Velocity distribution in the narrow annular region in annular flow with inner cylinder moving axially

Input(s)

$\rho$: Density (ppg)

$\mathrm{g}$ : Acceleration due to Gravity $\left(\mathrm{ft} / \mathrm{s}^{2}\right)$

$\mathrm{R}$: Radius (ft)

r: Position from Point $(\mathrm{ft})$

a: Ratio of Distance of Rod from Centre (fraction)

$\mu$ : Viscosity $(\mathrm{cP})$

Output(s)

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

Formula(s)

$$ v_{z}=\left(\frac{\rho * g *\left(R^{2}\right)}{4 * \mu}\right) *\left(1-\left(\left(\frac{r}{R}\right)^{2}\right)+2 *\left(a^{2}\right) * \ln \left(\frac{r}{R}\right)\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 2, Page: 65.