Mass rate of flow through annulus
Input(s)
po: Pressure at initial point \((\mathrm{Pa})\)
\(\mathrm{pL}\): Pressure at point \(\mathrm{L}(\mathrm{Pa})\)
\(\mathrm{R}\): Radius \((\mathrm{m})\)
\(\rho\): Density \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\)
\(\mathrm{mu}\): Viscosity \((\mathrm{kg} /(\mathrm{ms}))\)
L: Length \((\mathrm{m})\)
\(\mathrm{K}\): Boltzmann Constant \(\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right)\)
Output(s)
\(\Psi\): Mass Rate of Flow \((\mathrm{kg} / \mathrm{s})\)
Formula(s)
\[
\Psi=\frac{\pi *(p o-p L) * R^{4} * \rho}{8 * \mu * L} *\left(\left(1-K^{4}\right)-\frac{\left(1-K^{2}\right)^{2}}{\ln \left(\frac{1}{K}\right)}\right)
\]
Reference(s)
Transport Phenomena, Second Edition, Bird, Chapter 2.