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Stokes' Law




In 1851 , George Gabriel Stokes derived an expression for the Friction al Force exerted on spherical objects with very small Reynolds Number s (e.g., very small particles) in a Viscous Fluid by solving the generally unsolvable Navier-Stokes Equations :
:F = 6 \pi r \eta v
where:
F

r

:η is the fluid viscosity, and
v


If the particles are falling in the viscous fluid by their own weight, then we can derive their settling velocity by equating this frictional force with the Gravitational Force :
:V_s = rac{2}{9} rac{r^2 g ( ho_p - ho_f)}{\eta}
where:
Vs

g

ρp

ρf



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