# Average velocity of flow through a circular tube

## Input(s)

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

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

R: Radius (m)

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

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

## Output(s)

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

\(v_{z, \max }\): Maximum Velocity (Occurs at \(\left.\mathrm{R}=0\right)(\mathrm{m} / \mathrm{s})\)

## Formula(s)

\[
\begin{gathered}
v_{z}=\frac{\left(P_{o}-P_{L}\right) * R^{2}}{8 * \mu * L} \\
v_{z, \max }=\frac{\left(P_{o}-P_{L}\right) * R^{2}}{4 * \mu * L}
\end{gathered}
\]

## Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons., Chapter: 2, Page: 51.