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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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