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.