Stokes settling

How fast does the particulate fall out of the carrier?

The formula

vs = \frac{(ρp - ρf) g d^{2}}{18 η0}

LaTeX

vs = \frac{(ρp - ρf) \cdot g \cdot d^2}{18 \cdot η0}

Work it out

m Particulate

The solid. Only its density matters here.

c Carrier fluid

The liquid the solid falls through. Its density buoys the particle and its viscosity drags on it.

d Particle diameter

µm

The settling speed goes with the square of this — ten times the diameter, a hundred times the speed.

D Tube bore

The distance a particle has to fall to reach the bottom of the tube.

T Temperature

°C

Sets the thermal energy that keeps a fine enough particle suspended regardless of gravity.

or see a worked example with typical numbers

Take the particle's density less the carrier's: the excess that gravity acts on. Iron in water is about 6.9 g/cm³ of excess.
Multiply by g and by the square of the diameter, and divide by eighteen times the carrier's viscosity. That is Stokes' terminal velocity — where the sphere's excess weight, ⅙πd³·Δρ·g, equals its drag, 3πηdv.
Divide the bore by the velocity for the time to fall from the top of the tube to the bottom.
Check the particle Reynolds number, ρ_f·v·d ÷ η. Stokes' drag law is exact only for creeping flow, below about 1; above it the drag is larger and the speed lower than shown.
Check the gravitational length, k_BT ÷ (Δρ·g·V) — the height over which thermal energy competes with gravity. If it exceeds the bore the particle is a colloid and does not settle at all.
Set the time against the loop: at 50 in/s a metre of tube takes 0.79 s, so a settling time of a minute is some seventy laps.

A smooth rigid sphere falling alone in a liquid at rest — Stokes' 1851 result. Filings are neither spherical nor smooth and fall somewhat slower for their mass; a dense slurry settles more slowly again, because the particles hinder one another's fall.
A liquid at rest. In a flowing loop the turbulence resuspends what would settle in still water, and in laminar flow it does not; the flow-regime calculation decides which applies, and settling matters most in the dead legs and at the pump's stop.
Carrier density and viscosity at 20 °C, whatever temperature is entered — the temperature affects the thermal-suspension check here, not the viscosity table.
Nothing here is Meyer's. The estate material specifies the speed of the medium and not its particle size; the calculation exists because a coarse iron slurry falls out of its water between one run and the next, and a fine one does not, and a reader should know which they have.