Average velocity of flow through an annulus

Input(s)

$\boldsymbol{P}_{\boldsymbol{o}}$: Pressure at Initial Point $(\mathrm{Pa})$

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

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

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

$\boldsymbol{L}$: Length $(\mathrm{m})$

к: Ratio of Inner Pipe's Radius to Outer Pipe's Radius (fraction)

Output(s)

$\boldsymbol{v}_{z}$: Average Velocity $(\mathrm{m} / \mathrm{s})$

Formula(s)

$$ v_{z}=\frac{\left(P_{o}-P_{L}\right) * R^{2}}{8 * \mu * L} *\left[\frac{1-\kappa^{4}}{1-\kappa^{2}}-\frac{1-\kappa^{2}}{\ln \left(\frac{1}{\kappa}\right)}\right] $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley \& Sons, Chapter: 2, Page: 55.