Spherical grit particles of radius 0.01 mm and specific gravity 3.0 are to be separated in a settling chamber. Given $g=9.81$ m/s², liquid density 1000 kg/m³ and kinematic viscosity $10^{-6}$ m²/s, assume laminar settling and find terminal velocity in mm/s, to one decimal place.
Stokes settling for a sphere gives $v_s=(\rho_s-\rho)gd^2/(18\mu)=(s-1)gd^2/(18\nu)$. The diameter is twice the stated radius: $d=0.02$ mm $=2\times10^{-5}$ m. Hence $v_s=2(9.81)(2\times10^{-5})^2/[18\times10^{-6}]=0.000436$ m/s = 0.436 mm/s, rounding to 0.4 mm/s. The corresponding Reynolds number is much smaller than one.
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