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

Input(s)

ρ\rho: Density (ppg)

g\mathrm{g} : Acceleration due to Gravity (ft/s2)\left(\mathrm{ft} / \mathrm{s}^{2}\right)

R\mathrm{R}: Radius (ft)

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

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

μ\mu : Viscosity (cP)(\mathrm{cP})

Output(s)

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

Formula(s)

vz=(ρg(R2)4μ)(1((rR)2)+2(a2)ln(rR))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.


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