Mach Wave behind Shock Calculator

✖The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.ⓘ Freestream Velocity [V_∞]			+10% -10%
✖Local shock velocity for Mach Wave, is the shock velocity after the shock wave.ⓘ Local Shock Velocity for Mach Wave [W_mach]			+10% -10%
✖The speed of sound is defined as the dynamic propagation of sound waves.ⓘ Speed of Sound [c_speed]			+10% -10%

✖Mach Number behind shock is the Mach number over the body after a shockwave has occurred.ⓘ Mach Wave behind Shock [M₂]

⎘ Copy

👎

Formula

✖

Mach Wave behind Shock

Formula

`"M"_{"2"} = ("V"_{"∞"}-"W"_{"mach"})/"c"_{"speed"}`

Example

`"0.017493"=("98m/s"-"92m/s")/"343m/s"`

Calculator

LaTeX

Reset

👍

Download Hypersonic Flow Formula PDF

Mach Wave behind Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound
M₂ = (V_∞-W_mach)/c_speed
This formula uses 4 Variables

Variables Used

Mach Number behind shock - Mach Number behind shock is the Mach number over the body after a shockwave has occurred.
Freestream Velocity - (Measured in Meter per Second) - The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.
Local Shock Velocity for Mach Wave - (Measured in Meter per Second) - Local shock velocity for Mach Wave, is the shock velocity after the shock wave.
Speed of Sound - (Measured in Meter per Second) - The speed of sound is defined as the dynamic propagation of sound waves.

STEP 1: Convert Input(s) to Base Unit

Freestream Velocity: 98 Meter per Second --> 98 Meter per Second No Conversion Required
Local Shock Velocity for Mach Wave: 92 Meter per Second --> 92 Meter per Second No Conversion Required
Speed of Sound: 343 Meter per Second --> 343 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M₂ = (V_∞-W_mach)/c_speed --> (98-92)/343

Evaluating ... ...

M₂ = 0.0174927113702624

STEP 3: Convert Result to Output's Unit

0.0174927113702624 --> No Conversion Required

FINAL ANSWER

0.0174927113702624 ≈ 0.017493 <-- Mach Number behind shock

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Hypersonic Inviscid Flow » Shock Dynamics and Aerodynamic Shape » Mach Wave behind Shock

Credits

Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has created this Calculator and 300+ more calculators!

Verified by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has verified this Calculator and 200+ more calculators!

< 10+ Shock Dynamics and Aerodynamic Shape Calculators

Pressure Ratio for Unsteady Waves

Go Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Ratio of New and Old Temperature

Go Temperature Ratio across Shock = (1+((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2)

Grid Point Calculation for Shock Waves

Go Grid Points = (Distance from X-Axis-Body shape in hypersonic flow)/Local Shock-detachment Distance

Mach Wave behind Shock

Go Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound

Local Shock Velocity Equation

Go Local Shock Velocity = Speed of Sound*(Mach Number-Mach Number ahead of shock)

Mach Wave behind Shock with Mach Infinity

Go Mach Number ahead of shock = Mach Number-Local Shock Velocity/Speed of Sound

Nose Radius of Cylinder-Wedge

Go Radius = Local Shock-detachment Distance/(0.386*exp(4.67/(Mach Number^2)))

Nose Radius of Sphere Cone

Go Radius = Local Shock-detachment Distance/(0.143*exp(3.24/(Mach Number^2)))

Detachment Distance of Cylinder Wedge Body Shape

Go Local Shock-detachment Distance = Radius*0.386*exp(4.67/(Mach Number^2))

Detachment Distance of Sphere Cone Body Shape

Go Local Shock-detachment Distance = Radius*0.143*exp(3.24/(Mach Number^2))

Mach Wave behind Shock Formula

Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound
M₂ = (V_∞-W_mach)/c_speed

wWat is a shock wave?

Shock wave, strong pressure wave in any elastic medium such as air, water, or a solid substance, produced by supersonic aircraft, explosions, lightning, or other phenomena that create violent changes in pressure

How to Calculate Mach Wave behind Shock?

Mach Wave behind Shock calculator uses Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound to calculate the Mach Number behind shock, The Mach wave behind shock formula is defined as the ratio of freestream velocity minus the local shock velocity to the speed of sound. Mach Number behind shock is denoted by M₂ symbol.

How to calculate Mach Wave behind Shock using this online calculator? To use this online calculator for Mach Wave behind Shock, enter Freestream Velocity (V_∞), Local Shock Velocity for Mach Wave (W_mach) & Speed of Sound (c_speed) and hit the calculate button. Here is how the Mach Wave behind Shock calculation can be explained with given input values -> -2.577259 = (98-92)/343.

FAQ

What is Mach Wave behind Shock?

The Mach wave behind shock formula is defined as the ratio of freestream velocity minus the local shock velocity to the speed of sound and is represented as M₂ = (V_∞-W_mach)/c_speed or Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound. The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air, Local shock velocity for Mach Wave, is the shock velocity after the shock wave & The speed of sound is defined as the dynamic propagation of sound waves.

How to calculate Mach Wave behind Shock?

The Mach wave behind shock formula is defined as the ratio of freestream velocity minus the local shock velocity to the speed of sound is calculated using Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound. To calculate Mach Wave behind Shock, you need Freestream Velocity (V_∞), Local Shock Velocity for Mach Wave (W_mach) & Speed of Sound (c_speed). With our tool, you need to enter the respective value for Freestream Velocity, Local Shock Velocity for Mach Wave & Speed of Sound and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search