# 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.