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Prandtl-Meyer Expansion Fan Angle & Downstream Mach Number Calculator

Easily calculate and compute prandtl-meyer expansion fan angle & downstream mach number calculator with accurate equations, live formulas, and expert guidance.

Approach Mach number prior to convex corner.

Corner deflection expansion turn angle.

Gas heat capacity ratio (1.4 for air).

Calculated Result
1.91

Downstream Mach (M₂)

Downstream Mach (M₂)

1.91

Downstream Mach M2

1.91

Initial Prandtl Meyer Angle Nu1 Deg

11.9

Final Prandtl Meyer Angle Nu2 Deg

23.9

Static Pressure Ratio P2 Over P1

0.538

1.91

Calculation Breakdown

  1. Applied FormulaApplies isentropic Prandtl-Meyer expansion fan theory to determine flow acceleration, downstream supersonic Mach number, and static pressure drop around sharp convex corners.\nu(M) = \sqrt{\frac{\gamma+1}{\gamma-1}} \arctan\left(\sqrt{\frac{\gamma-1}{\gamma+1}(M^2-1)}\right) - \arctan(\sqrt{M^2-1})

Prandtl-Meyer Expansion Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.51.01.41.9Downstream Mach (M₂)

What Is the Prandtl-Meyer Expansion Fan Angle & Downstream Mach Number Calculator?

This tool computes prandtl-meyer expansion fan angle & downstream mach number calculator with high precision arithmetic.

How Does the Prandtl-Meyer Expansion Fan Angle & Downstream Mach Number Calculator Work?

Applies isentropic Prandtl-Meyer expansion fan theory to determine flow acceleration, downstream supersonic Mach number, and static pressure drop around sharp convex corners.

Prandtl-Meyer Expansion Fan Angle & Downstream Mach Number 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\left(\sqrt{\frac{\gamma-1}{\gamma+1}(M^2-1)}\right) - \arctan(\sqrt{M^2-1})

Applies isentropic Prandtl-Meyer expansion fan theory to determine flow acceleration, downstream supersonic Mach number, and static pressure drop around sharp convex corners.

How to Use the Prandtl-Meyer Expansion Fan Angle & Downstream Mach Number Calculator

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

Step-by-Step Example Calculation

Prandtl-Meyer Expansion Fan Angle & Downstream Mach Number Calculator Example

Input Values:

initialMachNumberM1:1.5
convexTurnAngleThetaDeg:12.0
specificHeatRatioGamma:1.40
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required Downstream Mach (M₂).

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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