Stokes' Law

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Stokes' law ( \(St\) ) 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