Prandtl Meyer Function at Upstream Mach Number Calculator

✖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 Ahead of Expansion Fan is the Mach number of the upstream flow.ⓘ Mach Number Ahead of Expansion Fan [M_e1]			+10% -10%

✖Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.ⓘ Prandtl Meyer Function at Upstream Mach Number [v_M1]

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Prandtl Meyer Function at Upstream Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
v_M1 = sqrt((γ_e+1)/(γ_e-1))*atan(sqrt(((γ_e-1)*(M_e1^2-1))/(γ_e+1)))-atan(sqrt(M_e1^2-1))
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 at Upstream Mach no. - (Measured in Radian) - Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.
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 Ahead of Expansion Fan - Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio Expansion Wave: 1.41 --> No Conversion Required
Mach Number Ahead of Expansion Fan: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_M1 = sqrt((γ_e+1)/(γ_e-1))*atan(sqrt(((γ_e-1)*(M_e1^2-1))/(γ_e+1)))-atan(sqrt(M_e1^2-1)) --> sqrt((1.41+1)/(1.41-1))*atan(sqrt(((1.41-1)*(5^2-1))/(1.41+1)))-atan(sqrt(5^2-1))

Evaluating ... ...

v_M1 = 1.32473545821219

STEP 3: Convert Result to Output's Unit

1.32473545821219 Radian -->75.9017507269022 Degree (Check conversion here)

FINAL ANSWER

75.9017507269022 ≈ 75.90175 Degree <-- Prandtl Meyer Function at Upstream Mach no.

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

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< Expansion Waves Calculators

Pressure behind Expansion Fan

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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)

Prandtl Meyer Function at Upstream Mach Number Formula

LaTeX Go

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How to Calculate Prandtl Meyer Function at Upstream Mach Number?

Prandtl Meyer Function at Upstream Mach Number calculator 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 calculate 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 calculate Prandtl Meyer Function at Upstream Mach Number using this online calculator? To use this online calculator 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. Here is how the Prandtl Meyer Function at Upstream Mach Number calculation can be explained with given input values -> 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)).

FAQ

What is Prandtl Meyer Function at Upstream Mach Number?

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 and is represented as v_M1 = sqrt((γ_e+1)/(γ_e-1))*atan(sqrt(((γ_e-1)*(M_e1^2-1))/(γ_e+1)))-atan(sqrt(M_e1^2-1)) or 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)). The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.

How to calculate Prandtl Meyer Function at Upstream Mach Number?

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 is calculated using 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 calculate Prandtl Meyer Function at Upstream Mach Number, you need Specific Heat Ratio Expansion Wave (γ_e) & Mach Number Ahead of Expansion Fan (M_e1). With our tool, you need to enter the respective value for Specific Heat Ratio Expansion Wave & Mach Number Ahead of Expansion Fan and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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