How To Calculate Settling Velocity

Settling Velocity Equation:

\[ v = \frac{2}{9} \times \frac{(\rho_p - \rho_f)}{\mu} \times g \times r^2 \]

Particle Density (ρ_p):

kg/m³

Fluid Density (ρ_f):

kg/m³

Viscosity (μ):

Pa·s

Particle Radius (r):

Settling Velocity (v):

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1. What is Settling Velocity?

Settling velocity is the speed at which a particle falls through a fluid medium when the gravitational force is balanced by the drag force. It's derived from Stokes' law for small spherical particles in laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the Stokes' law equation:

\[ v = \frac{2}{9} \times \frac{(\rho_p - \rho_f)}{\mu} \times g \times r^2 \]

Where:

\( v \) — Settling velocity (m/s)
\( \rho_p \) — Particle density (kg/m³)
\( \rho_f \) — Fluid density (kg/m³)
\( \mu \) — Dynamic viscosity (Pa·s)
\( g \) — Gravitational acceleration (9.81 m/s²)
\( r \) — Particle radius (m)

Explanation: The equation shows that settling velocity increases with particle size and density difference, and decreases with higher fluid viscosity.

3. Importance of Settling Velocity

Details: Settling velocity calculations are crucial in sedimentation processes, water treatment, air pollution control, and various industrial applications where particle separation is needed.

4. Using the Calculator

Tips: Enter all values in SI units (kg/m³ for densities, Pa·s for viscosity, meters for radius). Ensure particle radius is small (typically <100 μm) for Stokes' law validity.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Stokes' law?
A: Stokes' law applies only to small, spherical particles in laminar flow (low Reynolds number <1). It's invalid for non-spherical particles or turbulent conditions.

Q2: How does temperature affect settling velocity?
A: Temperature affects fluid viscosity (μ). Higher temperature typically reduces viscosity, increasing settling velocity for the same particle.

Q3: What if my particle isn't spherical?
A: For non-spherical particles, use equivalent spherical diameter or more complex equations that account for shape factors.

Q4: When should I consider fluid density?
A: Fluid density becomes important when it's significant compared to particle density (e.g., gas bubbles in liquid or very light particles).

Q5: What's the maximum particle size for this equation?
A: Generally valid for particles <100 μm in water. Larger particles may require corrections for higher Reynolds numbers.