Mach Angle Calculator

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✖Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]

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✖Mach Angle is defined as the angle between the Mach line and the direction of motion of the body.ⓘ Mach Angle [μ]

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Formula

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Mach Angle

Formula

`"μ" = asin(1/"M")`

Example

`"30°"=asin(1/"2")`

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Mach Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mach Angle = asin(1/Mach Number)
μ = asin(1/M)
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)
asin - The inverse sine 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., asin(Number)

Variables Used

Mach Angle - (Measured in Radian) - Mach Angle is defined as the angle between the Mach line and the direction of motion of the body.
Mach Number - Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Mach Number: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ = asin(1/M) --> asin(1/2)

Evaluating ... ...

μ = 0.523598775598299

STEP 3: Convert Result to Output's Unit

0.523598775598299 Radian -->30.0000000000056 Degree (Check conversion here)

FINAL ANSWER

30.0000000000056 ≈ 30 Degree <-- Mach Angle

(Calculation completed in 00.004 seconds)

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Credits

Created by Vinay Mishra

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

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< 19 Thermodynamics and Governing Equations Calculators

Max work output in Brayton cycle

Go Maximum Work done in Brayton Cycle = (1005*1/Compressor Efficiency)*Temperature at Inlet of Compressor in Brayton*(sqrt(Temperature at Inlet to Turbine in Brayton Cycle/Temperature at Inlet of Compressor in Brayton*Compressor Efficiency*Turbine Efficiency)-1)^2

Choked Mass Flow Rate given specific heat ratio

Go Choked Mass Flow Rate = (Heat Capacity Ratio/(sqrt(Heat Capacity Ratio-1)))*((Heat Capacity Ratio+1)/2)^(-((Heat Capacity Ratio+1)/(2*Heat Capacity Ratio-2)))

Choked Mass Flow Rate

Go Choked Mass Flow Rate = (Mass Flow Rate*sqrt(Specific Heat Capacity at Constant Pressure*Temperature))/(Nozzle Throat Area*Throat Pressure)

Stagnation Velocity of Sound given Specific Heat at Constant Pressure

Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Specific Heat Capacity at Constant Pressure*Stagnation Temperature)

Specific Heat of mixed out gas

Go Specific Heat of Mixed Gas = (Specific Heat of Core Gas+Bypass Ratio*Specific Heat of Bypass Air)/(1+Bypass Ratio)

Stagnation Temperature

Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)

Stagnation Velocity of Sound

Go Stagnation Velocity of Sound = sqrt(Heat Capacity Ratio*[R]*Stagnation Temperature)

Speed of Sound

Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)

Stagnation Velocity of Sound given Stagnation Enthalpy

Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Stagnation Enthalpy)

Heat Capacity Ratio

Go Heat Capacity Ratio = Specific Heat Capacity at Constant Pressure/Specific Heat Capacity at Constant Volume

Efficiency of cycle

Go Efficiency of Cycle = (Turbine Work-Compressor Work)/Heat

Internal Energy of Perfect Gas at given Temperature

Go Internal Energy = Specific Heat Capacity at Constant Volume*Temperature

Enthalpy of Ideal Gas at given Temperature

Go Enthalpy = Specific Heat Capacity at Constant Pressure*Temperature

Stagnation enthalpy

Go Stagnation Enthalpy = Enthalpy+(Velocity of Fluid Flow^2)/2

Efficiency of Joule cycle

Go Efficiency of Joule Cycle = Net Work Output/Heat

Pressure Ratio

Go Pressure Ratio = Final Pressure/Initial Pressure

Work ratio in practical cycle

Go Work Ratio = 1-(Compressor Work/Turbine Work)

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Mach Angle

Go Mach Angle = asin(1/Mach Number)

< 18 Governing Equations and Sound Wave Calculators

Speed of Sound Downstream of Sound Wave

Go Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))

Speed of Sound Upstream of Sound Wave

Go Sound Speed Upstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Downstream of Sound^2-Flow Velocity Upstream of Sound^2)/2+Sound Speed Downstream^2/(Specific Heat Ratio-1)))

Flow Velocity Downstream of Sound Wave

Go Flow Velocity Downstream of Sound = sqrt(2*((Sound Speed Upstream^2-Sound Speed Downstream^2)/(Specific Heat Ratio-1)+Flow Velocity Upstream of Sound^2/2))

Flow Velocity Upstream of Sound Wave

Go Flow Velocity Upstream of Sound = sqrt(2*((Sound Speed Downstream^2-Sound Speed Upstream^2)/(Specific Heat Ratio-1)+Flow Velocity Downstream of Sound^2/2))

Ratio of Stagnation and Static Pressure

Go Stagnation to Static Pressure = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(Specific Heat Ratio/(Specific Heat Ratio-1))

Critical Pressure

Go Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure

Stagnation Temperature

Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)

Speed of Sound

Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)

Ratio of Stagnation and Static Density

Go Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))

Critical Density

Go Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))

Mayer's Formula

Go Specific Gas Constant = Specific Heat Capacity at Constant Pressure-Specific Heat Capacity at Constant Volume

Ratio of Stagnation and Static Temperature

Go Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2

Critical Temperature

Go Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)

Isentropic Compressibility for given Density and Speed of Sound

Go Isentropic Compressibility = 1/(Density*Speed of Sound^2)

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Speed of Sound given Isentropic Change

Go Speed of Sound = sqrt(Isentropic Change)

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Isentropic Change across Sound Wave

Go Isentropic Change = Speed of Sound^2

Mach Angle Formula

Mach Angle = asin(1/Mach Number)
μ = asin(1/M)

What is the Mach cone?

Mach cone is defined as the conical pressure wavefront produced by a body moving at a speed greater than that of sound.

How to Calculate Mach Angle?

Mach Angle calculator uses Mach Angle = asin(1/Mach Number) to calculate the Mach Angle, The Mach Angle is an angle that describes the oblique shock wave formed when a body moves through a fluid at a supersonic speed. It represents the angle between the direction of motion of the body and the direction of the oblique shock wave. Mach Angle is denoted by μ symbol.

How to calculate Mach Angle using this online calculator? To use this online calculator for Mach Angle, enter Mach Number (M) and hit the calculate button. Here is how the Mach Angle calculation can be explained with given input values -> 1718.873 = asin(1/2).

FAQ

What is Mach Angle?

The Mach Angle is an angle that describes the oblique shock wave formed when a body moves through a fluid at a supersonic speed. It represents the angle between the direction of motion of the body and the direction of the oblique shock wave and is represented as μ = asin(1/M) or Mach Angle = asin(1/Mach Number). Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Mach Angle?

The Mach Angle is an angle that describes the oblique shock wave formed when a body moves through a fluid at a supersonic speed. It represents the angle between the direction of motion of the body and the direction of the oblique shock wave is calculated using Mach Angle = asin(1/Mach Number). To calculate Mach Angle, you need Mach Number (M). With our tool, you need to enter the respective value for Mach Number 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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