Ratio Of New And Old Temperature For Expansion Waves Calculator

Temperature Ratio Formula:

\[ \text{Temperature Ratio across Shock} = \left(1 - \frac{(\gamma - 1)}{2} \cdot \frac{V_n}{c_{\text{old}}}\right)^2 \]

Temperature Ratio across Shock:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Temperature Ratio for Expansion Waves?

The Temperature Ratio across shock is the ratio of downstream temperature to upstream temperature across the shock wave in expansion wave phenomena. It provides important insights into thermodynamic changes during shock wave propagation.

2. How Does the Calculator Work?

The calculator uses the temperature ratio formula:

\[ \text{Temperature Ratio} = \left(1 - \frac{(\gamma - 1)}{2} \cdot \frac{V_n}{c_{\text{old}}}\right)^2 \]

Where:

\( \gamma \) — Specific heat ratio of the gas
\( V_n \) — Normal velocity (m/s)
\( c_{\text{old}} \) — Old speed of sound before shock (m/s)

Explanation: This formula calculates the temperature ratio across a shock wave by considering the specific heat properties of the gas and the velocity relationships.

3. Importance of Temperature Ratio Calculation

Details: Accurate temperature ratio calculation is crucial for understanding shock wave dynamics, analyzing thermodynamic changes in compressible flows, and designing aerodynamic systems.

4. Using the Calculator

Tips: Enter specific heat ratio (≥1), normal velocity (≥0 m/s), and old speed of sound (>0 m/s). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of temperature ratio?
A: The temperature ratio indicates how much the temperature changes across a shock wave, which is important for understanding energy transfer and thermodynamic efficiency.

Q2: What are typical values for specific heat ratio?
A: For air, γ ≈ 1.4; for monatomic gases like helium, γ ≈ 1.67; for diatomic gases, γ typically ranges from 1.3 to 1.4.

Q3: When is this calculation most relevant?
A: This calculation is particularly important in supersonic flow analysis, aerospace engineering, and shock tube experiments.

Q4: Are there limitations to this equation?
A: The equation assumes ideal gas behavior and may have limitations in extreme conditions or for complex molecular structures.

Q5: How does normal velocity affect the temperature ratio?
A: Higher normal velocities relative to the speed of sound generally result in larger temperature changes across the shock wave.