Diameter Given Settling Velocity With Respect To Dynamic Viscosity Calculator

Formula Used:

\[ D = \sqrt{\frac{18 \times V_s \times \mu}{[g] \times (\rho - \rho_{liquid})}} \]

Settling Velocity (Vs):

m/s

Dynamic Viscosity (μ):

Pa·s

Mass Density (ρ):

kg/m³

Liquid Density (ρ_liquid):

kg/m³

Diameter (D):

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1. What is the Diameter Calculation Formula?

This formula calculates the diameter of a particle based on its settling velocity, dynamic viscosity of the fluid, and the density difference between the particle and the fluid. It's derived from Stokes' law for spherical particles settling in a viscous fluid under gravity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \sqrt{\frac{18 \times V_s \times \mu}{[g] \times (\rho - \rho_{liquid})}} \]

Where:

\( D \) — Diameter of the particle (m)
\( V_s \) — Settling velocity (m/s)
\( \mu \) — Dynamic viscosity (Pa·s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \rho \) — Mass density of the particle (kg/m³)
\( \rho_{liquid} \) — Liquid density (kg/m³)

Explanation: This formula calculates the diameter of spherical particles based on their terminal settling velocity in a viscous fluid, accounting for gravitational forces and density differences.

3. Importance of Diameter Calculation

Details: Accurate particle diameter calculation is crucial for various applications including sedimentation studies, particle size analysis in environmental science, chemical engineering processes, and fluid mechanics research.

4. Using the Calculator

Tips: Enter settling velocity in m/s, dynamic viscosity in Pa·s, mass density and liquid density in kg/m³. All values must be positive, and mass density must be greater than liquid density for the calculation to be valid.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions behind this formula?
A: This formula assumes spherical particles, laminar flow conditions (low Reynolds number), and that the particles are settling in an infinite fluid medium.

Q2: What is the typical range of applicability?
A: This formula works best for small particles (typically < 100μm) settling in viscous fluids where Stokes' law is valid (Re < 0.3).

Q3: How does temperature affect the calculation?
A: Temperature affects both dynamic viscosity and density values. For accurate results, use viscosity and density values measured at the same temperature.

Q4: Can this be used for non-spherical particles?
A: The formula is specifically derived for spherical particles. For non-spherical particles, additional shape factors and corrections are needed.

Q5: What units should be used for input values?
A: Use consistent SI units: m/s for velocity, Pa·s for viscosity, and kg/m³ for densities to get diameter in meters.