Compressible Flow Calculator
Calculate compressible flow properties using Mach number and specific heat ratio
How to Use
- Enter the Mach number of the flow
- Enter the specific heat ratio (γ) for the gas
- Enter the static pressure, temperature, and density
- Click calculate to see flow regime and all ratios
- View stagnation properties and flow characteristics
What is Compressible Flow?
Compressible flow is the study of fluid flow where density changes significantly due to pressure variations. This typically occurs in high-speed flows where the Mach number (ratio of flow velocity to speed of sound) becomes significant.
When a fluid flows at high speeds, the pressure changes can cause significant density variations, making the flow compressible. This is fundamentally different from incompressible flow where density remains constant.
Mach Number and Flow Regimes
The Mach number (M) is the key parameter that determines the flow regime:
- Subsonic (M < 1): Flow velocity is less than the speed of sound
- Sonic (M ≈ 1): Flow velocity equals the speed of sound
- Supersonic (M > 1): Flow velocity exceeds the speed of sound
Different flow regimes exhibit vastly different behaviors and require different analysis methods.
Isentropic Flow Relations
For isentropic (reversible, adiabatic) flow, the following relations hold:
- Pressure ratio: P₀/P = (1 + (γ-1)/2 × M²)^(γ/(γ-1))
- Temperature ratio: T₀/T = 1 + (γ-1)/2 × M²
- Density ratio: ρ₀/ρ = (1 + (γ-1)/2 × M²)^(1/(γ-1))
Where γ is the specific heat ratio, P₀, T₀, ρ₀ are stagnation properties, and P, T, ρ are static properties.
Applications of Compressible Flow
- Aircraft design: Understanding flow over wings and fuselage
- Rocket propulsion: Nozzle design and thrust calculations
- Gas turbines: Compressor and turbine blade design
- Supersonic vehicles: Managing shock waves and pressure changes
- Wind tunnels: Testing high-speed aerodynamic models
- Spacecraft re-entry: Managing extreme heating and pressure
Frequently Asked Questions
- What is the difference between static and stagnation properties?
- Static properties (P, T, ρ) are measured in the moving fluid, while stagnation properties (P₀, T₀, ρ₀) are what you would measure if the flow were brought to rest isentropically. Stagnation properties represent the total energy content of the flow.
- Why is the specific heat ratio important in compressible flow?
- The specific heat ratio (γ = cp/cv) determines how the gas responds to pressure and temperature changes. It affects all the isentropic relations and is crucial for accurate calculations. Different gases have different γ values (air ≈ 1.4, helium ≈ 1.67).
- What happens when Mach number approaches 1?
- When Mach number approaches 1, the flow becomes choked, meaning the mass flow rate reaches a maximum. This is critical in nozzle design - the throat of a converging-diverging nozzle must be at Mach 1 for optimal performance.
- Can these relations be used for all compressible flows?
- These isentropic relations are valid for inviscid, adiabatic flows without heat transfer or friction. Real flows with viscosity, heat transfer, or shock waves require more complex analysis methods.
- What are the practical limits of these calculations?
- These calculations assume perfect gas behavior and isentropic flow. They become less accurate at very high temperatures (where real gas effects matter) or in flows with significant heat transfer, friction, or shock waves.