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.