Rearward Mach Angle of Expansion Fan Calculator

✖Mach Number Behind Expansion Fan is the Mach number of downstream flow across the expansion fan.ⓘ Mach Number Behind Expansion Fan [M_e2]

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✖Rearward Mach angle is the angle formed between the rearward Mach line and the downstream flow direction (parallel to the convex surface).ⓘ Rearward Mach Angle of Expansion Fan [μ₂]

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Rearward Mach Angle of Expansion Fan Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan)
μ₂ = arsin(1/M_e2)
This formula uses 2 Functions, 2 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
arsin - Arcsine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., arsin(Number)

Variables Used

Rearward Mach Angle - (Measured in Radian) - Rearward Mach angle is the angle formed between the rearward Mach line and the downstream flow direction (parallel to the convex surface).
Mach Number Behind Expansion Fan - Mach Number Behind Expansion Fan is the Mach number of downstream flow across the expansion fan.

STEP 1: Convert Input(s) to Base Unit

Mach Number Behind Expansion Fan: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ₂ = arsin(1/M_e2) --> arsin(1/6)

Evaluating ... ...

μ₂ = 0.167448079219689

STEP 3: Convert Result to Output's Unit

0.167448079219689 Radian -->9.59406822686227 Degree (Check conversion here)

FINAL ANSWER

9.59406822686227 ≈ 9.594068 Degree <-- Rearward Mach Angle

(Calculation completed in 00.004 seconds)

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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!

< 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)

Rearward Mach Angle of Expansion Fan Formula

LaTeX Go

Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan)
μ₂ = arsin(1/M_e2)

What quantitative change takes place across expansion wave?

Across the expansion fan, the Mach number increases, pressure, temperature and density decreases. The expansion fan is the continuous expansion region which can be visualized as a series of Mach waves, each making angle μ with the local flow direction. As the expansion takes place through the series of Mach waves and entropy change is zero for Mach waves, the expansion is isentropic.

How to Calculate Rearward Mach Angle of Expansion Fan?

Rearward Mach Angle of Expansion Fan calculator uses Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan) to calculate the Rearward Mach Angle, The Rearward Mach Angle of Expansion Fan formula is defined as the angle between the direction of flow within the fan and the Mach wave generated by the expansion of the flow. Rearward Mach Angle is denoted by μ₂ symbol.

How to calculate Rearward Mach Angle of Expansion Fan using this online calculator? To use this online calculator for Rearward Mach Angle of Expansion Fan, enter Mach Number Behind Expansion Fan (M_e2) and hit the calculate button. Here is how the Rearward Mach Angle of Expansion Fan calculation can be explained with given input values -> 0.167448 = arsin(1/6).

FAQ

What is Rearward Mach Angle of Expansion Fan?

The Rearward Mach Angle of Expansion Fan formula is defined as the angle between the direction of flow within the fan and the Mach wave generated by the expansion of the flow and is represented as μ₂ = arsin(1/M_e2) or Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan). Mach Number Behind Expansion Fan is the Mach number of downstream flow across the expansion fan.

How to calculate Rearward Mach Angle of Expansion Fan?

The Rearward Mach Angle of Expansion Fan formula is defined as the angle between the direction of flow within the fan and the Mach wave generated by the expansion of the flow is calculated using Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan). To calculate Rearward Mach Angle of Expansion Fan, you need Mach Number Behind Expansion Fan (M_e2). With our tool, you need to enter the respective value for Mach Number Behind 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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