Stokes' Law

Written by Jerry Ratzlaff on . Posted in Fluid Mechanics

Stokes' law is the force that is put on a small sphere, slowing down the movement through a viscous fluid.

Abbreviated as \(St\)

formula

\( v = \frac { g d^2 \left( \rho_p \;-\; \rho_m \right) } {18 \mu_m} \)

Where:

\(v\) = velocity

\(g\) = gravitational acceleration

\(d\) = diameter

\(\rho_p\) = density of particle

\(\rho_m\) = density of medium

\(\mu_m\) = viscosity of medium

Solve for:

\( g = \frac { 18 \mu_m   v } { d^2 \left( \rho_p \;-\; \rho_m \right) } \)

\( d =   \sqrt { \frac { 18 \mu_m   v } { g \left( \rho_p \;-\; \rho_m \right) }   }   \)

\( \rho_p =   \frac { 18 \mu_m   v } { g   d^2 } \; +\; \rho_m     \)

\( \rho_m = \rho_p   \frac { 18 \mu_m   v } { g   d^2 }   \)

\( \mu_m = \frac { g   d^2 \left( \rho_p \;-\; \rho_m \right) } {18 v} \)