How to Use Stokes’ Law Calculator
The Stokes’ Law Calculator solves two related problems in creeping-flow theory: computing the viscous drag force on a sphere moving at a specified velocity, and finding the terminal sedimentation velocity at which a settling sphere reaches force equilibrium.
- Choose calculation mode — “drag force” if you know the sphere velocity; “terminal velocity” if you want the equilibrium settling speed at force balance.
- Enter fluid dynamic viscosity μ — water at 20 °C: 1.002 × 10⁻³ Pa·s; air at 20 °C: 1.81 × 10⁻⁵ Pa·s; glycerine ≈ 1.5 Pa·s.
- Enter sphere radius r — for particles larger than about 1 mm in water, check that Re_p < 1 before trusting results.
- Enter velocity v (drag mode) or particle density ρ_p, fluid density ρ_f and gravity g (terminal velocity mode).
- Read the drag force in N and mN, or the terminal velocity in m/s and mm/s; the panel also shows the particle Reynolds number Re_p as a validity check for the Stokes regime.
Formula & Theory — Stokes’ Law Calculator
The Stokes’ Law Calculator applies the analytical solution for creeping flow (Re_p ≪ 1) around a solid sphere:
F_d = 6 · π · μ · r · v (Stokes drag)
v_t = 2 · r² · (ρ_p − ρ_f) · g / (9 · μ) (terminal velocity)
Re_p = 2 · r · v · ρ_f / μ (particle Reynolds)| Symbol | Meaning | SI Unit |
|---|---|---|
| F_d | Stokes drag force | N |
| v_t | Terminal settling velocity | m/s |
| μ | Dynamic viscosity of fluid | Pa·s |
| r | Sphere radius | m |
| ρ_p | Particle (sphere) density | kg/m³ |
| ρ_f | Surrounding fluid density | kg/m³ |
| g | Gravitational acceleration (9.81) | m/s² |
| Re_p | Particle Reynolds number | — |
Stokes’ law is strictly valid for Re_p < 0.1 (error < 1 %) and approximately valid up to Re_p ≈ 1. For Re_p from 1 to 1000, use the Oseen (1 + 3Re/16) correction or the Schiller–Naumann empirical drag correlation. Terminal velocity scales as r², so doubling particle size quadruples settling speed.
Use Cases for Stokes’ Law Calculator
- Particle settling and sedimentation — predict how quickly soil, clay or flocculated particles settle in water treatment sedimentation tanks or clarifiers.
- Centrifugation analysis — scale Stokes’ law to centrifugal acceleration g_eff = ω²r for microcentrifuge and ultracentrifuge separation design.
- Aerosol deposition and filtration — estimate gravitational settling velocity of dust, pollen, PM2.5 and fine-particle emissions in indoor and outdoor air quality modelling.
- Falling-sphere viscometry — determine the dynamic viscosity of an unknown fluid by timing a calibrated ball-bearing falling through a vertical viscometer tube.
- Pharmaceutical suspension stability — assess creaming or sedimentation velocity of drug particles to determine required stabiliser type and concentration.
- Educational demonstration of drag — show that drag is proportional to velocity (not v²) in the Stokes regime, contrasting with turbulent (high-Re) quadratic drag.