Example Data Table
| Case | η (Pa·s) | r (µm) | v (m/s) | Fd (N) | ρf (kg/m³) | Re |
|---|---|---|---|---|---|---|
| Water, microbead | 0.001 | 50 | 0.02 | ≈ 1.885e-08 | 998 | ≈ 0.0040 |
| Glycerin, small particle | 1.2 | 20 | 0.005 | ≈ 4.524e-06 | 1260 | ≈ 0.00000084 |
| Light oil, larger sphere | 0.05 | 500 | 0.01 | ≈ 4.712e-06 | 850 | ≈ 0.17 |
Values are illustrative and rounded for readability.
Formula Used
Stokes drag (creeping flow, sphere):
Fd = 6 π η r v
Reynolds number (sphere, diameter d = 2r):
Re = ρf · |v| · (2r) / η
Terminal velocity in Stokes regime:
vt = 2 r² (ρp − ρf) g / (9 η)
Notes: These relations are most accurate when Re ≪ 1, the particle is spherical, and the fluid is Newtonian.
How to Use This Calculator
- Enter the fluid’s dynamic viscosity and pick its unit.
- Enter particle radius or diameter, then choose the unit.
- Enter the relative velocity between particle and fluid.
- Optionally add fluid density to estimate Reynolds number.
- Optionally add particle density and gravity for terminal velocity.
- Press Calculate to show results above the form.
- Use Download CSV or Download PDF for exports.
FAQs
1) When is Stokes drag valid?
It’s most reliable for very small Reynolds numbers, typically far below 1. The flow should be laminar, the object nearly spherical, and the fluid behavior Newtonian.
2) Why does the calculator show a Reynolds warning?
If Re rises, inertial effects and wake formation grow. Then the linear Stokes relation can underpredict drag, and empirical drag-coefficient models may be needed instead.
3) Should I enter radius or diameter?
Either works. Select the size type so the calculator converts correctly. Stokes drag uses radius in the formula, so diameter is automatically halved.
4) What viscosity should I use for mixtures?
Use the dynamic viscosity of the fluid at the operating temperature. For mixtures, use a measured viscosity if possible, since blending rules can be inaccurate.
5) What does negative velocity mean here?
It indicates direction relative to your chosen reference. Drag force follows the velocity sign in this simplified output, while Reynolds uses the speed magnitude.
6) How is terminal velocity computed?
The calculator uses the Stokes-regime settling relation balancing weight, buoyancy, and viscous drag. It assumes a spherical particle and creeping flow throughout.
7) Can I use this for bubbles or droplets?
Often yes for first estimates, but interface conditions can change drag. For clean bubbles or deformable drops, specialized correlations may be more accurate.
8) Why do my results look extremely small or large?
Check units first. Microns vs meters and cP vs Pa·s cause big changes. Also verify radius, not diameter, and ensure viscosity is positive and realistic.