Velocity distribution in the annular slit of a falling-cylinder viscometer

Input(s)

$\kappa$: Ratio of inner Radius to Outer Radius (fraction)

$v_{o}$: Velocity $(\mathrm{cm} / \mathrm{s})$

$\xi$ : Radial Coordinate (dimensionless)

Output(s)

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

Formula(s)

$$ \frac{v_{z}}{v_{o}}=-\frac{\left(1-\xi^{2}\right)-\left(1+\kappa^{2}\right) * \ln \left(\frac{1}{\xi}\right)}{\left(1-\kappa^{2}\right)-\left(1+\kappa^{2}\right) * \ln \left(\frac{1}{\kappa}\right)} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 2, Page: 70.