Shock Wave Calculator

How the Shock Wave Calculator Works

This calculator estimates the post-shock properties for a fluid undergoing a shock wave, a key concept in aerodynamics and gas dynamics.

Steps to Calculate Post-Shock Properties

1. Enter the Pre-Shock Mach Number (M₁) (greater than 1).
2. Enter the Ratio of Specific Heats (γ) (typically 1.4 for air).
3. Click "Calculate" to determine the Post-Shock Mach Number, pressure ratio, density ratio, temperature ratio, velocities, and speed of sound before and after the shock.

Shock Wave Equations

The following equations are used to calculate the post-shock properties:

1. Post-Shock Mach Number (M₂)

The Post-Shock Mach Number is calculated using the following equation:

M₂ = √[( (γ - 1) M₁² + 2 ) / ( 2 γ M₁² - (γ - 1) )]

Where:

• M₂ = post-shock Mach number (dimensionless)
• γ = ratio of specific heats
• M₁ = pre-shock Mach number (dimensionless)

2. Pressure Ratio (p₂/p₁)

The pressure ratio is given by the following equation:

p₂/p₁ = ( 2 γ M₁² - (γ - 1) ) / ( γ + 1 )

Where:

• p₂ = post-shock pressure
• p₁ = pre-shock pressure

3. Density Ratio (ρ₂/ρ₁)

The density ratio is calculated using the following formula:

ρ₂/ρ₁ = ( (γ + 1) M₁² ) / ( (γ - 1) M₁² + 2 )

Where:

• ρ₂ = post-shock density
• ρ₁ = pre-shock density

4. Temperature Ratio (T₂/T₁)

The temperature ratio is given by the equation:

T₂/T₁ = ( (γ - 1) M₁² + 2 ) / ( γ + 1 )

Where:

• T₂ = post-shock temperature
• T₁ = pre-shock temperature

5. Pre-Shock and Post-Shock Velocity

The Pre-Shock Velocity (u₁) is calculated as:

u₁ = M₁ * c₁

The Post-Shock Velocity (u₂) is calculated as:

u₂ = M₂ * c₂

Where:

• u₁ = pre-shock velocity (m/s)
• u₂ = post-shock velocity (m/s)
• c₁ = pre-shock speed of sound (m/s)
• c₂ = post-shock speed of sound (m/s)

6. Speed of Sound Before and After the Shock

The speed of sound before the shock (c₁) is given by:

c₁ = √( γ * R * T₁ )

The speed of sound after the shock (c₂) is given by:

c₂ = √( γ * R * T₂ )

Frequently Asked Questions (FAQs)

1. What is a shock wave?

A shock wave is a sudden change in pressure, temperature, and density that occurs when a fluid travels faster than the speed of sound, resulting in a dramatic increase in these properties at the shock front.

2. Why do we need to calculate post-shock properties?

Calculating post-shock properties is essential for understanding the behavior of compressible flows, such as those in supersonic aircraft, rockets, and high-speed flows in pipes. It helps predict the impact of the shock wave on materials and structures.

3. How accurate is this calculator?

This calculator uses well-established fluid dynamics equations and provides accurate results for typical conditions. However, for extremely high Mach numbers or unusual gas properties, more specialized tools may be needed.

4. What values of γ should be used?

For air, the ratio of specific heats (γ) is typically around 1.4. For other gases, this value can vary (e.g., 1.3 for some combustion gases, 1.67 for monatomic gases like helium).