\boldsymbol{\rho}_{\text {avg }}$: Average Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$

Output(s)

$\omega$: Mass Rate of Flow $(\mathrm{kg} / \mathrm{s})$

Formula(s)

$$ \omega=\frac{\pi *\left(p_{0}-p_{L}\right) * R^{4} * \rho_{a v g}}{8 * \mu * L} $$

Reference(s)

Bird, R.B., Stewart, W.E., and Lightfoot, E.N., (2002). Transport Phenomena (Second ed.). John Wiley \& Sons, Chapter: 2, Page: 53.