New Pressure After Shock Formation For Compression Wave Calculator

Formula Used:

\[ P = \rho_1 \times \left(1 + \frac{(\gamma - 1)}{2} \times \frac{V_n}{c_{old}}\right)^{\frac{2\gamma}{(\gamma - t_{sec})}} \]

Density Ahead of Shock (ρ₁):

kg/m³

Specific Heat Ratio (γ):

Normal Velocity (Vₙ):

m/s

Old Speed of Sound (cₒₗ𝒹):

m/s

Time in Seconds (tₛₑ𝒸):

New Pressure (P):

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1. What is the New Pressure After Shock Formation Formula?

The formula calculates the pressure after shock formation for compression waves in fluid dynamics. It accounts for density ahead of the shock, specific heat ratio, normal velocity, old speed of sound, and time to determine the resulting pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = \rho_1 \times \left(1 + \frac{(\gamma - 1)}{2} \times \frac{V_n}{c_{old}}\right)^{\frac{2\gamma}{(\gamma - t_{sec})}} \]

Where:

\( P \) — New pressure after shock formation (Pa)
\( \rho_1 \) — Density ahead of shock (kg/m³)
\( \gamma \) — Specific heat ratio (dimensionless)
\( V_n \) — Normal velocity (m/s)
\( c_{old} \) — Old speed of sound (m/s)
\( t_{sec} \) — Time in seconds (s)

Explanation: The formula describes how pressure changes when a compression wave forms a shock, considering the fluid properties and wave characteristics.

3. Importance of Pressure Calculation in Shock Waves

Details: Accurate pressure calculation is crucial for understanding shock wave behavior, designing supersonic vehicles, analyzing explosive effects, and studying astrophysical phenomena.

4. Using the Calculator

Tips: Enter density in kg/m³, specific heat ratio (typically 1.4 for air), normal velocity in m/s, old speed of sound in m/s, and time in seconds. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a compression wave shock formation?
A: It occurs when compression waves coalesce to form a discontinuous shock wave with sudden pressure increase.

Q2: What are typical values for specific heat ratio?
A: For air γ ≈ 1.4, for monatomic gases γ ≈ 1.67, for diatomic gases γ ≈ 1.4, for polyatomic gases γ ≈ 1.1-1.3.

Q3: How does normal velocity affect pressure?
A: Higher normal velocity generally leads to higher pressure after shock formation due to stronger wave compression.

Q4: What is the significance of old speed of sound?
A: It represents the speed at which small disturbances propagate in the fluid before shock formation occurs.

Q5: Are there limitations to this formula?
A: The formula assumes ideal gas behavior and may have limitations for very strong shocks, real gas effects, or non-ideal conditions.