Terminal Settling Velocity Of Single Particle Calculator

Formula Used:

\[ Terminal\ Velocity\ of\ Single\ Particle = \frac{Settling\ Velocity\ of\ Group\ of\ Particles}{(Void\ fraction)^{Richardsonb\ Zaki\ Index}} \] \[ V_t = \frac{V}{\epsilon^n} \]

Settling Velocity of Group of Particles (V):

m/s

Void Fraction (ε):

Richardsonb Zaki Index (n):

Terminal Velocity of Single Particle (Vt):

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1. What is Terminal Settling Velocity of Single Particle?

Terminal Velocity of single particle is the velocity resulting from the action of accelerating and drag forces. It represents the maximum velocity attained by a particle as it falls through a fluid under gravity when the drag force equals the gravitational force.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_t = \frac{V}{\epsilon^n} \]

Where:

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

Explanation: This formula relates the terminal velocity of a single particle to the settling velocity of a group of particles, accounting for the void fraction and the Richardson-Zaki index which characterizes the hindered settling behavior.

3. Importance of Terminal Velocity Calculation

Details: Calculating terminal settling velocity is crucial in various industrial processes including sedimentation, fluidization, and particle separation. It helps in designing equipment like settling tanks, clarifiers, and fluidized bed reactors.

4. Using the Calculator

Tips: Enter settling velocity in m/s, void fraction (between 0 and 1), and Richardsonb Zaki index. All values must be valid positive numbers with void fraction ≤ 1.

5. Frequently Asked Questions (FAQ)

Q1: What is void fraction?
A: Void fraction is the fraction of the channel volume that is occupied by the gas phase or the empty space between particles in a mixture.

Q2: What is Richardsonb Zaki Index?
A: Richardsonb Zaki Index is the fractional volumetric concentration of solid particles that characterizes the hindered settling behavior in particle-fluid systems.

Q3: When is this formula applicable?
A: This formula is applicable for calculating the terminal velocity of single particles in hindered settling conditions where particle interactions affect the settling behavior.

Q4: What are typical values for Richardsonb Zaki Index?
A: The Richardsonb Zaki Index typically ranges from 2.4 to 4.6 depending on the Reynolds number and particle characteristics.

Q5: How does void fraction affect terminal velocity?
A: As void fraction decreases (more particles present), the terminal velocity increases due to reduced fluid resistance and hindered settling effects.