Enter values and choose units. Use advanced options only when needed.
The Stokes settling velocity for a small, spherical particle in laminar flow is:
- v is terminal settling velocity.
- ρp is particle density, ρf is fluid density.
- d is particle diameter, μ is dynamic viscosity.
- Cc is an optional slip correction; use 1.0 for liquids.
- χ is an optional shape factor; use 1.0 for spheres.
If hindered settling is enabled, the calculator applies: v_h = v · (1 − φ)ⁿ.
- Enter particle diameter, densities, viscosity, and gravity.
- Pick units for each input using the dropdowns.
- Keep advanced options off for classic settling in water.
- Press Calculate to show results above the form.
- Check the Reynolds number warning to confirm validity.
- Use the download buttons to export CSV or PDF.
| Case | d (mm) | ρp (kg/m³) | ρf (kg/m³) | μ (mPa·s) | g (m/s²) | Expected v (mm/s) |
|---|---|---|---|---|---|---|
| Fine sand in water | 0.20 | 2650 | 998 | 1.002 | 9.80665 | ~3.6 |
| Silt in water | 0.05 | 2650 | 998 | 1.002 | 9.80665 | ~0.23 |
| Low contrast density | 0.20 | 1200 | 998 | 1.002 | 9.80665 | ~0.44 |
Values are indicative and depend on temperature and particle shape.
- Use Stokes settling when flow is laminar and particles are small.
- For larger grains, drag changes and velocity rises slower than d².
- In concentrated suspensions, hindered settling can dominate.
- Temperature mainly affects viscosity; update μ for accuracy.
1) Why settling velocity matters
Settling velocity links particle properties to separation time in clarifiers, grit chambers, and sedimentation basins. A change from 0.2 mm sand to 0.05 mm silt can reduce velocity by about 16× because Stokes settling scales with diameter squared. That sensitivity makes clean inputs and unit handling essential.
2) Stokes assumptions and usable range
Stokes settling assumes a spherical particle, creeping flow, and a steady terminal speed where drag balances buoyancy-corrected weight. A practical indicator is the Reynolds number, using the computed velocity and particle diameter. Many water-treatment designs keep Re < 0.2 for confident Stokes behavior, while Re > 1 often needs non‑Stokes drag models.
3) What the calculator needs
You provide diameter d, particle density ρp, fluid density ρf, dynamic viscosity μ, and gravity g. Typical values include quartz at about 2650 kg/m³, freshwater near 998 kg/m³ at 20 °C, and viscosity near 1.00 mPa·s at 20 °C. The calculator converts common units to consistent SI internally.
4) Interpreting Reynolds number output
Reynolds number combines fluid density, velocity, particle size, and viscosity. If you see warnings, treat the Stokes velocity as an initial estimate. Increasing diameter, decreasing viscosity, or increasing density contrast raises velocity and often pushes Re upward. For coarse sand and gravel in water, transitional or turbulent settling is common.
5) Temperature and viscosity effects
Viscosity is highly temperature dependent, so settling can change significantly with season or process heating. As a reference, water viscosity is roughly 1.31 mPa·s at 10 °C and about 0.89 mPa·s at 25 °C. Because velocity is inversely proportional to μ, warming from 10 °C to 25 °C can increase settling speed by nearly 47%.
6) Shape and slip corrections
Natural sediments are rarely perfect spheres. The optional shape factor χ reduces the ideal Stokes velocity to represent extra drag from angular grains or flakes. The Cunningham correction Cc is mainly for very small particles in gases; for liquids, using Cc=1 is normally appropriate.
7) Hindered settling in suspensions
In concentrated slurries, particles interact and settling slows. The calculator can apply a simple hindered settling factor (1−φ)n, where φ is solids volume fraction. For example, with φ=0.10 and n=4.65, velocity becomes about 0.63 of the dilute value, a large reduction for thickened flows.
8) Using results in design work
Use the computed velocity to estimate residence time or settling distance: distance equals velocity times time. Convert to m/day for basin-scale intuition, or mm/s for laboratory comparisons. When sizing units, combine this result with flow rate, overflow rate targets, and safety factors, and revisit assumptions if the Reynolds number warning appears.
1) What particle sizes fit Stokes settling best?
Very small particles in laminar conditions, often silt-sized and smaller. Use the Reynolds output; values below about 0.2 typically indicate Stokes assumptions are reasonable.
2) Why does density difference matter so much?
The driving force is proportional to (ρp − ρf). Lower contrast reduces buoyancy-corrected weight, so velocity drops even if particle size and viscosity stay the same.
3) Should I use kinematic viscosity instead of dynamic viscosity?
This calculator uses dynamic viscosity μ. If you have kinematic viscosity ν, convert using μ = ρf·ν before entering values to keep units consistent.
4) When should I apply a shape factor?
Apply it when grains are noticeably non-spherical, such as flakes, needles, or angular fragments. A larger χ represents more drag and reduces the predicted settling velocity.
5) Is Cunningham correction needed for water treatment?
Usually no. It is mainly for sub‑micron particles settling in gases. For liquids like water, set Cc to 1 unless you have a specific micro‑scale slip reason.
6) How do I estimate settling time for a tank depth?
Time ≈ depth / velocity. Use consistent units: meters with m/s, or convert velocity to m/day for daily residence calculations in basins.
7) What if Reynolds number is high?
Treat the output as a starting estimate. High Re suggests transitional or turbulent settling, so use a broader drag correlation or a specialized settling model for improved accuracy.