Stokes Settling Velocity Calculator (Sedimentation of Particles)
How fast a small sphere sinks (or rises) through a fluid by Stokes' law, with its Reynolds number, whether the law applies, and the time to settle a given height.
Results
The dashed line marks the value you entered.
What this tool does
A small particle reaches its terminal speed almost at once, when its weight less the buoyancy equals the viscous drag 3π μ d v. Stokes' law then gives a speed proportional to the square of the diameter: halve the particle and it settles four times slower, which is why fine silt and clay stay cloudy for days while sand drops in seconds. The law only holds while the flow around the particle is creeping, with a Reynolds number below about 1; above that the real speed is lower than the result shown. Particles lighter than the fluid come out negative: they rise.
Formula
v = g d² (ρp − ρf) ÷ (18 μ) (Stokes' law, valid for Re = ρf v d ÷ μ below about 1)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d | Particle diameter | µm |
rp | Particle density | kg/m³ |
rf | Fluid density | kg/m³ |
mu | Fluid dynamic viscosity | mPa·s |
h | Height to settle through | m |
V | Settling velocity (negative if it rises) | mm/s |
RE | Particle Reynolds number | — |
T | Time to settle through that height | min |
VAL | Is Stokes' law valid? | — |
Worked example
- Particle diameter50 µm
- Particle density2650 kg/m³
- Fluid density998 kg/m³
- Fluid dynamic viscosity1 mPa·s
- Height to settle through1 m
- Settling velocity (negative if it rises)2.2501 mm/s
- Particle Reynolds number0.1123
- Time to settle through that height7.4 min
- Is Stokes' law valid?Roughly — Reynolds number between 0.1 and 1
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.