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.