Viscosity by a falling-cylinder viscometer
Input(s)
\(\rho\): Density of Fluid \((\mathrm{ppg})\)
\(\boldsymbol{\rho}_{\boldsymbol{o}}\): Density of Slug (ppg)
g: Acceleration due to Gravity \(\left(\mathrm{ft} / \mathrm{s}^{2}\right)\)
\(\kappa\): Ratio of Inner to Outer Radii (fraction)
\(\mathrm{R}\): Outer Radius (ft)
\(v_{\boldsymbol{o}}\): Slug Velocity \((\mathrm{ft} / \mathrm{s})\)
Output(s)
\(\mu\): Viscosity \((\mathrm{cP})\)
Formula(s)
\[
\mu=\left(\frac{\left(\rho_{\mathrm{o}}-\rho\right) * \mathrm{~g} *\left((\kappa * \mathrm{R})^{2}\right)}{2 * \mathrm{v}_{\mathrm{o}}}\right) *\left(\left(\ln \left(\frac{1}{\kappa}\right)\right)-\frac{1-\kappa^{2}}{1+\kappa^{2}}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 2, Page: 70.