1. What is the Isentropic Temperature Ratio?

The isentropic temperature ratio relates the static temperature (T) to the stagnation temperature (T₀) in isentropic flow. It's a fundamental relationship in compressible flow analysis, particularly for aircraft and propulsion systems.

2. How Does the Calculator Work?

The calculator uses the isentropic temperature ratio equation:

Where:

• \( T \) — Static temperature (K)
• \( T_0 \) — Stagnation temperature (K)
• \( \gamma \) — Heat capacity ratio (dimensionless)
• \( M \) — Mach number (dimensionless)

Explanation: The equation shows how temperature changes in isentropic flow as a function of Mach number and the gas property γ.

3. Importance of Temperature Ratio

Details: This calculation is essential for analyzing compressible flows in nozzles, diffusers, and around aircraft. It helps determine temperature changes in high-speed flows without heat transfer or work.

4. Using the Calculator

Tips: Enter stagnation temperature in Kelvin, heat capacity ratio (γ = 1.4 for air), and Mach number. All values must be valid (T₀ > 0, 1 ≤ γ ≤ 2, M ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is isentropic flow?
A: Isentropic flow is reversible adiabatic flow with constant entropy - no heat transfer, no friction losses.

Q2: What's a typical γ value for air?
A: For air at standard conditions, γ ≈ 1.4. For other gases: monatomic = 1.67, diatomic = ~1.4, polyatomic = ~1.3.

Q3: What is stagnation temperature?
A: The temperature a fluid would reach if brought to rest isentropically (all kinetic energy converted to enthalpy).

Q4: When is this equation valid?
A: For steady, one-dimensional, isentropic flow of a perfect gas with constant γ.

Q5: How does Mach number affect temperature?
A: As Mach number increases, static temperature decreases relative to stagnation temperature.