Settling Velocity Given Specific Gravity of Particle and Viscosity Calculator

Settling Velocity Formula:

\[ V_s = \frac{[g] \times (G - 1) \times D^2}{18 \times \nu} \]

Specific Gravity of Particle (G):

(dimensionless)

Diameter (D):

meters

Kinematic Viscosity (ν):

m²/s

Settling Velocity (V_s):

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1. What is Settling Velocity?

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

2. How Does the Calculator Work?

The calculator uses the Stokes' law formula for settling velocity:

\[ V_s = \frac{[g] \times (G - 1) \times D^2}{18 \times \nu} \]

Where:

\( V_s \) — Settling velocity (m/s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( G \) — Specific gravity of particle (dimensionless)
\( D \) — Diameter of particle (meters)
\( \nu \) — Kinematic viscosity of fluid (m²/s)

Explanation: This formula applies to spherical particles settling in a viscous fluid under laminar flow conditions (low Reynolds number).

3. Importance of Settling Velocity Calculation

Details: Calculating settling velocity is 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 specific gravity of the particle (ratio of particle density to fluid density), particle diameter in meters, and kinematic viscosity of the fluid in m²/s. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this formula?
A: This formula is valid for spherical particles in laminar flow conditions (Reynolds number less than 0.3).

Q2: How does temperature affect settling velocity?
A: Temperature affects kinematic viscosity, which inversely affects settling velocity. Higher temperature generally increases settling velocity.

Q3: What if the particle is not spherical?
A: For non-spherical particles, shape factors and equivalent diameter concepts must be used, making the calculation more complex.

Q4: Can this formula be used for all fluid types?
A: The formula works best for Newtonian fluids. For non-Newtonian fluids, additional considerations are needed.

Q5: What are typical settling velocity values?
A: Settling velocities vary widely depending on particle size and density, ranging from micrometers per second for fine particles to centimeters per second for larger particles.