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Prandtl Meyer Function at Upstream Mach Number Formula

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Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave. Check FAQs

v M1 = \sqrt{\frac{γ e + 1}{γ e - 1}} \cdot a \tan (\sqrt{\frac{(γ e - 1) \cdot ({M e1}^{2} - 1)}{γ e + 1}}) - a \tan (\sqrt{{M e1}^{2} - 1})

v_M1 - Prandtl Meyer Function at Upstream Mach no.?γ_e - Specific Heat Ratio Expansion Wave?M_e1 - Mach Number Ahead of Expansion Fan?

Prandtl Meyer Function at Upstream Mach Number Example

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Here is how the Prandtl Meyer Function at Upstream Mach Number equation looks like with Values.

Here is how the Prandtl Meyer Function at Upstream Mach Number equation looks like with Units.

Here is how the Prandtl Meyer Function at Upstream Mach Number equation looks like.

75.9018 = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (5^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{5^{2} - 1})

75.9018° = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (5^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{5^{2} - 1})

75.9018 = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (5^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{5^{2} - 1})

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Prandtl Meyer Function at Upstream Mach Number Solution

Follow our step by step solution on how to calculate Prandtl Meyer Function at Upstream Mach Number?

FIRST Step Consider the formula

v M1 = \sqrt{\frac{γ e + 1}{γ e - 1}} \cdot a \tan (\sqrt{\frac{(γ e - 1) \cdot ({M e1}^{2} - 1)}{γ e + 1}}) - a \tan (\sqrt{{M e1}^{2} - 1})

Next Step Substitute values of Variables

∴

v M1 = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (5^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{5^{2} - 1})

Next Step Prepare to Evaluate

∴

v M1 = \sqrt{\frac{1.41 + 1}{1.41 - 1}} \cdot a \tan (\sqrt{\frac{(1.41 - 1) \cdot (5^{2} - 1)}{1.41 + 1}}) - a \tan (\sqrt{5^{2} - 1})

Next Step Evaluate

∴

v M1 = 1.32473545821219rad

Next Step Convert to Output's Unit

∴

v M1 = 75.9017507269022°

LAST Step Rounding Answer

∴

v M1 = 75.9018°

Prandtl Meyer Function at Upstream Mach Number Formula Elements

Variables

Functions

Prandtl Meyer Function at Upstream Mach no.

Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.

Symbol: v_M1

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Prandtl Meyer Function at Upstream Mach no.

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 Ahead of Expansion Fan

Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.

Symbol: M_e1

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Ahead of Expansion Fan

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 at Upstream Mach Number?

Prandtl Meyer Function at Upstream Mach Number evaluator uses 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)) to evaluate the Prandtl Meyer Function at Upstream Mach no., Prandtl Meyer Function at Upstream Mach Number formula describes the relationship between the Mach number of the flow and the corresponding Prandtl-Meyer angle, which characterizes the amount of expansion or turning required to achieve the specified Mach number. Prandtl Meyer Function at Upstream Mach no. is denoted by v_M1 symbol.

How to evaluate Prandtl Meyer Function at Upstream Mach Number using this online evaluator? To use this online evaluator for Prandtl Meyer Function at Upstream Mach Number, enter Specific Heat Ratio Expansion Wave (γ_e) & Mach Number Ahead of Expansion Fan (M_e1) and hit the calculate button.

FAQs on Prandtl Meyer Function at Upstream Mach Number

What is the formula to find Prandtl Meyer Function at Upstream Mach Number?

The formula of Prandtl Meyer Function at Upstream Mach Number is expressed as 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)). Here is an example- 4407.204 = sqrt((1.41+1)/(1.41-1))*atan(sqrt(((1.41-1)*(5^2-1))/(1.41+1)))-atan(sqrt(5^2-1)).

How to calculate Prandtl Meyer Function at Upstream Mach Number?

With Specific Heat Ratio Expansion Wave (γ_e) & Mach Number Ahead of Expansion Fan (M_e1) we can find Prandtl Meyer Function at Upstream Mach Number using the formula - 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)). This formula also uses Tangent (tan)Inverse Tan (atan), Square Root (sqrt) function(s).

Can the Prandtl Meyer Function at Upstream Mach Number be negative?

Yes, the Prandtl Meyer Function at Upstream Mach Number, measured in Angle can be negative.

Which unit is used to measure Prandtl Meyer Function at Upstream Mach Number?

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

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