Velocity of Particle One at Distance from Explosion Calculator

Velocity of Particle Formula:

\[ v_1 = v_2 \times \left( \frac{D_2}{D_1} \right)^{1.5} \]

Velocity of Particle with Mass m2:

m/s

Distance of Particle 2 from Explosion:

Distance of Particle 1 from Explosion:

Velocity of Particle with Mass m1:

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1. What is the Velocity of Particle Formula?

The velocity of particle formula calculates the velocity of one particle relative to another based on their distances from an explosion point. This formula demonstrates the inverse relationship between distance from explosion and particle velocity.

2. How Does the Calculator Work?

The calculator uses the velocity formula:

\[ v_1 = v_2 \times \left( \frac{D_2}{D_1} \right)^{1.5} \]

Where:

\( v_1 \) — Velocity of particle with mass m1 (m/s)
\( v_2 \) — Velocity of particle with mass m2 (m/s)
\( D_2 \) — Distance of particle 2 from explosion (m)
\( D_1 \) — Distance of particle 1 from explosion (m)

Explanation: The formula shows that particle velocity decreases with increasing distance from the explosion point, following an inverse power law relationship.

3. Importance of Velocity Calculation

Details: Calculating particle velocities from explosions is crucial for understanding blast dynamics, assessing damage potential, and designing safety measures in various industries including mining, demolition, and defense.

4. Using the Calculator

Tips: Enter velocity of particle 2 in m/s, distances of both particles from explosion in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the exponent 1.5 in the formula?
A: The exponent 1.5 represents the scaling relationship between distance and velocity in explosion dynamics, accounting for energy dissipation in three-dimensional space.

Q2: Does particle mass affect the velocity calculation?
A: While mass isn't explicitly in the formula, it's implicitly accounted for through the measured velocities of the particles.

Q3: What are typical velocity ranges for explosion particles?
A: Velocities can range from a few m/s for distant particles to hundreds of m/s for particles close to the explosion center, depending on the explosive force.

Q4: Are there limitations to this formula?
A: This formula provides an approximation and may not account for all factors like air resistance, particle shape, or heterogeneous explosive materials.

Q5: Can this formula be used for underwater explosions?
A: The formula may need modification for underwater applications as water density and compression characteristics differ significantly from air.