Stokes Law Calculator

About the Stokes Law Calculator

Stokes' law describes the drag force on a small spherical particle moving through a viscous fluid at low Reynolds numbers (Re < 1): Fd = 6πµrv. When gravity, buoyancy, and drag are in balance, the particle reaches terminal (settling) velocity vt = 2r²(ρp − ρf)g/(9µ). This relationship is fundamental to sedimentation analysis, particle sizing, and fluid mechanics.

The law applies remarkably well to a wide range of phenomena: sand settling in rivers, blood cells in centrifuges, fog droplets in air, and nanoparticles in colloidal suspensions. The key requirement is that the Reynolds number remains below about 1, ensuring viscous forces dominate over inertial forces.

For the same particle, settling velocity varies enormously with fluid viscosity: a 0.5 mm sand grain settles at ~6 cm/s in water but would take hours in honey. This calculator computes terminal velocity, drag force, Reynolds number validation, and provides a multi-fluid comparison for your particle specifications.

When This Page Helps

Use this calculator when you need a first-pass settling or drag estimate in the creeping-flow regime.

It is useful for particle transport, sedimentation intuition, separator design, and showing when the elegant low-Reynolds-number form of Stokes drag is valid and when it is not. That makes it a quick screen for whether a Stokes-model assumption is actually justified.

How to Use the Inputs

1. Select a preset scenario or enter custom values.
2. Choose mode: settling velocity or drag force at a given speed.
3. Enter particle diameter in millimeters.
4. Enter particle and fluid densities, plus dynamic viscosity.
5. Check the Reynolds number — Stokes law requires Re < 1.
6. Compare settling behavior across different fluids in the table.

Example Calculation

Tips & Best Practices

• If Re > 1, the Stokes prediction overestimates velocity — use the Oseen or empirical corrections.
• For Re > 1000, use the drag coefficient Cd ≈ 0.44 instead of Stokes' 24/Re.
• Settling velocity scales as d² — doubling diameter quadruples settling speed.
• Non-spherical particles settle slower; apply a shape factor (Wadell sphericity).
• Temperature affects viscosity significantly: water at 5°C has 60% higher µ than at 25°C.

Practical Guidance

Stokes' law works best as a clean low-Reynolds-number model for small particles in viscous flow. It is especially useful when you want to understand how diameter, viscosity, and density difference scale the settling speed before moving to broader drag correlations.

Common Pitfalls

The most common mistake is using the Stokes terminal velocity formula outside the creeping-flow regime. Once Reynolds number grows, inertia changes the drag law and the simple linear relation in velocity is no longer accurate. Particle shape, wall effects, and non-Newtonian fluids can also shift the result materially, so the calculation should be treated as a regime check as much as a velocity estimate.

Frequently Asked Questions

• When does Stokes law break down?

  When Re > 1, inertial effects become significant. For Re > 1000, turbulent wake drag dominates. Also breaks down for non-spherical particles and near boundaries.

• What if the particle is lighter than the fluid?

  The particle rises instead of sinking (negative settling velocity). Examples: air bubbles in water, oil droplets in water.

• How is this used in centrifuges?

  Centrifuges replace g with centrifugal acceleration (ω²r), greatly increasing settling velocity. This separates particles that would take hours to settle under gravity.

• What is the Cunningham correction?

  For particles smaller than ~1 µm, the continuum assumption breaks down. The Cunningham slip correction factor increases the settling velocity of very small particles.

• Can I use this for bubbles?

  Not directly. Bubbles have internal circulation that changes the drag coefficient. The Hadamard-Rybczynski solution gives Fd = 4πµrv for gas bubbles with free surfaces.

• What viscosity should I use for blood?

  Whole blood viscosity is about 3-4 mPa·s at normal shear rates. It is non-Newtonian (shear-thinning), so Stokes law gives approximate results for blood sedimentation.