What is Settling Velocity?

Settling velocity, also known as terminal velocity, is the speed at which a particle falls through a fluid (like water or air) under the influence of gravity when the drag force and buoyancy combined equal the weight of the particle. This calculation is vital in fields such as environmental engineering, wastewater treatment, and geology to determine how quickly sediments or pollutants will settle at the bottom of a tank or river.

Understanding Stokes' Law

For small particles in a laminar flow (low Reynolds number), settling velocity is governed by Stokes' Law. The formula is expressed as:
v = (g * d² * (ρ_s - ρ_f)) / (18 * μ)

Where:

• v: Settling velocity (m/s)
• g: Gravitational acceleration (~9.81 m/s²)
• d: Particle diameter (m)
• ρ_s: Density of the particle (kg/m³)
• ρ_f: Density of the fluid (kg/m³)
• μ: Dynamic viscosity of the fluid (kg/m·s or Pa·s)

How to Use the Calculator

1. Enter the particle diameter in millimeters (the tool will automatically convert this to meters for the calculation).
2. Input the density of the particle (sand is typically 2650 kg/m³).
3. Input the fluid density (water is 1000 kg/m³).
4. Provide the dynamic viscosity of the fluid (water at 20°C is roughly 0.001 kg/m·s).
5. Click Calculate to view the result and the step-by-step derivation.

Frequently Asked Questions

What factors affect settling velocity?

Settling velocity is primarily influenced by particle size, particle shape, fluid viscosity, and the density difference between the particle and the fluid. Larger and denser particles settle faster.

Does this calculator work for all particle sizes?

This calculator uses Stokes' Law, which is most accurate for small, spherical particles (typically less than 0.1 mm in water) where the flow around the particle remains laminar.