Settling Velocity Calculator

Settling Velocity Formula:

\[ V_s = \sqrt{\frac{4 \cdot [g] \cdot (\rho_p - \rho_{liquid}) \cdot D_E}{3 \cdot C_D \cdot \rho_{liquid}}} \]

Density of Particle:

kg/m³

Liquid Density:

kg/m³

Effective Particle Diameter:

Drag Coefficient:

Settling Velocity:

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1. What is Settling Velocity?

Settling velocity refers to the terminal velocity of a particle in a still fluid. It is the constant speed that a particle eventually reaches when the resistance of the fluid equals the force of gravity acting on the particle.

2. How Does the Calculator Work?

The calculator uses the settling velocity formula:

\[ V_s = \sqrt{\frac{4 \cdot [g] \cdot (\rho_p - \rho_{liquid}) \cdot D_E}{3 \cdot C_D \cdot \rho_{liquid}}} \]

Where:

\( V_s \) — Settling velocity (m/s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \rho_p \) — Density of particle (kg/m³)
\( \rho_{liquid} \) — Liquid density (kg/m³)
\( D_E \) — Effective particle diameter (m)
\( C_D \) — Drag coefficient (dimensionless)

Explanation: The formula calculates the terminal velocity of a particle settling in a fluid based on the balance between gravitational force and fluid drag resistance.

3. Importance of Settling Velocity Calculation

Details: Settling velocity calculations are crucial in various engineering applications including sedimentation processes, water treatment, mineral processing, and environmental studies of particle transport in fluids.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Density of particle and liquid density should be in kg/m³, effective particle diameter in meters, and drag coefficient as a dimensionless value. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect settling velocity?
A: Settling velocity is affected by particle size, particle density, fluid density, fluid viscosity, and the shape of the particle through the drag coefficient.

Q2: How does particle shape influence settling velocity?
A: Particle shape affects the drag coefficient. Spherical particles have different drag characteristics than irregularly shaped particles, which influences their settling behavior.

Q3: What is the typical range of drag coefficients?
A: For spheres, drag coefficients range from about 0.1 to 0.5 depending on Reynolds number. For irregular particles, values can vary more significantly.

Q4: When is this formula most accurate?
A: This formula provides good accuracy for spherical particles settling in Newtonian fluids under laminar flow conditions.

Q5: How does temperature affect settling velocity?
A: Temperature affects fluid density and viscosity, which in turn influence the drag coefficient and thus the settling velocity of particles.