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

Input(s)

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

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

ξ\xi : Radial Coordinate (dimensionless)

Output(s)

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

Formula(s)

vzvo=(1ξ2)(1+κ2)ln(1ξ)(1κ2)(1+κ2)ln(1κ)\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.


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