Engineering & Scientific
Stokes’ Law Terminal Settling Velocity, Particle Reynolds Gate & Clarifier Capture
Calculate laminar gravitational settling velocity v_s = g*(rho_p - rho_f)*d^2 / (18*mu), validate creeping flow via particle Reynolds number Re_p <= 1, and check sedimentation basin capture.
Balancing submerged weight against Stokes viscous drag (6*pi*mu*r*v)
A small spherical particle of diameter d and density rho_p suspended in a fluid of density rho_f and dynamic viscosity mu accelerates until net buoyant weight (pi/6)*d^3*(rho_p - rho_f)*g equals Stokes creeping-flow drag 3*pi*mu*d*v_s. Solving for terminal velocity yields v_s = g * (rho_p - rho_f) * d^2 / (18 * mu) in m/s (negative when rho_p < rho_f, such as oil droplets rising in water).
Because Stokes drag C_D = 24 / Re_p neglects fluid inertia, you must verify the particle Reynolds number Re_p = (rho_f * ABS(v_s) * d) / mu <= 1.0. Above Re_p = 1, inertial wake drag slows settling below the Stokes prediction (Schiller-Naumann transitional regime).
| Clarifier Metric | Formula | 100 um Quartz Silt in 20 °C Water | Status |
|---|---|---|---|
| Settling Velocity v_s | g * (rho_p - rho_f) * d^2 / (18 * mu) | 0.008993 m/s (8.9925 mm/s) | Downward sedimentation |
| Particle Reynolds Re_p | rho_f * ABS(v_s) * d / mu | 0.8993 | Re_p <= 1 -> STOKES_LAMINAR |
| Surface Overflow Rate v_o | Flow_Q / Basin_Area | 5.0000 mm/s | v_s >= v_o -> CAPTURED_100PCT |
Stokes Terminal Velocity Formula (in mm/s)
Evaluate SI terminal velocity in m/s and multiply by 1,000 for practical water-treatment and aerosol mm/s reporting.
=ROUND((9.81 * (B2 - B3) * (B4 ^ 2) / (18 * B5)) * 1000, 4)Particle Reynolds Regime & Clarifier Capture Check
Compute Re_p from unrounded SI velocity so coarse particles > ~110 um in water automatically flag TRANSITIONAL_DRAG.
=IF(E3 <= 1, "STOKES_LAMINAR", "TRANSITIONAL_DRAG")Try the example
Use the original values or change them to test your understanding.