Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number Calculator

Formula Used:

\[ M_{n2} = \sqrt{\frac{1 + 0.5 \times (\gamma_o - 1) \times M_{n1}^2}{\gamma_o \times M_{n1}^2 - 0.5 \times (\gamma_o - 1)}} \]

Downstream Mach Normal to Oblique Shock (Mn2):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Downstream Mach Normal to Oblique Shock?

The Downstream Mach Normal to Oblique Shock (Mn2) denotes the Mach number component aligned with the shock wave's normal direction after passing through an oblique shock. It is a crucial parameter in compressible flow analysis and shock wave studies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{n2} = \sqrt{\frac{1 + 0.5 \times (\gamma_o - 1) \times M_{n1}^2}{\gamma_o \times M_{n1}^2 - 0.5 \times (\gamma_o - 1)}} \]

Where:

\( M_{n2} \) — Downstream Mach Normal to Oblique Shock (dimensionless)
\( \gamma_o \) — Specific Heat Ratio Oblique Shock (dimensionless)
\( M_{n1} \) — Upstream Mach Normal to Oblique Shock (dimensionless)

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

3. Importance of Mach Number Calculation

Details: Accurate calculation of Mach number components across shock waves is essential for analyzing compressible flow behavior, designing supersonic aircraft components, and understanding shock wave interactions in various engineering applications.

4. Using the Calculator

Tips: Enter the specific heat ratio (typically 1.4 for air) and the upstream Mach normal component. Both values must be positive, and the specific heat ratio must be greater than 1 for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for specific heat ratio?
A: For most gases, the specific heat ratio ranges from 1.1 to 1.67. For air at standard conditions, it's approximately 1.4.

Q2: What values of Mn1 produce valid results?
A: Mn1 must be greater than 1 for an oblique shock to exist. The denominator must remain positive for valid calculation.

Q3: How does Mn2 relate to the overall downstream Mach number?
A: Mn2 is the normal component. The total downstream Mach number can be found using trigonometric relations with the shock angle.

Q4: What are the limitations of this formula?
A: This formula assumes ideal gas behavior and is valid for steady, two-dimensional oblique shocks in calorically perfect gases.

Q5: When would this calculation be used in practical applications?
A: This calculation is essential in aerospace engineering for designing supersonic inlets, analyzing shock patterns, and studying compressible flow phenomena.