# Stokes' Law

Written by Jerry Ratzlaff. 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:

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

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

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

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

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