Engineering
Stokes's Law Terminal Settling Velocity & Particle Reynolds Check formulas
Calculate the ideal terminal speed of an isolated sphere in a Newtonian fluid and screen the estimated particle Reynolds number.
An isolated rigid sphere in creeping flow
Balance submerged weight against Stokes drag to obtain v=(rho_p-rho_f)*g*d²/(18*mu). Use SI units: densities kg/m³, diameter m, gravity m/s² and dynamic viscosity Pa·s. Positive velocity denotes downward motion; a lighter rigid sphere has negative velocity.
The model assumes terminal motion, an isolated rigid sphere, a Newtonian fluid and negligible wall and particle-interaction effects. Flocs, nonspherical microplastics, liquid drops, concentrated suspensions and cyclones need additional models. A diameter-squared scaling applies only when the other assumptions and properties remain unchanged.
Creeping flow requires Reynolds number much smaller than one. The worksheet uses 0.2 as a screening threshold, not a universal validation certificate. The Reynolds estimate uses the unrounded predicted speed. Failure of the screen means this speed should not be used as a reliable terminal-velocity prediction; it does not by itself imply turbulent flow.
| Sedimentation Parameter | Formula / SI Inputs | 50 um Quartz Silt in Water | Lighter rigid sphere |
|---|---|---|---|
| Densities rho_p & rho_f | B2 = 2,650, B3 = 1,000 kg/m^3 | g=9.81, d=50E-6 m, mu=0.001 Pa*s | rho_p set to 900 kg/m^3 |
| Settling Velocity (mm/s) | 1000 * ((B2-B3)*B4*B5^2)/(18*B6) | +2.2481 mm/s (Sinks) | -0.1363 mm/s (Rises!) |
| Particle Reynolds Re_p | (B3 * ABS(v_ms) * B5) / B6 | 0.1124 (passes the chosen screen) | 0.0068 (passes the chosen screen) |
Stokes Terminal Settling Velocity in millimeters per second (mm/s)
Multiplies m/s by 1,000 so fine micron-scale settling velocities read cleanly in mm/s.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<=0,B4<=0,B5<=0,B6<=0),"Invalid inputs",ROUND(1000 * (((B2 - B3) * B4 * (B5 ^ 2)) / (18 * B6)), 4)))Particle Reynolds number
Inertial drag corrections become relevant as Reynolds number increases; laminar flow alone does not establish the creeping-flow approximation.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<=0,B4<=0,B5<=0,B6<=0),"Invalid inputs",ROUND((B3 * ABS(((B2 - B3) * B4 * (B5 ^ 2)) / (18 * B6)) * B5) / B6, 4)))Screen the unrounded Reynolds estimate
Passing this numerical screen does not check particle shape, dilution, wall effects or whether terminal motion has been reached.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<=0,B4<=0,B5<=0,B6<=0),"Invalid inputs",IF(((B3 * ABS(((B2 - B3) * B4 * (B5 ^ 2)) / (18 * B6)) * B5) / B6) <= 0.2, "Passes Re screen", "Outside Re screen")))Try the example
Use the original values or change them to test your understanding.