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.