Velocity distribution of flow through a circular tube

Input(s)

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

$p_{L}$: Pressure at Point $\mathrm{L}(\mathrm{Pa})$

R: Radius of the Tube $(m)$

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

L: Length of the Tube (m)

r: Cylindrical Shell of Thickness (m)

Output(s)

$v_{z}$: Velocity Distribution $(\mathrm{m} / \mathrm{s})$

Formula(s)

$$ \mathrm{v}_{\mathrm{z}}=\frac{\left(\mathrm{p}_{\mathrm{o}}-\mathrm{p}_{\mathrm{L}}\right) * \mathrm{R}^{2}}{4 * \mu * \mathrm{~L}} *\left(1-\left(\frac{\mathrm{r}}{\mathrm{R}}\right)^{2}\right) $$

Reference(s)

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