Forward Mach Angle of Expansion Fan Calculator

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

Forward Mach Angle - (Measured in Radian) - Forward Mach Angle is the angle formed between the forward Mach line and upstream flow direction.
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

Mach Number Ahead of Expansion Fan: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ₁ = arsin(1/M_e1) --> arsin(1/5)

Evaluating ... ...

μ₁ = 0.201357920790331

STEP 3: Convert Result to Output's Unit

0.201357920790331 Radian -->11.5369590328177 Degree (Check conversion here)

FINAL ANSWER

11.5369590328177 ≈ 11.53696 Degree <-- Forward Mach Angle

(Calculation completed in 00.020 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Expansion Waves » Forward Mach Angle of Expansion Fan

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ 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)

Forward Mach Angle of Expansion Fan Formula

Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan)
μ₁ = arsin(1/M_e1)

Why inlets designers would love to have compression process carried by isentropic compression waves?

The isentropic compression process is a more efficient compression process, yielding a downstream Mach number and pressure that are considerably higher than the shock wave. The inefficiency of the shock wave is measured by the loss of total pressure across the shock.

How to Calculate Forward Mach Angle of Expansion Fan?

Forward Mach Angle of Expansion Fan calculator uses Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan) to calculate the Forward Mach Angle, The Forward Mach Angle of Expansion Fan refers to the angle between the direction of flow within the expansion fan and the Mach wave generated by the expansion process. Forward Mach Angle is denoted by μ₁ symbol.

How to calculate Forward Mach Angle of Expansion Fan using this online calculator? To use this online calculator for Forward Mach Angle of Expansion Fan, enter Mach Number Ahead of Expansion Fan (M_e1) and hit the calculate button. Here is how the Forward Mach Angle of Expansion Fan calculation can be explained with given input values -> 661.0191 = arsin(1/5).

FAQ

What is Forward Mach Angle of Expansion Fan?

The Forward Mach Angle of Expansion Fan refers to the angle between the direction of flow within the expansion fan and the Mach wave generated by the expansion process and is represented as μ₁ = arsin(1/M_e1) or Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan). Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.

How to calculate Forward Mach Angle of Expansion Fan?

The Forward Mach Angle of Expansion Fan refers to the angle between the direction of flow within the expansion fan and the Mach wave generated by the expansion process is calculated using Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan). To calculate Forward Mach Angle of Expansion Fan, you need Mach Number Ahead of Expansion Fan (M_e1). With our tool, you need to enter the respective value for 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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