Prandtl Meyer Function Calculator

↳

⤿

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

⤿

Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

⤿

Expansion Waves

Oblique Shock

✖The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Expansion Wave [γ_e]			+10% -10%
✖Mach Number is a dimensionless quantity representing the ratio of flow velocity to the local speed of sound.ⓘ Mach Number [M]			+10% -10%

✖Prandtl Meyer Function calculates the turning angle of supersonic flows around corners or through expansion fans.ⓘ Prandtl Meyer Function [ν_M]

⎘ Copy

👎

Formula

✖

Prandtl Meyer Function

Formula

`"ν"_{"M"} = sqrt(("γ"_{"e"}+1)/("γ"_{"e"}-1))*atan(sqrt((("γ"_{"e"}-1)*("M"^2-1))/("γ"_{"e"}+1)))-atan(sqrt("M"^2-1))`

Example

`"94.20208°"=sqrt(("1.41"+1)/("1.41"-1))*atan(sqrt((("1.41"-1)*(("8")^2-1))/("1.41"+1)))-atan(sqrt(("8")^2-1))`

Calculator

LaTeX

Reset

👍

Download Oblique Shock and Expansion Waves Formulas PDF

Prandtl Meyer Function Solution

STEP 0: Pre-Calculation Summary

Formula Used

Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1))
ν_M = sqrt((γ_e+1)/(γ_e-1))*atan(sqrt(((γ_e-1)*(M^2-1))/(γ_e+1)))-atan(sqrt(M^2-1))
This formula uses 3 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Prandtl Meyer Function - (Measured in Radian) - Prandtl Meyer Function calculates the turning angle of supersonic flows around corners or through expansion fans.
Specific Heat Ratio Expansion Wave - The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number - Mach Number is a dimensionless quantity representing the ratio of flow velocity to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio Expansion Wave: 1.41 --> No Conversion Required
Mach Number: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ν_M = sqrt((γ_e+1)/(γ_e-1))*atan(sqrt(((γ_e-1)*(M^2-1))/(γ_e+1)))-atan(sqrt(M^2-1)) --> sqrt((1.41+1)/(1.41-1))*atan(sqrt(((1.41-1)*(8^2-1))/(1.41+1)))-atan(sqrt(8^2-1))

Evaluating ... ...

ν_M = 1.64413649773194

STEP 3: Convert Result to Output's Unit

1.64413649773194 Radian -->94.2020822634783 Degree (Check conversion here)

FINAL ANSWER

94.2020822634783 ≈ 94.20208 Degree <-- Prandtl Meyer Function

(Calculation completed in 00.012 seconds)

You are here -

Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Expansion Waves » Prandtl Meyer Function

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has verified this Calculator and 100+ more calculators!

< 10+ Expansion Waves Calculators

Flow Deflection Angle due to Expansion Wave

Go Flow Deflection Angle = (sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Behind Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Behind Expansion Fan^2-1)))-(sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Ahead of Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Ahead of Expansion Fan^2-1)))

Prandtl Meyer Function at Upstream Mach Number

Go Prandtl Meyer Function at Upstream Mach no. = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Ahead of Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Ahead of Expansion Fan^2-1))

Prandtl Meyer Function

Go Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1))

Pressure behind Expansion Fan

Go Pressure Behind Expansion Fan = Pressure Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))

Pressure Ratio across Expansion Fan

Go Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))

Temperature behind Expansion Fan

Go Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))

Temperature Ratio across Expansion Fan

Go Temperature Ratio Across Expansion Fan = (1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)

Flow Deflection Angle using Prandtl Meyer Function

Go Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.

Forward Mach Angle of Expansion Fan

Go Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan)

Rearward Mach Angle of Expansion Fan

Go Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan)

Prandtl Meyer Function Formula

How to obtain the maximum angle by which a sonic flow can be turned around convex corner?

The maximum angle through which a sonic (M = 1) flow can be turned around a convex corner is obtained by evaluating Prandtl Meyer function at infinite downstream Mach number and unit upstream Mach number and then subtracting the upstream value of the Prandtl Meyer function with the downstream value.

How to Calculate Prandtl Meyer Function?

Prandtl Meyer Function calculator uses Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1)) to calculate the Prandtl Meyer Function, The Prandtl Meyer function, denoted as is a fundamental concept in compressible fluid dynamics, particularly in the study of supersonic flows. It represents the angle by which a supersonic flow must be turned to achieve a specified Mach number. Prandtl Meyer Function is denoted by ν_M symbol.

How to calculate Prandtl Meyer Function using this online calculator? To use this online calculator for Prandtl Meyer Function, enter Specific Heat Ratio Expansion Wave (γ_e) & Mach Number (M) and hit the calculate button. Here is how the Prandtl Meyer Function calculation can be explained with given input values -> 5397.382 = sqrt((1.41+1)/(1.41-1))*atan(sqrt(((1.41-1)*(8^2-1))/(1.41+1)))-atan(sqrt(8^2-1)).

FAQ

What is Prandtl Meyer Function?

The Prandtl Meyer function, denoted as is a fundamental concept in compressible fluid dynamics, particularly in the study of supersonic flows. It represents the angle by which a supersonic flow must be turned to achieve a specified Mach number and is represented as ν_M = sqrt((γ_e+1)/(γ_e-1))*atan(sqrt(((γ_e-1)*(M^2-1))/(γ_e+1)))-atan(sqrt(M^2-1)) or Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1)). The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number is a dimensionless quantity representing the ratio of flow velocity to the local speed of sound.

How to calculate Prandtl Meyer Function?

The Prandtl Meyer function, denoted as is a fundamental concept in compressible fluid dynamics, particularly in the study of supersonic flows. It represents the angle by which a supersonic flow must be turned to achieve a specified Mach number is calculated using Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1)). To calculate Prandtl Meyer Function, you need Specific Heat Ratio Expansion Wave (γ_e) & Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio Expansion Wave & Mach Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search