Question

The particle Reynolds number (Re) in fluid classification is given by:

• A. \( \text{Re} = (\rho d V) / \mu \)
• B. \( \text{Re} = (\mu V) / \rho \)
• C. \( \text{Re} = (\rho g V) / \sigma \)
• D. \( \text{Re} = (\rho^2 V) / \mu^2 \)

Hint:

Double check the units of each term to verify dimensionlessness:
\( [ \rho ] = \text{kg/m}^3 \), \( [ d ] = \text{m} \), \( [ V ] = \text{m/s} \), and \( [ \mu ] = \text{kg/(m}\cdot\text{s)} \).
They cancel out completely, yielding a dimensionless value.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the mathematical expression of the particle Reynolds number (Re) used in fluid classification processes.
Reynolds number is a dimensionless quantity in fluid mechanics used to characterize fluid flow regimes and particle settling behavior.

Step 2: Key Formula or Approach:
The Reynolds number represents the ratio of inertial forces to viscous forces acting on a body moving relative to a fluid:
\[ \text{Re} = \frac{\text{Inertial Forces}}{\text{Viscous Forces}} = \frac{\rho \cdot d \cdot V}{\mu} \]
where:
\( \rho \) is the density of the fluid,
\( d \) is the characteristic diameter of the solid particle,
\( V \) is the relative velocity between the particle and the fluid, and
\( \mu \) is the dynamic viscosity of the fluid.

Step 3: Detailed Explanation:

• Significance in Settling Regimes:
- At low Reynolds numbers (\( \text{Re} \lt 0.1 \)), viscous forces dominate. This is the laminar flow regime described by Stokes' law, where settling drag force is directly proportional to particle velocity.
- At high Reynolds numbers (\( \text{Re} \gt 1000 \)), inertial forces dominate, leading to turbulent flow described by Newton's law of settling, where drag is proportional to the square of velocity.

• Fluid Classification Applications: This dimensionless parameter is essential for designing and analyzing mineral processing equipment like hydrocyclones, classifiers, and gravity concentrators, where particle separation depends on relative settling velocities.


Step 4: Final Answer:
The correct expression for the particle Reynolds number is \( \text{Re} = (\rho d V) / \mu \), which is Option (A).