Pressure Behind Expansion Fan Calculator

Expansion Fan Pressure Formula:

\[ P_2 = P_1 \times \left( \frac{1 + 0.5 \times (\gamma_e - 1) \times M_{e1}^2}{1 + 0.5 \times (\gamma_e - 1) \times M_{e2}^2} \right)^{\frac{\gamma_e}{\gamma_e - 1}} \]

Pressure Ahead of Expansion Fan (P₁):

Specific Heat Ratio Expansion Wave (γₑ):

Mach Number Ahead of Expansion Fan (Mₑ₁):

Mach Number Behind Expansion Fan (Mₑ₂):

Pressure Behind Expansion Fan (P₂):

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1. What is the Expansion Fan Pressure Equation?

The expansion fan pressure equation calculates the pressure behind an expansion fan in supersonic flow. It relates the pressure change across the expansion wave to the Mach numbers and specific heat ratio of the fluid.

2. How Does the Calculator Work?

The calculator uses the expansion fan pressure equation:

\[ P_2 = P_1 \times \left( \frac{1 + 0.5 \times (\gamma_e - 1) \times M_{e1}^2}{1 + 0.5 \times (\gamma_e - 1) \times M_{e2}^2} \right)^{\frac{\gamma_e}{\gamma_e - 1}} \]

Where:

\( P_2 \) — Pressure behind expansion fan (Pa)
\( P_1 \) — Pressure ahead of expansion fan (Pa)
\( \gamma_e \) — Specific heat ratio expansion wave
\( M_{e1} \) — Mach number ahead of expansion fan
\( M_{e2} \) — Mach number behind expansion fan

Explanation: The equation describes the pressure change across an expansion wave in supersonic flow, accounting for the isentropic expansion process.

3. Importance of Expansion Fan Pressure Calculation

Details: Accurate pressure calculation across expansion fans is crucial for supersonic aerodynamics, nozzle design, and understanding wave interactions in compressible flows.

4. Using the Calculator

Tips: Enter pressure in Pascals, specific heat ratio (typically 1.4 for air), and Mach numbers. All values must be positive with specific heat ratio > 1.

5. Frequently Asked Questions (FAQ)

Q1: What is an expansion fan in fluid dynamics?
A: An expansion fan is a series of expansion waves that occur when a supersonic flow turns away from itself, causing the flow to accelerate and pressure to decrease.

Q2: What is the typical value of specific heat ratio for air?
A: For air at standard conditions, the specific heat ratio (γ) is approximately 1.4.

Q3: How does Mach number affect pressure across an expansion fan?
A: As the flow accelerates through an expansion fan (Mₑ₂ > Mₑ₁), the pressure decreases according to the isentropic relations.

Q4: Are there limitations to this equation?
A: This equation assumes isentropic flow, perfect gas behavior, and applies only to continuous expansion waves (not shock waves).

Q5: What units should be used for pressure input?
A: Pressure should be entered in Pascals (Pa), though the equation is dimensionally consistent and will work with any consistent pressure units.