Large Mach Number Over Flat Plate Using Static Temperature And Wall Temperature Calculator

Mach Number Formula:

\[ M = \sqrt{\frac{T_w/T_{static}}{(\gamma - 1)/2}} \]

Mach Number (M):

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1. What is the Mach Number Formula?

The Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound. This specific formula calculates Mach number using wall temperature, static temperature, and specific heat ratio for large Mach numbers over a flat plate.

2. How Does the Calculator Work?

The calculator uses the Mach number formula:

\[ M = \sqrt{\frac{T_w/T_{static}}{(\gamma - 1)/2}} \]

Where:

\( M \) — Mach Number (dimensionless)
\( T_w \) — Wall Temperature (K)
\( T_{static} \) — Static Temperature (K)
\( \gamma \) — Specific Heat Ratio (dimensionless)

Explanation: The formula relates the temperature ratio to the Mach number through the specific heat ratio, providing the flow velocity relative to the speed of sound.

3. Importance of Mach Number Calculation

Details: Mach number is crucial in aerodynamics and fluid dynamics for characterizing flow regimes (subsonic, transonic, supersonic, hypersonic) and analyzing compressibility effects in high-speed flows.

4. Using the Calculator

Tips: Enter wall temperature and static temperature in Kelvin, and specific heat ratio (must be greater than 1). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Mach number in fluid dynamics?
A: Mach number determines whether compressibility effects are important in a flow and classifies flow regimes from subsonic to hypersonic.

Q2: What are typical values for specific heat ratio?
A: For air at standard conditions, γ ≈ 1.4. For monatomic gases, γ ≈ 1.67, and for diatomic gases, γ ≈ 1.4.

Q3: When is this specific formula applicable?
A: This formula is particularly useful for calculating Mach number in high-speed flows over flat plates where temperature measurements are available.

Q4: What are the limitations of this calculation?
A: The formula assumes ideal gas behavior and may not be accurate for extremely high temperatures or pressures where real gas effects become significant.

Q5: How does wall temperature affect Mach number?
A: Higher wall temperature relative to static temperature generally results in higher Mach numbers, indicating faster flow velocities relative to the speed of sound.