Stokes’ Law Settling Velocity

Estimates the terminal settling velocity of a spherical particle in still fluid, used as a first-order check on whether a particle settles in basins or stays suspended and requires filtration.

$$v=\frac{d^2({\rho }_p-{\rho }_w)g}{18\mu }$$

Variables

Symbol	Meaning	Unit
v	settling velocity	m/s
d	particle diameter	m
${\rho }_p$	particle density	kg/m^3
${\rho }_w$	water density (about 998 at 20 C)	kg/m^3
g	gravitational acceleration (9.81)	m/s^2
$\mu$	dynamic viscosity of water (about 0.001 at 20 C)	Pa.s

Worked example

A 100 micron sand particle (density about 2,650 kg/m^3) settles at roughly 8 mm/s in still water. A 10 micron silt particle settles at roughly 0.08 mm/s, about 100 times slower, so at typical cooling tower flow velocities of 3 to 6 ft/s the silt stays suspended indefinitely unless mechanically filtered.

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Part of The Blueprint of Water