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Supersonic Isentropic Flow Calculator — result sheet
Calculate ideal supersonic flow ratios, critical-area ratio, Mach angle, and Prandtl-Meyer angle from Mach number and heat-capacity ratio.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: With F = 1 + (γ − 1)M²/2: p/p₀ = F^(−γ/(γ−1)), T/T₀ = F⁻¹, ρ/ρ₀ = F^(−1/(γ−1)), and A/A* = M⁻¹[2F/(γ+1)]^((γ+1)/(2(γ−1))).
The calculator exposes the standard calorically perfect, isentropic supersonic ratios instead of hiding them behind a single nozzle answer. It also reports the Mach angle and Prandtl-Meyer angle for the same state.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mach number — M; This page intentionally uses a supersonic Mach number so the Mach and Prandtl-Meyer angles are defined.; minimum 1.000001; maximum 100
- Specific-heat ratio γ — γ; minimum 1.000001; maximum 2.5
Worked example
| Input | Value |
|---|---|
| Mach number | 2 |
| Specific-heat ratio γ | 1.4 |
At M = 2 and γ = 1.4, p/p₀ ≈ 0.1278045, T/T₀ ≈ 0.5555556, A/A* ≈ 1.6875, and the Mach angle is 30°.
Assumptions and limits
- The gas is calorically perfect with constant specific-heat ratio γ greater than one.
- The flow is steady, adiabatic, inviscid, and reversible with no shock or heat addition.
- Mach number is strictly greater than one so both angular outputs are defined.
- The result is a teaching and comparison model, not a nozzle certification or flight-safety calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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