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

Mach Number Formula:

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

Mach Number:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Mach Number Over Flat Plate?

The Mach number over a flat plate represents the ratio of flow velocity past the plate to the local speed of sound. It's a dimensionless quantity used in aerodynamics to characterize flow conditions, particularly in compressible flow analysis.

2. How Does the Calculator Work?

The calculator uses the Mach Number formula:

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

Where:

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

Explanation: This formula calculates the Mach number based on the temperature ratio between the wall temperature and static temperature, adjusted by the specific heat ratio of the gas.

3. Importance of Mach Number Calculation

Details: Accurate Mach number calculation is crucial for aerodynamic analysis, particularly in high-speed flow applications. It helps determine flow regimes (subsonic, transonic, supersonic, hypersonic) and predict aerodynamic heating effects on surfaces.

4. Using the Calculator

Tips: Enter wall temperature and static temperature in Kelvin, and specific heat ratio (γ ≥ 1). All values must be positive and valid for the calculation to proceed.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of wall temperature in Mach number calculation?
A: Wall temperature affects the boundary layer development and heat transfer characteristics, which influence the local flow properties including Mach number.

Q2: How does specific heat ratio affect the Mach number?
A: The specific heat ratio (γ) represents the thermodynamic properties of the gas. Different gases have different γ values, which affect the compressibility and thus the Mach number calculation.

Q3: What are typical Mach number ranges for different flow regimes?
A: Subsonic: M < 0.8, Transonic: 0.8 ≤ M ≤ 1.2, Supersonic: 1.2 < M < 5.0, Hypersonic: M ≥ 5.0

Q4: When is this formula particularly useful?
A: This formula is especially useful in aerodynamic heating analysis and boundary layer studies where temperature measurements are available but velocity measurements are challenging.

Q5: Are there limitations to this calculation method?
A: This method assumes ideal gas behavior and may have limitations in extreme temperature conditions or for complex flow geometries where additional factors need to be considered.