Enter the density of the solids, density of the fluid, diameter of the solids, and kinematic viscosity into the calculator to determine the settling velocity.
Settling Velocity Formula
The settling velocity is the estimated downward speed of a particle moving through a fluid when gravity is balanced by viscous resistance. This calculator uses the Stokes-law form shown below.
V_s = \frac{g\left(\frac{\rho_s}{\rho_f}-1\right)d^2}{18\nu}| Symbol | Meaning | Typical SI Unit | Role in the Calculation |
|---|---|---|---|
| Vs | Settling velocity | m/s | Calculated output |
| ρs | Density of the solid particle | kg/m³ | Higher values increase settling speed |
| ρf | Density of the fluid | kg/m³ | Higher values reduce the density contrast |
| d | Particle diameter | m | Strongest input effect because diameter is squared |
| ν | Kinematic viscosity | m²/s | Higher viscosity slows settling |
| g | Gravitational acceleration | m/s² | Usually taken as 9.81 m/s² |
Because d is squared, small diameter changes can produce large differences in the final answer.
How to Calculate Settling Velocity
- Enter the density of the solid particle.
- Enter the density of the surrounding fluid.
- Enter the particle diameter, not the radius.
- Enter the fluid’s kinematic viscosity.
- Calculate the settling velocity and confirm the result is physically reasonable.
Unit note: if you only know the fluid’s dynamic viscosity, convert it to kinematic viscosity first.
\nu = \frac{\mu}{\rho_f}| Input Change | Effect on Settling Velocity |
|---|---|
| Larger diameter | Increases strongly; doubling the diameter makes the settling velocity about 4 times larger. |
| Higher solid density | Increases settling speed. |
| Higher fluid density | Decreases the relative density difference and slows settling. |
| Higher viscosity | Decreases settling speed. |
When This Estimate Is Most Reliable
| Condition | Why It Matters |
|---|---|
| Small, nearly spherical particles | The Stokes form is derived for spherical-particle settling behavior. |
| Very low Reynolds number settling | Accuracy is best in the Stokes or creeping-flow range. |
| Particle Reynolds number less than about 1 | This is the usual range where the Stokes-law settling expression is most dependable. |
| Relatively calm fluid | Strong turbulence can change actual settling behavior and particle paths. |
If the calculated speed is large, use the result as a first estimate and verify that Stokes settling assumptions still make sense for your case.
Common Input Mistakes
- Using radius instead of diameter.
- Entering dynamic viscosity when the calculator expects kinematic viscosity.
- Mixing units while checking the math by hand.
- Using bulk material density instead of the actual particle density.
- Applying the equation to particles that are too large for Stokes settling.
Interpreting the Result
| Result | What It Means |
|---|---|
| Positive value | The particle tends to settle downward through the fluid. |
| Near zero | Settling is very slow, so particles may remain suspended longer. |
| Negative value | The particle is less dense than the fluid and will tend to rise rather than settle. |
| Unexpectedly large value | Recheck diameter and viscosity units first, then confirm the Stokes approximation is appropriate. |
Example
For a particle with ρs = 2650 kg/m³, ρf = 1000 kg/m³, d = 0.0002 m, and ν = 1.0 × 10-6 m²/s:
V_s = \frac{9.81\left(\frac{2650}{1000}-1\right)\left(0.0002\right)^2}{18\left(1.0\times10^{-6}\right)} \approx 0.036\ \text{m/s}That is approximately 3.6 cm/s downward.
