Density Behind Oblique Shock For Given Upstream Density And Normal Upstream Mach Number Calculator

Density Behind Oblique Shock Formula:

\[ \rho_2 = \rho_1 \times \frac{(\gamma_o + 1) \times M_{n1}^2}{2 + (\gamma_o - 1) \times M_{n1}^2} \]

Density Ahead of Oblique Shock (ρ₁):

kg/m³

Specific Heat Ratio Oblique Shock (γₒ):

Upstream Mach Normal to Oblique Shock (Mₙ₁):

Density Behind Oblique Shock (ρ₂):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Density Behind Oblique Shock Formula?

The density behind oblique shock formula calculates the air or fluid density after passing through an oblique shock wave. This is a fundamental equation in compressible flow and aerodynamics that describes how density changes across an oblique shock wave.

2. How Does the Calculator Work?

The calculator uses the density behind oblique shock formula:

\[ \rho_2 = \rho_1 \times \frac{(\gamma_o + 1) \times M_{n1}^2}{2 + (\gamma_o - 1) \times M_{n1}^2} \]

Where:

\( \rho_2 \) — Density behind oblique shock (kg/m³)
\( \rho_1 \) — Density ahead of oblique shock (kg/m³)
\( \gamma_o \) — Specific heat ratio oblique shock
\( M_{n1} \) — Upstream Mach normal to oblique shock

Explanation: The formula calculates the density ratio across an oblique shock wave based on the normal component of the upstream Mach number and the specific heat ratio of the fluid.

3. Importance of Density Calculation

Details: Calculating density behind oblique shocks is crucial for analyzing compressible flows, designing supersonic aircraft components, understanding shock wave behavior, and predicting aerodynamic performance in high-speed applications.

4. Using the Calculator

Tips: Enter density ahead of shock in kg/m³, specific heat ratio (typically 1.4 for air), and upstream Mach normal to oblique shock. All values must be positive with specific heat ratio ≥ 1.

5. Frequently Asked Questions (FAQ)

Q1: What is an oblique shock wave?
A: An oblique shock wave is a shock wave that forms at an angle to the flow direction, typically occurring when supersonic flow encounters a compression corner or obstacle.

Q2: How does this differ from normal shock density calculation?
A: The formula is similar to normal shock density calculation but uses the normal component of the Mach number relative to the shock wave rather than the full Mach number.

Q3: What are typical values for specific heat ratio?
A: For air at standard conditions, γ = 1.4. For other gases: monatomic gases = 1.67, diatomic gases = 1.4, triatomic gases = 1.33.

Q4: When is this formula applicable?
A: This formula applies to perfect gases experiencing oblique shock waves where the flow is steady, adiabatic, and without external forces.

Q5: What are the limitations of this calculation?
A: The formula assumes ideal gas behavior, constant specific heats, and that the shock wave is thin and straight. It may not be accurate for very strong shocks or non-ideal gases.