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Mach Number behind Shock Formula

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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. Check FAQs

M 2 = {(\frac{2 + γ \cdot {M 1}^{2} - {M 1}^{2}}{2 \cdot γ \cdot {M 1}^{2} - γ + 1})}^{\frac{1}{2}}

M₂ - Mach Number Behind Normal Shock?γ - Specific Heat Ratio?M₁ - Mach Number Ahead of Normal Shock?

Mach Number behind Shock Example

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Here is how the Mach Number behind Shock equation looks like with Values.

Here is how the Mach Number behind Shock equation looks like with Units.

Here is how the Mach Number behind Shock equation looks like.

0.7047 = {(\frac{2 + 1.4 \cdot {1.49}^{2} - {1.49}^{2}}{2 \cdot 1.4 \cdot {1.49}^{2} - 1.4 + 1})}^{\frac{1}{2}}

0.7047 = {(\frac{2 + 1.4 \cdot {1.49}^{2} - {1.49}^{2}}{2 \cdot 1.4 \cdot {1.49}^{2} - 1.4 + 1})}^{\frac{1}{2}}

0.7047 = {(\frac{2 + 1.4 \cdot {1.49}^{2} - {1.49}^{2}}{2 \cdot 1.4 \cdot {1.49}^{2} - 1.4 + 1})}^{\frac{1}{2}}

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Mach Number behind Shock Solution

Follow our step by step solution on how to calculate Mach Number behind Shock?

FIRST Step Consider the formula

M 2 = {(\frac{2 + γ \cdot {M 1}^{2} - {M 1}^{2}}{2 \cdot γ \cdot {M 1}^{2} - γ + 1})}^{\frac{1}{2}}

Next Step Substitute values of Variables

∴

M 2 = {(\frac{2 + 1.4 \cdot {1.49}^{2} - {1.49}^{2}}{2 \cdot 1.4 \cdot {1.49}^{2} - 1.4 + 1})}^{\frac{1}{2}}

Next Step Prepare to Evaluate

∴

M 2 = {(\frac{2 + 1.4 \cdot {1.49}^{2} - {1.49}^{2}}{2 \cdot 1.4 \cdot {1.49}^{2} - 1.4 + 1})}^{\frac{1}{2}}

Next Step Evaluate

∴

M 2 = 0.704658912439046

LAST Step Rounding Answer

∴

M 2 = 0.7047

Mach Number behind Shock Formula Elements

Variables

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.

Symbol: M₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Behind Normal Shock

Specific Heat Ratio

The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be between 1 to 2.

Formulas to find Specific Heat Ratio

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.

Symbol: M₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Ahead of Normal Shock

Other formulas in Downstream Shock Waves category

Go Characteristic Mach Number behind Shock

M2 cr = \frac{1}{M1 cr}

Go Velocity behind Normal Shock

V 2 = \frac{V 1}{\frac{γ + 1}{(γ - 1) + \frac{2}{M^{2}}}}

Go Static Pressure behind Normal Shock using Normal Shock Momentum Equation

P 2 = P 1 + ρ 1 \cdot {V 1}^{2} - ρ 2 \cdot {V 2}^{2}

Go Density behind Normal Shock using Normal Shock Momentum Equation

ρ 2 = \frac{P 1 + ρ 1 \cdot {V 1}^{2} - P 2}{{V 2}^{2}}

How to Evaluate Mach Number behind Shock?

Mach Number behind Shock evaluator 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 evaluate the Mach Number Behind Normal Shock, The Mach Number behind Shock calculates the Mach number of a fluid behind a normal shock wave. It utilizes parameters such as the Mach number ahead of the shock and the ratio of specific heats for the fluid. This formula provides insight into the change in Mach number as the fluid passes through the shock wave, aiding in the analysis of compressible flow behavior. Mach Number Behind Normal Shock is denoted by M₂ symbol.

How to evaluate Mach Number behind Shock using this online evaluator? To use this online evaluator for Mach Number behind Shock, enter Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button.

FAQs on Mach Number behind Shock

What is the formula to find Mach Number behind Shock?

The formula of Mach Number behind Shock is expressed as 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). Here is an example- 0.704659 = ((2+1.4*1.49^2-1.49^2)/(2*1.4*1.49^2-1.4+1))^(1/2).

How to calculate Mach Number behind Shock?

With Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) we can find Mach Number behind Shock using the formula - 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).

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Mach Number behind Shock Formula

Mach Number behind Shock Example

Mach Number behind Shock Solution

Mach Number behind Shock Formula Elements

Other formulas in Downstream Shock Waves category

How to Evaluate Mach Number behind Shock?

FAQs on Mach Number behind Shock

Variable Name