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 .