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

Formula Used:

\[ P_b = P_a \times \left(1 + \frac{2\gamma_o}{\gamma_o + 1} \times (M_{n1}^2 - 1)\right) \]

Static Pressure Ahead of Oblique Shock (Pa):

Specific Heat Ratio Oblique Shock (γo):

Upstream Mach Normal to Oblique Shock (Mn1):

Static Pressure Behind Oblique Shock (Pb):

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1. What is the Pressure Behind Oblique Shock?

The pressure behind an oblique shock wave represents the static pressure of a fluid or airflow after passing through an oblique shock wave. This is a fundamental parameter in compressible flow and aerodynamics, particularly in supersonic flow applications.

2. How Does the Calculator Work?

The calculator uses the oblique shock pressure ratio formula:

\[ P_b = P_a \times \left(1 + \frac{2\gamma_o}{\gamma_o + 1} \times (M_{n1}^2 - 1)\right) \]

Where:

\( P_b \) — Static pressure behind oblique shock (Pa)
\( P_a \) — Static pressure ahead of oblique shock (Pa)
\( \gamma_o \) — Specific heat ratio (dimensionless)
\( M_{n1} \) — Upstream Mach number normal to oblique shock (dimensionless)

Explanation: This formula calculates the pressure increase 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 Pressure Calculation

Details: Accurate pressure calculation behind oblique shocks is crucial for designing supersonic aircraft, rocket nozzles, and other high-speed aerodynamic systems. It helps predict shock wave behavior and its effects on vehicle performance.

4. Using the Calculator

Tips: Enter static pressure ahead of shock in Pascals, specific heat ratio (typically 1.4 for air), and upstream Mach normal component. All values must be valid (pressure > 0, gamma ≥ 1, Mn1 ≥ 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 a supersonic flow encounters a compression corner or other obstruction.

Q2: How does the specific heat ratio affect the pressure ratio?
A: The specific heat ratio (γ) directly influences the pressure increase across the shock. Higher γ values generally result in higher pressure ratios for the same Mach number.

Q3: What is the normal Mach number component?
A: The normal Mach number component is the projection of the upstream Mach vector onto the normal direction of the shock wave.

Q4: 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.

Q5: When is this formula applicable?
A: This formula applies to perfect gases experiencing oblique shock waves in steady, adiabatic flow with constant specific heats.