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## Credits

Indian Institute of Technology (IIT), Bombay
Shikha Maurya has created this Calculator and 100+ more calculators!
PSG College of Technology (PSGCT), Coimbatore
Maiarutselvan V has verified this Calculator and 200+ more calculators!

## Forward Mach angle of expansion fan Solution

STEP 0: Pre-Calculation Summary
Formula Used
forward_mach_angle = arsin(1/Mach no. ahead expansion fan)
μ 1 = arsin(1/M 1)
This formula uses 2 Functions, 1 Variables
Functions Used
sin - Trigonometric sine function, sin(Angle)
arsin - Inverse trigonometric sine function, arsin(Number)
Variables Used
Mach no. ahead expansion fan- Mach no. ahead expansion fan is the Mach number of the upstream flow.
STEP 1: Convert Input(s) to Base Unit
Mach no. ahead expansion fan: 5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
μ 1 = arsin(1/M 1) --> arsin(1/5)
Evaluating ... ...
μ 1 = 0.201357920790331
STEP 3: Convert Result to Output's Unit
0.201357920790331 Radian --> No Conversion Required
0.201357920790331 Radian <-- Forward Mach angle
(Calculation completed in 00.002 seconds)

## < 10+ Oblique Shock and Expansion Waves Calculators

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number
temp_behind_shock = Temperature ahead of shock*((1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))) Go
Temperature ratio across the oblique shock
temperature_ratio_across_shock = (1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))) Go
Pressure behind expansion fan
pressure_behind_expansion_fan = Pressure ahead expansion fan*((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1)) Go
Component of downstream Mach number normal to oblique shock for given normal upstream Mach number
component_of_downstream_mach_normal_to_obliqueshock = sqrt((1+0.5*((Specific heat ratio-1)*Component of upstream mach normal to oblique shock^2))/(Specific heat ratio*Component of upstream mach normal to oblique shock^2-0.5*(Specific heat ratio-1))) Go
Pressure ratio across the expansion fan
pressure_ratio_across_expansion_fan = ((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1)) Go
Density behind oblique shock for given upstream density and normal upstream Mach number
density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))) Go
Density ratio across the oblique shock
density_ratio_across_shock = (Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))) Go
Pressure behind oblique shock for given upstream pressure and normal upstream Mach number
static_pressure_behind_shock = Static pressure ahead of shock*(1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1)) Go
Temperature ratio across the expansion fan
temp_ratio_across_expansion_fan = (1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)) Go
Pressure ratio across the oblique shock
pressure_ratio_across_shock = 1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1) Go

### Forward Mach angle of expansion fan Formula

forward_mach_angle = arsin(1/Mach no. ahead expansion fan)
μ 1 = arsin(1/M 1)

## 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 no. ahead expansion fan) to calculate the Forward Mach angle, The Forward Mach angle of expansion fan formula is defined as the sine inverse of reciprocal of upstream Mach number of the flow. Forward Mach angle and is denoted by μ 1 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 no. ahead expansion fan (M 1) and hit the calculate button. Here is how the Forward Mach angle of expansion fan calculation can be explained with given input values -> 0.201358 = arsin(1/5).

### FAQ

What is Forward Mach angle of expansion fan?
The Forward Mach angle of expansion fan formula is defined as the sine inverse of reciprocal of upstream Mach number of the flow and is represented as μ 1 = arsin(1/M 1) or forward_mach_angle = arsin(1/Mach no. ahead expansion fan). Mach no. ahead 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 formula is defined as the sine inverse of reciprocal of upstream Mach number of the flow is calculated using forward_mach_angle = arsin(1/Mach no. ahead expansion fan). To calculate Forward Mach angle of expansion fan, you need Mach no. ahead expansion fan (M 1). With our tool, you need to enter the respective value for Mach no. ahead expansion fan and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Forward Mach angle?
In this formula, Forward Mach angle uses Mach no. ahead expansion fan. We can use 10 other way(s) to calculate the same, which is/are as follows -
• density_ratio_across_shock = (Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))
• component_of_downstream_mach_normal_to_obliqueshock = sqrt((1+0.5*((Specific heat ratio-1)*Component of upstream mach normal to oblique shock^2))/(Specific heat ratio*Component of upstream mach normal to oblique shock^2-0.5*(Specific heat ratio-1)))
• density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))
• static_pressure_behind_shock = Static pressure ahead of shock*(1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))
• temp_behind_shock = Temperature ahead of shock*((1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))))
• pressure_ratio_across_shock = 1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1)
• temperature_ratio_across_shock = (1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))
• pressure_ratio_across_expansion_fan = ((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1))
• temp_ratio_across_expansion_fan = (1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2))
• pressure_behind_expansion_fan = Pressure ahead expansion fan*((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1))
Where is the Forward Mach angle of expansion fan calculator used?
Among many, Forward Mach angle of expansion fan calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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