Skip to main content
CalcPro

Prandtl-Meyer Supersonic Expansion Fan Function & Mach Calculator

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

Calculated Result
11.91 deg

Prandtl-Meyer Function nu(M)

Prandtl-Meyer Function nu(M)

11.91 deg

Upstream Prandtl Meyer Nu1 Deg

11.905208826739662

Downstream Prandtl Meyer Nu2 Deg

23.905208826739663

Downstream Mach Number M2

1.9112934641301764

Static Pressure Ratio P2 P1

0.5383838924634715

11.91 — deg

Calculation Breakdown

  1. Applied FormulaEvaluates the Prandtl-Meyer expansion angle nu(M in deg) and computes downstream expansion Mach number (M2) and static pressure drops around sharp convex supersonic corners.\nu(M) = \sqrt{\frac{\gamma+1}{\gamma-1}} \arctan\left(\sqrt{\frac{\gamma-1}{\gamma+1}(M^2-1)}\right) - \arctan\left(\sqrt{M^2-1}\right)

Prandtl-Meyer Expansion Fan Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.03.06.08.912Prandtl-Meyer Function nu(M)

What Is the Prandtl-Meyer Supersonic Expansion Fan Function & Mach Calculator?

The Prandtl-Meyer Supersonic Expansion Fan Function & Mach Calculator computes results using established domain formulas, verified conversion factors, and user-entered parameters.

How Does the Prandtl-Meyer Supersonic Expansion Fan Function & Mach Calculator Work?

Evaluates the Prandtl-Meyer expansion angle nu(M in deg) and computes downstream expansion Mach number (M2) and static pressure drops around sharp convex supersonic corners.

Prandtl-Meyer Supersonic Expansion Fan Function & 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\left(\sqrt{\frac{\gamma-1}{\gamma+1}(M^2-1)}\right) - \arctan\left(\sqrt{M^2-1}\right)

Evaluates the Prandtl-Meyer expansion angle nu(M in deg) and computes downstream expansion Mach number (M2) and static pressure drops around sharp convex supersonic corners.

How to Use the Prandtl-Meyer Supersonic Expansion Fan Function & Mach Calculator

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

Step-by-Step Example Calculation

Prandtl-Meyer Supersonic Expansion Fan Function & Mach Calculator Example

Input Values:

upstreamMachNumberM1:1.5
cornerDeflectionAngleDeg:12
specificHeatRatioGamma:1.4
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required deg.

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.

\n

Related Calculators

Explore more tools and calculators in Physics Calculators

Length Converter

Convert length and distance between metric and imperial units including meters, feet, inches, kilometers, miles, and yards with exact SI definitions.

Percentage Calculator

Calculate percentages: what % X is of Y, P% of X, % change, discount price, and percentage points.

Temperature Converter

Convert temperatures between Celsius (°C), Fahrenheit (°F), Kelvin (K), and Rankine (°R) with step-by-step thermodynamic formulas.

Ohm's Law & Electrical Power Calculator

Calculate Voltage (V), Current (I), Resistance (R), and Electrical Power (P) across DC circuits.

Density, Mass & Volume Calculator

Calculate density (ρ = m/V), material mass, or physical volume for solids, liquids, and gases.

Steam Turbine Surface Condenser Cooling Water Duty Calculator

Calculates surface condenser thermal heat rejection (MWth), circulating cooling water pumping volume (m³/h), and steam condensation rate.