Viscosity by a falling-cylinder viscometer

Input(s)

ρ\rho: Density of Fluid (ppg)(\mathrm{ppg})

ρo\boldsymbol{\rho}_{\boldsymbol{o}}: Density of Slug (ppg)

g: Acceleration due to Gravity (ft/s2)\left(\mathrm{ft} / \mathrm{s}^{2}\right)

κ\kappa: Ratio of Inner to Outer Radii (fraction)

R\mathrm{R}: Outer Radius (ft)

vov_{\boldsymbol{o}}: Slug Velocity (ft/s)(\mathrm{ft} / \mathrm{s})

Output(s)

μ\mu: Viscosity (cP)(\mathrm{cP})

Formula(s)

μ=((ρoρ) g((κR)2)2vo)((ln(1κ))1κ21+κ2)\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.


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