Radius Of Particle Given Effective Weight Of Particle Calculator

Formula Used:

\[ r_p = \left( \frac{W_p}{\left( \frac{4}{3} \right) \pi \left( \gamma_s - \gamma_w \right)} \right)^{\frac{1}{3}} \]

Effective Weight of Particle (Wp):

Unit Weight of Particle (γs):

N/m³

Unit Weight of Water (γw):

N/m³

Radius of Particle (rp):

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1. What is Radius of Particle?

The radius of a particle is the measure of the distance from the center of a particle to its outer surface. It's a fundamental parameter in particle physics, fluid mechanics, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_p = \left( \frac{W_p}{\left( \frac{4}{3} \right) \pi \left( \gamma_s - \gamma_w \right)} \right)^{\frac{1}{3}} \]

Where:

\( r_p \) — Radius of Particle (m)
\( W_p \) — Effective Weight of Particle (kg)
\( \gamma_s \) — Unit Weight of Particle (N/m³)
\( \gamma_w \) — Unit Weight of Water (N/m³)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The formula calculates the radius of a particle based on its effective weight (weight minus buoyancy) and the density difference between the particle material and water.

3. Importance of Particle Radius Calculation

Details: Calculating particle radius is crucial in sedimentation analysis, filtration processes, particle size distribution studies, and various industrial applications involving particulate materials.

4. Using the Calculator

Tips: Enter effective weight in kg, unit weights in N/m³. All values must be positive, and unit weight of particle must be greater than unit weight of water for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is effective weight of a particle?
A: Effective weight is the difference between the total weight of the particle and the buoyant force acting on it when submerged in fluid.

Q2: Why is unit weight difference important in this calculation?
A: The difference between particle unit weight and water unit weight determines the net gravitational force acting on the submerged particle.

Q3: What are typical unit weight values for common materials?
A: Unit weight of water is approximately 9810 N/m³. Common materials range from 15000-30000 N/m³ for minerals to 7000-12000 N/m³ for organic particles.

Q4: Can this formula be used for non-spherical particles?
A: This formula assumes spherical particles. For non-spherical particles, equivalent spherical radius or shape factors need to be considered.

Q5: What are the limitations of this calculation?
A: The calculation assumes ideal conditions, spherical particles, and doesn't account for factors like particle surface roughness, fluid viscosity effects, or particle interactions.