Diameter For Settling Velocity With Respect To Kinematic Viscosity Calculator

Formula Used:

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

Settling Velocity (Vs):

m/s

Kinematic Viscosity (ν):

m²/s

Specific Gravity of Particle (G):

Specific Gravity of Fluid (Gf):

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 differences between particle and fluid. This formula is derived from Stokes' law and is widely used in fluid mechanics and particle sedimentation studies.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

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
\( G_f \) — Specific gravity of fluid

Explanation: The formula calculates the diameter of a spherical particle 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 values (dimensionless). All values must be positive, and particle specific gravity must be greater than fluid specific gravity.

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, typically Re < 0.3).

Q2: Can this formula be used for non-spherical particles?
A: The formula assumes spherical particles. For non-spherical particles, shape factors and equivalent spherical diameter concepts must be considered.

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

Q4: Why is specific gravity difference important?
A: The buoyant force depends on the density difference between particle and fluid, which is proportional to the specific gravity difference.

Q5: What if the particle specific gravity is less than fluid specific gravity?
A: The particle would float rather than settle, making the calculation invalid for such cases.