Diameter Given Specific Gravity Of Particle And Viscosity Calculator

Formula Used:

\[ D = \sqrt{\frac{V_s \cdot \nu \cdot 18}{g \cdot (G - 1)}} \]

Diameter (D):

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1. What is the Diameter Calculation Formula?

The diameter calculation formula determines the particle diameter based on settling velocity, kinematic viscosity, and specific gravity of the particle. It's derived from Stokes' law and accounts for gravitational forces acting on particles in fluid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \sqrt{\frac{V_s \cdot \nu \cdot 18}{g \cdot (G - 1)}} \]

Where:

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

Explanation: This formula calculates the diameter of spherical particles settling in a fluid under gravity, considering the balance between gravitational, buoyant, and drag forces.

3. Importance of Diameter Calculation

Details: Accurate diameter calculation is crucial for particle size analysis, sedimentation studies, filtration system design, and understanding particle behavior in fluid environments.

4. Using the Calculator

Tips: Enter settling velocity in m/s, kinematic viscosity in m²/s, and specific gravity (must be greater than 1). All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this formula?
A: This formula is valid for small spherical particles in laminar flow conditions (low Reynolds numbers).

Q2: How does specific gravity affect the diameter calculation?
A: Higher specific gravity particles settle faster and therefore would have larger calculated diameters for the same settling velocity.

Q3: What units should be used for input values?
A: Use SI units: m/s for velocity, m²/s for kinematic viscosity, and dimensionless for specific gravity.

Q4: Can this formula be used for non-spherical particles?
A: The formula assumes spherical particles. For non-spherical particles, the result represents an equivalent spherical diameter.

Q5: What are typical applications of this calculation?
A: This calculation is used in sedimentology, water treatment, mineral processing, and environmental engineering for particle size analysis.