Effective Weight Of Particle Calculator

Formula Used:

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

Effective Weight of Particle:

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1. What is Effective Weight of Particle?

Effective Weight of Particle is the difference between the total weight of a particle and its buoyant force in a fluid. It represents the actual weight that the particle exerts when submerged in a fluid medium.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the effective weight by considering the particle's volume and the density difference between the particle material and the surrounding fluid.

3. Importance of Effective Weight Calculation

Details: Calculating effective weight is crucial in sediment transport studies, filtration processes, and various engineering applications where particles interact with fluid environments. It helps determine settling velocities and particle behavior in fluid flows.

4. Using the Calculator

Tips: Enter the radius of particle in meters, unit weight of particle in N/m³, and unit weight of water in N/m³. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of effective weight in fluid mechanics?
A: Effective weight determines the net gravitational force acting on a submerged particle, which influences its settling behavior and transport characteristics in fluid flows.

Q2: How does particle radius affect the effective weight?
A: The effective weight increases with the cube of the particle radius, meaning larger particles have significantly greater effective weights than smaller ones.

Q3: What happens when unit weight of particle equals unit weight of water?
A: When γs = γw, the effective weight becomes zero, resulting in neutral buoyancy where the particle neither sinks nor rises in the fluid.

Q4: Can this formula be used for non-spherical particles?
A: The formula is specifically derived for spherical particles. For non-spherical particles, shape factors and equivalent diameters need to be considered.

Q5: What are typical unit weight values for common materials?
A: Unit weight of water is approximately 9810 N/m³. Common soil particles range from 25,000-27,000 N/m³, while lighter materials like plastics may have lower unit weights.