Terminal velocity in a separator
Input(s)
g: Acceleration Due to Gravity \(\left(\mathrm{ft} / \mathrm{s}^{2}\right)\)
\(\mathrm{D}_{\mathrm{p}}\): Particle Diameter \((\mathrm{ft})\)
\(\mathrm{N}\): Drag Coefficient (fraction)
\(\rho_{\mathrm{p}}\): Particle Density \((\mathrm{g} / \mathrm{cc})\)
\(\rho_{\mathrm{f}}\): Fluid Density \((\mathrm{g} / \mathrm{cc})\)
A: Flow Regime Constant (dimensionless) (dimensionless)
\(\mu\): Viscosity \((\mathrm{cP})\)
Output(s)
\(v_{t}\): Terminal Velocity of a Particle falling through a fluid by the pull of Gravity \((\mathrm{ft} / \mathrm{s})\)
Formula(s)
\[
\mathrm{v}_{\mathrm{t}}=\left(\frac{4 * \mathrm{~g} *\left(\mathrm{D}_{\mathrm{p}}^{\mathrm{N}+1}\right) *\left(\rho_{\mathrm{p}}-\rho_{\mathrm{f}}\right)}{3 * \mathrm{~A} *\left(\mu^{\mathrm{N}}\right) *\left(\rho_{\mathrm{f}}^{1-\mathrm{N}}\right)}\right)^{\frac{1}{2-\mathrm{N}}}
\]
Reference(s)
John M. Campbell, Gas Conditioning and Processing, Campbell Petroleum Series, Oklahoma, 1992, Vol. 2, Page: 71 .