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Prandtl-Meyer Expansion Calculator — result sheet
Calculate downstream Mach number and ideal pressure, temperature, and density ratios through a supersonic expansion fan.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: ν(M) = √((γ+1)/(γ−1)) atan√((γ−1)(M²−1)/(γ+1)) − atan√(M²−1); set ν₂ = ν₁ + turn angle and invert for M₂.
A centered expansion fan increases supersonic Mach number while reducing static pressure and temperature. The page solves the Prandtl-Meyer function numerically and then applies isentropic total-state ratios.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Upstream Mach number — M₁; minimum 1.000001; maximum 100
- Convex expansion angle — degrees; minimum 0; maximum 50
- Specific-heat ratio γ — γ; minimum 1.000001; maximum 2.5
Worked example
| Input | Value |
|---|---|
| Upstream Mach number | 2 |
| Convex expansion angle | 10 |
| Specific-heat ratio γ | 1.4 |
For M₁ = 2 and a 10° expansion at γ = 1.4, the downstream Mach number is about 2.385 and the static pressure ratio is about 0.448.
Assumptions and limits
- The gas is calorically perfect with constant γ greater than one.
- The turn is a convex, centered, isentropic expansion with upstream Mach number above one.
- The expansion angle stays below the maximum value allowed by the Prandtl-Meyer function.
- Shock waves, viscous effects, heat transfer, chemistry, and three-dimensional geometry are outside the model.
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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