Diameter Of Particle Given Settling Velocity Of Spherical Particle Calculator

Formula Used:

\[ D_p = \sqrt{\frac{V_{sp}}{(\frac{g}{18}) \times (G - 1) \times (\frac{1}{\nu})}} \]

Settling Velocity of Spherical Particle (Vsp):

m/s

Acceleration due to Gravity (g):

m/s²

Specific Gravity of Sediment (G):

Kinematic Viscosity (ν):

m²/s

Diameter of Particle (Dp):

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1. What is the Diameter of Particle Formula?

The formula calculates the diameter of a spherical particle based on its settling velocity in a fluid, using the principles of fluid dynamics and Stokes' law. It considers gravitational acceleration, specific gravity of the sediment, and kinematic viscosity of the fluid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_p = \sqrt{\frac{V_{sp}}{(\frac{g}{18}) \times (G - 1) \times (\frac{1}{\nu})}} \]

Where:

\( D_p \) — Diameter of Particle (m)
\( V_{sp} \) — Settling Velocity of Spherical Particle (m/s)
\( g \) — Acceleration due to Gravity (m/s²)
\( G \) — Specific Gravity of Sediment
\( \nu \) — Kinematic Viscosity (m²/s)

Explanation: The formula derives from Stokes' law and calculates particle diameter based on its terminal settling velocity in a fluid medium.

3. Importance of Particle Diameter Calculation

Details: Accurate particle diameter calculation is crucial for sediment transport studies, water treatment processes, environmental engineering, and understanding particle behavior in fluid systems.

4. Using the Calculator

Tips: Enter settling velocity in m/s, acceleration due to gravity in m/s² (default 9.8), specific gravity (must be greater than 1), and kinematic viscosity in m²/s. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of specific gravity in this calculation?
A: Specific gravity indicates the density of sediment particles relative to water, which affects the buoyancy force and thus the settling behavior.

Q2: Why is kinematic viscosity important?
A: Kinematic viscosity represents the fluid's resistance to flow and affects the drag force on the particle during settling.

Q3: What are typical values for kinematic viscosity?
A: For water at 20°C, kinematic viscosity is approximately 1.0 × 10⁻⁶ m²/s. Values vary with temperature.

Q4: What assumptions does this formula make?
A: The formula assumes spherical particles, laminar flow conditions, and applies Stokes' law which is valid for small Reynolds numbers.

Q5: When is this calculation not applicable?
A: This calculation may not be accurate for non-spherical particles, high Reynolds numbers (turbulent flow), or when particle interactions affect settling.