Settling Velocity Of Group Of Particles Calculator

Settling Velocity of Group of Particles Formula:

\[ V = V_t \times (\epsilon)^n \]

Terminal Velocity of Single Particle (Vt):

m/s

Void Fraction (ε):

Richardsonb Zaki Index (n):

Settling Velocity of Group of Particles (V):

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1. What is Settling Velocity of Group of Particles?

The Settling Velocity of Group of Particles represents the velocity at which particles settle in a fluid medium, accounting for interactions between particles. It is typically lower than the terminal velocity of a single particle due to particle-particle interactions.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ V = V_t \times (\epsilon)^n \]

Where:

\( V \) — Settling Velocity of Group of Particles (m/s)
\( V_t \) — Terminal Velocity of Single Particle (m/s)
\( \epsilon \) — Void Fraction (-)
\( n \) — Richardsonb Zaki Index (-)

Explanation: This formula accounts for the reduced settling velocity in particle groups due to increased fluid resistance and particle interactions.

3. Importance of Settling Velocity Calculation

Details: Accurate calculation of group settling velocity is crucial for designing sedimentation tanks, clarifiers, and other separation processes in water treatment, mining, and chemical industries.

4. Using the Calculator

Tips: Enter terminal velocity in m/s, void fraction (between 0-1), and Richardsonb Zaki index. All values must be valid (velocity > 0, void fraction 0-1, index > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is void fraction?
A: Void fraction is the fraction of the total volume that is occupied by the fluid phase rather than by solid particles.

Q2: What factors affect the Richardsonb Zaki index?
A: The index depends on particle Reynolds number, particle shape, and concentration. It typically ranges from 2.4 to 4.6.

Q3: How does particle concentration affect settling velocity?
A: Higher particle concentrations generally result in lower settling velocities due to increased fluid resistance and particle interactions.

Q4: When is this formula applicable?
A: This formula is applicable for hindered settling conditions where particle concentrations are significant enough to affect settling behavior.

Q5: What are typical values for terminal velocity?
A: Terminal velocity varies widely depending on particle size, density, and fluid properties, typically ranging from 0.001 to 0.1 m/s for many industrial applications.