Discrete-Particle Settling Velocity (Stokes' Law)

Vs = g(rho_p - rho_w)d^2/(18 mu) -- the workhorse of grit-chamber and Type I sedimentation-basin design. Water density and viscosity are computed from the temperature, so colder water settles grit more slowly. A 0.05 mm silt grain (SG 2.65) at 68 F settles about 2.25 mm/s (0.44 ft/min) at a particle Reynolds number of 0.11, well inside the Stokes regime. Stokes holds only while Re = rho_w Vs d / mu stays below about 1; a 0.5 mm sand grain hits Re ~ 112, which is flagged: there the transition/Newton law applies and the real velocity is lower. The overflow rate of an ideal clarifier equals this critical settling velocity. A discrete (Type I) settling screen; flocculent, hindered, and compression settling, particle shape, and short-circuiting are separate. Distinct from a rising oil droplet in an oil-water separator.

settling_velocity Vs = g x (rho_p - rho_w) x d^2 / (18 mu) (Stokes, SI, reported in mm/s and ft/min); reynolds Re = rho_w x Vs x d / mu; Stokes valid for Re < ~1. Water mu from the Vogel correlation and rho_w from a table fit, both by temperature.

Stokes' law for discrete-particle (Type I) settling, first-principles; Davis & Cornwell, Introduction to Environmental Engineering, by name. The engineer governs the basin.

Stokes' law and the particle Reynolds number are public physics; the water viscosity and density correlations are standard published fits; the particle size and density come from the grit or floc being settled.

Estimate. Operator of record and primacy agency govern.

Field names used by the API: particle_diameter_mm, particle_sg, water_temp_f, settling_velocity_mm_s, settling_velocity_ft_min, reynolds

• Stokes settling Vs = g(rho_p - rho_w)d^2/(18 mu) for a discrete sphere in the laminar (Re < ~1) regimeStokes' law / Davis & Cornwell
• Regime check Re = rho_w Vs d / mu; above ~1 the transition/Newton law applies and the tile flags itsedimentation practice