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Prandtl Meyer Function Formula

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Prandtl Meyer Function calculates the turning angle of supersonic flows around corners or through expansion fans. Check FAQs

ν M = \sqrt{\frac{γ e + 1}{γ e - 1}} \cdot a \tan (\sqrt{\frac{(γ e - 1) \cdot (M^{2} - 1)}{γ e + 1}}) - a \tan (\sqrt{M^{2} - 1})

ν_M - Prandtl Meyer Function?γ_e - Specific Heat Ratio Expansion Wave?M - Mach Number?

Prandtl Meyer Function Example

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Here is how the Prandtl Meyer Function equation looks like with Values.

Here is how the Prandtl Meyer Function equation looks like with Units.

Here is how the Prandtl Meyer Function equation looks like.

94.2021 = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (8^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{8^{2} - 1})

94.2021° = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (8^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{8^{2} - 1})

94.2021 = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (8^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{8^{2} - 1})

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Prandtl Meyer Function Solution

Follow our step by step solution on how to calculate Prandtl Meyer Function?

FIRST Step Consider the formula

ν M = \sqrt{\frac{γ e + 1}{γ e - 1}} \cdot a \tan (\sqrt{\frac{(γ e - 1) \cdot (M^{2} - 1)}{γ e + 1}}) - a \tan (\sqrt{M^{2} - 1})

Next Step Substitute values of Variables

∴

ν M = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (8^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{8^{2} - 1})

Next Step Prepare to Evaluate

∴

ν M = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (8^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{8^{2} - 1})

Next Step Evaluate

∴

ν M = 1.64413649773194rad

Next Step Convert to Output's Unit

∴

ν M = 94.2020822634783°

LAST Step Rounding Answer

∴

ν M = 94.2021°

Prandtl Meyer Function Formula Elements

Variables

Functions

Prandtl Meyer Function

Prandtl Meyer Function calculates the turning angle of supersonic flows around corners or through expansion fans.

Symbol: ν_M

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Prandtl Meyer Function

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.

Symbol: γ_e

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Specific Heat Ratio Expansion Wave

Mach Number

Mach Number is a dimensionless quantity representing the ratio of flow velocity to the local speed of sound.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

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.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

Other formulas in Expansion Waves category

Go Pressure Ratio across Expansion Fan

P e,r = {(\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})}^{\frac{γ e}{γ e - 1}}

Go Temperature Ratio across Expansion Fan

T e,r = \frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}}

Go Pressure behind Expansion Fan

P 2 = P 1 \cdot {(\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})}^{\frac{γ e}{γ e - 1}}

Go Temperature behind Expansion Fan

T 2 = T 1 \cdot (\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})

How to Evaluate Prandtl Meyer Function?

Prandtl Meyer Function evaluator 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 evaluate 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 evaluate Prandtl Meyer Function using this online evaluator? To use this online evaluator for Prandtl Meyer Function, enter Specific Heat Ratio Expansion Wave (γ_e) & Mach Number (M) and hit the calculate button.

FAQs on Prandtl Meyer Function

What is the formula to find Prandtl Meyer Function?

The formula of Prandtl Meyer Function is expressed as 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)). Here is an example- 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)).

How to calculate Prandtl Meyer Function?

With Specific Heat Ratio Expansion Wave (γ_e) & Mach Number (M) we can find Prandtl Meyer Function using the formula - 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)). This formula also uses Tangent (tan)Inverse Tan (atan), Square Root (sqrt) function(s).

Can the Prandtl Meyer Function be negative?

Yes, the Prandtl Meyer Function, measured in Angle can be negative.

Which unit is used to measure Prandtl Meyer Function?

Prandtl Meyer Function is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Prandtl Meyer Function can be measured.

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