Mach Number behind Shock Calculator

✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.ⓘ Mach Number Ahead of Normal Shock [M₁]			+10% -10%

✖Mach Number Behind Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound after passing through a normal shock wave.ⓘ Mach Number behind Shock [M₂]

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Mach Number behind Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2)
M₂ = ((2+γ*M₁^2-M₁^2)/(2*γ*M₁^2-γ+1))^(1/2)
This formula uses 3 Variables

Variables Used

Mach Number Behind Normal Shock - Mach Number Behind Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound after passing through a normal shock wave.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number Ahead of Normal Shock - Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number Ahead of Normal Shock: 1.49 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M₂ = ((2+γ*M₁^2-M₁^2)/(2*γ*M₁^2-γ+1))^(1/2) --> ((2+1.4*1.49^2-1.49^2)/(2*1.4*1.49^2-1.4+1))^(1/2)

Evaluating ... ...

M₂ = 0.704658912439046

STEP 3: Convert Result to Output's Unit

0.704658912439046 --> No Conversion Required

FINAL ANSWER

0.704658912439046 ≈ 0.704659 <-- Mach Number Behind Normal Shock

(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!

< Downstream Shock Waves Calculators

Mach Number behind Shock

LaTeX Go Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2)

Static Pressure behind Normal Shock using Normal Shock Momentum Equation

LaTeX Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Density Behind Normal Shock*Velocity Downstream of Shock^2

Velocity behind Normal Shock

LaTeX Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))

Characteristic Mach Number behind Shock

LaTeX Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Mach Number behind Shock Formula

LaTeX Go

What is the regime of Mach number behind a normal shock?

The Mach number behind a normal shock is always subsonic since there is a loss in speed of body after the shockwave.

How to Calculate Mach Number behind Shock?

Mach Number behind Shock calculator uses Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2) to calculate the Mach Number Behind Normal Shock, Mach Number behind Shock formula is defined as a relationship that describes the change in Mach number across a normal shock wave, illustrating how compressible flow characteristics alter due to shock wave interactions in aerospace applications. Mach Number Behind Normal Shock is denoted by M₂ symbol.

How to calculate Mach Number behind Shock using this online calculator? To use this online calculator for Mach Number behind Shock, enter Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button. Here is how the Mach Number behind Shock calculation can be explained with given input values -> 0.704659 = ((2+1.4*1.49^2-1.49^2)/(2*1.4*1.49^2-1.4+1))^(1/2).

FAQ

What is Mach Number behind Shock?

Mach Number behind Shock formula is defined as a relationship that describes the change in Mach number across a normal shock wave, illustrating how compressible flow characteristics alter due to shock wave interactions in aerospace applications and is represented as M₂ = ((2+γ*M₁^2-M₁^2)/(2*γ*M₁^2-γ+1))^(1/2) or Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2). The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

How to calculate Mach Number behind Shock?

Mach Number behind Shock formula is defined as a relationship that describes the change in Mach number across a normal shock wave, illustrating how compressible flow characteristics alter due to shock wave interactions in aerospace applications is calculated using Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2). To calculate Mach Number behind Shock, you need Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁). With our tool, you need to enter the respective value for Specific Heat Ratio & Mach Number Ahead of Normal Shock 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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