Unit Weight Of Particle Given Effective Weight Of Particle Calculator

Formula Used:

\[ \text{Unit Weight of Particle} = \frac{\text{Effective Weight of Particle}}{\frac{4}{3} \pi (\text{Radius})^3} + \text{Unit Weight of Water} \] \[ \gamma_s = \frac{W_p}{\frac{4}{3} \pi r^3} + \gamma_w \]

Unit Weight of Particle (γs):

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1. What is Unit Weight of Particle?

Unit Weight of Particle is defined as weight per unit volume of the particle. It represents the density of the particle material and is a fundamental property in geotechnical engineering and soil mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_s = \frac{W_p}{\frac{4}{3} \pi r^3} + \gamma_w \]

Where:

\( \gamma_s \) — Unit Weight of Particle (N/m³)
\( W_p \) — Effective Weight of Particle (kg)
\( r \) — Radius of Particle (m)
\( \gamma_w \) — Unit Weight of Water (N/m³)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the unit weight by dividing the effective weight by the volume of the spherical particle and adding the unit weight of water to account for buoyancy effects.

3. Importance of Unit Weight Calculation

Details: Accurate calculation of unit weight is crucial for determining particle density, analyzing soil properties, designing foundations, and understanding sedimentation processes in various engineering applications.

4. Using the Calculator

Tips: Enter effective weight in kg, radius in meters, and unit weight of water in N/m³. All values must be positive numbers. For water at standard conditions, use 9810 N/m³.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between unit weight and density?
A: Unit weight is weight per unit volume (N/m³), while density is mass per unit volume (kg/m³). They are related by gravitational acceleration.

Q2: Why add unit weight of water in the formula?
A: The unit weight of water is added to account for buoyancy effects when the particle is submerged in water.

Q3: What is effective weight of particle?
A: Effective weight is the difference between total weight and buoyancy force acting on the particle when submerged.

Q4: Can this formula be used for non-spherical particles?
A: This formula assumes spherical particles. For irregular shapes, equivalent spherical radius or shape factors may be needed.

Q5: What are typical values for unit weight of particles?
A: Typical values range from 25,000-30,000 N/m³ for mineral particles, depending on the specific material composition.