Diameter Of Particle Given Settling Velocity Calculator

Formula Used:

\[ \text{Effective Particle Diameter} = \frac{3 \times \text{Drag Coefficient} \times \text{Liquid Density} \times \text{Settling Velocity}^2}{4 \times g \times (\text{Density of Particle} - \text{Liquid Density})} \]

Drag Coefficient:

Liquid Density:

kg/m³

Settling Velocity:

m/s

Density of Particle:

kg/m³

Effective Particle Diameter:

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1. What is Effective Particle Diameter?

The Effective Particle Diameter is the diameter of the particles in a granular sample for which 10 percent of the total grains are smaller and 90 percent larger on a weight basis. It's a crucial parameter in sedimentation and fluid mechanics calculations.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Effective Particle Diameter} = \frac{3 \times C_D \times \rho_{\text{liquid}} \times V_s^2}{4 \times g \times (\rho_p - \rho_{\text{liquid}})} \]

Where:

\( C_D \) — Drag Coefficient (dimensionless)
\( \rho_{\text{liquid}} \) — Liquid Density (kg/m³)
\( V_s \) — Settling Velocity (m/s)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( \rho_p \) — Density of Particle (kg/m³)

Explanation: This formula calculates the effective diameter of particles based on their settling behavior in a fluid, accounting for drag forces and density differences.

3. Importance of Particle Diameter Calculation

Details: Accurate particle diameter calculation is essential for sedimentation studies, filtration system design, environmental engineering, and various industrial processes involving particle-fluid interactions.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure particle density is greater than liquid density for valid results. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of drag coefficient?
A: The drag coefficient quantifies the resistance of a particle in a fluid environment and depends on the particle's shape and flow conditions.

Q2: Why is gravitational acceleration constant used?
A: Gravitational acceleration affects the settling velocity of particles and is a fundamental constant in sedimentation calculations.

Q3: What happens if particle density equals liquid density?
A: If densities are equal, the denominator becomes zero, making the result undefined as the particle would neither sink nor float.

Q4: What are typical values for drag coefficient?
A: Drag coefficient varies with particle shape and flow regime, typically ranging from 0.1 for streamlined shapes to 2.0 for irregular shapes.

Q5: Can this formula be used for all particle sizes?
A: This formula is generally applicable for spherical particles in various flow regimes, but may need adjustments for very small or non-spherical particles.