Diameter Of Particle Given Settling Velocity Within Transition Zone Calculator

Formula Used:

\[ D_p = \left( \frac{\left( \frac{V_s'^{1/0.714}}{g \cdot (G-1)} \right)}{13.88 \cdot \nu^{0.6}} \right)^{1/1.6} \]

Settling Velocity in Transition Zone (Vs'):

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 Calculation?

The diameter of particle calculation determines the size of sediment particles based on their settling velocity in the transition zone, accounting for gravitational forces, specific gravity, and fluid viscosity.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ D_p = \left( \frac{\left( \frac{V_s'^{1/0.714}}{g \cdot (G-1)} \right)}{13.88 \cdot \nu^{0.6}} \right)^{1/1.6} \]

Where:

\( D_p \) — Diameter of Particle (m)
\( V_s' \) — Settling Velocity in Transition Zone (m/s)
\( g \) — Acceleration due to Gravity (m/s²)
\( G \) — Specific Gravity of Sediment
\( \nu \) — Kinematic Viscosity (m²/s)

Explanation: The equation calculates particle diameter based on the settling behavior in the transition zone between Stokes' law and Newton's law settling regimes.

3. Importance of Particle Diameter Calculation

Details: Accurate particle diameter estimation is crucial for sediment transport studies, hydraulic engineering, environmental assessments, and understanding sedimentation processes in natural and engineered systems.

4. Using the Calculator

Tips: Enter settling velocity in m/s, acceleration due to gravity in m/s², 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 transition zone in settling velocity?
A: The transition zone occurs between Stokes' law (laminar flow) and Newton's law (turbulent flow) regimes, where neither law fully applies and intermediate equations are used.

Q2: What are typical values for kinematic viscosity?
A: For water at 20°C, kinematic viscosity is approximately 1.0 × 10⁻⁶ m²/s. The value decreases with increasing temperature.

Q3: How does specific gravity affect particle diameter calculation?
A: Higher specific gravity (denser particles) results in larger calculated diameters for the same settling velocity, as denser particles settle faster.

Q4: What is the range of applicability for this formula?
A: This formula is specifically designed for the transition zone where Reynolds numbers are typically between 0.3 and 1000.

Q5: Can this calculator be used for non-spherical particles?
A: The formula assumes spherical particles. For non-spherical particles, results should be interpreted as equivalent spherical diameters.