# Stokes' Law

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

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

### Stokes' Law formula

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

Where:

$$\large{ v }$$ = velocity

$$\large{ \rho_m }$$ = medium density

$$\large{ \rho_p }$$ = particle density

$$\large{ d }$$ = diameter

$$\large{ g }$$ = gravitational acceleration

$$\large{ \eta }$$ = medium viscosity

Solve for:

$$\large{ \rho_m = \rho_p \; \frac { 18\; \eta \; v } { g \; d^2 } }$$

$$\large{ \rho_p = \frac { 18\; \eta \; v } { g \; d^2 } + \rho_m }$$

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

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

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

Tags: Equations for Force