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Prandtl-Meyer Expansion Fan Function (ν) & Downstream Mach Calculator

Easily calculate and compute prandtl-meyer expansion fan function (ν) & downstream mach calculator with accurate equations, live formulas, and expert guidance.

Must be supersonic (M₁ >= 1.0).

Flow turn angle away from itself.

Standard air γ = 1.40.

Calculated Result
1.91 Mach

Expanded Mach (M₂)

Expanded Mach (M₂)

1.91 Mach

Downstream Mach M2

1.91

Initial Prandtl Meyer Angle Deg

11.9

Final Prandtl Meyer Angle Deg

23.9

Initial Mach Angle Mu1 Deg

41.8

1.91 — Mach

Calculation Breakdown

  1. Applied FormulaCalculates supersonic expansion acceleration over convex corners using the Prandtl-Meyer expansion function ν(M) and characteristic Mach wave angles.\nu(M) = \sqrt{\frac{\gamma + 1}{\gamma - 1}} \arctan\sqrt{\frac{\gamma - 1}{\gamma + 1}(M^2 - 1)} - \arctan\sqrt{M^2 - 1}

Prandtl-Meyer Expansion Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.51.01.41.9Expanded Mach (M₂)

What Is the Prandtl-Meyer Expansion Fan Function (ν) & Downstream Mach Calculator?

This tool computes prandtl-meyer expansion fan function (ν) & downstream mach calculator with high precision arithmetic.

How Does the Prandtl-Meyer Expansion Fan Function (ν) & Downstream Mach Calculator Work?

Calculates supersonic expansion acceleration over convex corners using the Prandtl-Meyer expansion function ν(M) and characteristic Mach wave angles.

Prandtl-Meyer Expansion Fan Function (ν) & Downstream Mach Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

ν(M)=γ+1γ−1arctan⁡γ−1γ+1(M2−1)−arctan⁡M2−1\nu(M) = \sqrt{\frac{\gamma + 1}{\gamma - 1}} \arctan\sqrt{\frac{\gamma - 1}{\gamma + 1}(M^2 - 1)} - \arctan\sqrt{M^2 - 1}

Calculates supersonic expansion acceleration over convex corners using the Prandtl-Meyer expansion function ν(M) and characteristic Mach wave angles.

How to Use the Prandtl-Meyer Expansion Fan Function (ν) & Downstream Mach Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Prandtl-Meyer Expansion Fan Function (ν) & Downstream Mach Calculator Example

Input Values:

upstreamMachM1:1.5
turnAngleThetaDeg:12
ratioOfSpecificHeatsGamma:1.4
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required Mach.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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