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.