Terminal Velocity Of Fluids For Irregular Shaped Particles Calculator

Terminal Velocity Formula:

\[ u_t = \left( \frac{18}{(d_p')^2} + \frac{2.335 - 1.744 \cdot \Phi_p}{\sqrt{d_p'}} \right)^{-1} \]

Terminal Velocity of Fluid (u_t):

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1. What is Terminal Velocity of Fluid?

Terminal Velocity of Fluid is the maximum velocity achieved by a particle when the drag force equals the gravitational force in a fluid medium. For irregular shaped particles, this velocity depends on both the dimensionless diameter and the sphericity of the particle.

2. How Does the Calculator Work?

The calculator uses the terminal velocity formula for irregular shaped particles:

\[ u_t = \left( \frac{18}{(d_p')^2} + \frac{2.335 - 1.744 \cdot \Phi_p}{\sqrt{d_p'}} \right)^{-1} \]

Where:

\( u_t \) — Terminal velocity of fluid (m/s)
\( d_p' \) — Dimensionless diameter
\( \Phi_p \) — Sphericity of particle (0 to 1)

Explanation: This formula accounts for both the size and shape characteristics of irregular particles in fluid flow, providing an accurate estimation of terminal velocity.

3. Importance of Terminal Velocity Calculation

Details: Calculating terminal velocity is crucial for various engineering applications including sedimentation processes, fluidized bed operations, particle separation, and environmental studies involving particle transport in fluids.

4. Using the Calculator

Tips: Enter the dimensionless diameter (must be greater than 0) and sphericity of particle (value between 0 and 1, where 1 represents a perfect sphere). The calculator will compute the terminal velocity in meters per second.

5. Frequently Asked Questions (FAQ)

Q1: What is dimensionless diameter?
A: Dimensionless diameter is a parameter used to characterize the size of solid particles relative to the flow conditions of the gas phase, accounting for fluid properties and particle characteristics.

Q2: How is sphericity defined?
A: Sphericity is a measure of how closely the shape of a particle resembles that of a perfect sphere, with values ranging from 0 (completely irregular) to 1 (perfect sphere).

Q3: What factors affect terminal velocity?
A: Terminal velocity depends on particle size, shape, density, fluid density, and fluid viscosity. The formula incorporates these through the dimensionless parameters.

Q4: When is this formula applicable?
A: This formula is specifically designed for irregular shaped particles in fluid flow and provides accurate results across a wide range of particle shapes and sizes.

Q5: What are typical terminal velocity values?
A: Terminal velocity values vary significantly depending on particle characteristics and fluid properties, ranging from millimeters per second for fine particles to meters per second for larger particles.