Isentropic Mach Number Calculator

Isentropic Flow Equation:

\[ M = \sqrt{\frac{2}{\gamma - 1} \left[ \left( \frac{P_0}{P} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]} \]

Isentropic Mach Number (M):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Isentropic Mach Number?

The isentropic Mach number represents the Mach number in an isentropic (constant entropy) flow process. It relates the ratio of total to static pressure to the Mach number for an ideal gas undergoing an isentropic process.

2. How Does the Calculator Work?

The calculator uses the isentropic flow equation:

\[ M = \sqrt{\frac{2}{\gamma - 1} \left[ \left( \frac{P_0}{P} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]} \]

Where:

\( M \) — Mach number (dimensionless)
\( \gamma \) — Specific heat ratio (dimensionless)
\( P_0 \) — Total pressure (Pa)
\( P \) — Static pressure (Pa)

Explanation: This equation derives from the isentropic relations for ideal gases, connecting pressure ratio to 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 designing aircraft, nozzles, and other high-speed flow systems.

4. Using the Calculator

Tips: Enter specific heat ratio (typically 1.4 for air), total pressure and static pressure in Pascals. All values must be valid (γ > 1, P₀ > P > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value of γ for air?
A: For diatomic gases like air at standard conditions, γ is approximately 1.4.

Q2: Can this equation be used for all flow types?
A: This equation applies specifically to isentropic flows where entropy remains constant (no shocks, friction, or heat transfer).

Q3: What are the limitations of this calculation?
A: It assumes ideal gas behavior and isentropic flow conditions, which may not hold in real-world scenarios with shocks, viscosity, or heat transfer.

Q4: How does Mach number affect flow properties?
A: Mach number determines compressibility effects. At M < 0.3, flows are often treated as incompressible, while higher Mach numbers require compressible flow analysis.

Q5: What units should be used for pressure?
A: While Pascals are used here, any consistent pressure units can be used as the calculation depends on the pressure ratio (P₀/P), not absolute values.