Isentropic Flow Calculator
Calculate isentropic flow ratios — temperature, pressure, density, and area — for compressible nozzle flow at any Mach number and specific heat ratio.
Isentropic Flow
Isentropic flow is an idealized model of compressible gas flow through a nozzle where no heat transfer or friction occurs — entropy remains constant. It applies to supersonic nozzle design, wind tunnels, and rocket engine analysis.
Governing Parameter
The Mach number M = flow velocity / local speed of sound fully determines all flow ratios.
Key Ratios (static to stagnation)
| Ratio | Formula |
|---|---|
| T/T₀ | 1 / (1 + (γ−1)/2 × M²) |
| P/P₀ | (T/T₀)^(γ/(γ−1)) |
| ρ/ρ₀ | (T/T₀)^(1/(γ−1)) |
| A/A* | (1/M) × [(2/(γ+1)) × (1 + (γ−1)/2 × M²)]^((γ+1)/(2(γ−1))) |
Where T₀, P₀, ρ₀ are stagnation (total) conditions and A* is the throat area at M=1.
Specific Heat Ratio γ
| Gas | γ |
|---|---|
| Air (standard, diatomic) | 1.400 |
| Monatomic gas (He, Ar) | 1.667 |
| Hot combustion gas | ~1.300 |
| CO₂ | 1.289 |
Physical Interpretation
At M=0: all ratios equal 1 (static = stagnation). At M=1 (sonic throat): P/P₀ = 0.528 for air — the critical pressure ratio. Beyond M=1 (supersonic): temperature, pressure, and density all drop rapidly.
Applications
Rocket nozzle sizing uses A/A* to find the throat and exit areas. Wind tunnel test sections are designed for target Mach numbers using these ratios. Pitot tubes in aircraft use stagnation-to-static pressure to infer airspeed.