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Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Formula

GoEnthalpy behind Normal Shock from Normal Shock Energy Equation Formula

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Enthalpy Behind Normal Shock is the enthalpy of downstream of shock and it is defined as the sum of the system's internal energy and the product of its pressure and volume for per unit mass. Check FAQs

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

h₂ - Enthalpy Behind Normal Shock?h₁ - Enthalpy Ahead of Normal Shock?γ - Specific Heat Ratio?M₁ - Mach Number Ahead of Normal Shock?

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Example

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Here is how the Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number equation looks like with Values.

Here is how the Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number equation looks like with Units.

Here is how the Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number equation looks like.

262.9808 = 200.203 \cdot \frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.49}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}}

262.9808J/kg = 200.203J/kg \cdot \frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.49}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}}

262.9808 = 200.203 \cdot \frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.49}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}}

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Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Solution

Follow our step by step solution on how to calculate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h 2 = 200.203J/kg \cdot \frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.49}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}}

Next Step Prepare to Evaluate

∴

h 2 = 200.203 \cdot \frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.49}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}}

Next Step Evaluate

∴

h 2 = 262.980817074534J/kg

LAST Step Rounding Answer

∴

h 2 = 262.9808J/kg

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Formula Elements

Variables

Enthalpy Behind Normal Shock

Enthalpy Behind Normal Shock is the enthalpy of downstream of shock and it is defined as the sum of the system's internal energy and the product of its pressure and volume for per unit mass.

Symbol: h₂

Measurement: Specific EnergyUnit: J/kg

Note: Value should be greater than 0.

Formulas to find Enthalpy Behind Normal Shock

Enthalpy Ahead of Normal Shock

Enthalpy Ahead of Normal Shock is the enthalpy of upstream of shock and it is defined as the sum of the system's internal energy and the product of its pressure and volume for per unit mass.

Symbol: h₁

Measurement: Specific EnergyUnit: J/kg

Note: Value should be greater than 0.

Formulas to find Enthalpy Ahead of 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 to find Enthalpy Behind Normal Shock

Go Enthalpy behind Normal Shock from Normal Shock Energy Equation

h 2 = h 1 + \frac{{V 1}^{2} - {V 2}^{2}}{2}

Other formulas in Downstream Shock Waves category

Go Characteristic Mach Number behind Shock

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

Go Mach Number behind Shock

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

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}

How to Evaluate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number evaluator uses Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)) to evaluate the Enthalpy Behind Normal Shock, The Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number computes the enthalpy of a fluid behind a normal shock wave based on the enthalpy ahead of the shock and the Mach number of the flow. This formula accounts for the ratio of specific heats for the fluid and provides insights into the change in enthalpy resulting from the shock wave passage. Enthalpy Behind Normal Shock is denoted by h₂ symbol.

How to evaluate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number using this online evaluator? To use this online evaluator for Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number, enter Enthalpy Ahead of Normal Shock (h₁), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button.

FAQs on Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number

What is the formula to find Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

The formula of Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number is expressed as Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)). Here is an example- 200.3364 = 200.203*(1+((2*1.4)/(1.4+1))*(1.49^2-1))/((1.4+1)*(1.49^2)/(2+(1.4-1)*1.49^2)).

How to calculate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

With Enthalpy Ahead of Normal Shock (h₁), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) we can find Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number using the formula - Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)).

What are the other ways to Calculate Enthalpy Behind Normal Shock?

Here are the different ways to Calculate Enthalpy Behind Normal Shock-

Enthalpy Behind Normal Shock=Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2-Velocity Downstream of Shock^2)/2

Can the Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number be negative?

No, the Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number, measured in Specific Energy cannot be negative.

Which unit is used to measure Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number is usually measured using the Joule per Kilogram[J/kg] for Specific Energy. Joule per Gram[J/kg], Joule per Centigram[J/kg], Square Meter per Square Second[J/kg] are the few other units in which Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number can be measured.

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Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Formula

​GoEnthalpy behind Normal Shock from Normal Shock Energy Equation Formula

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Example

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Solution

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number Formula Elements

Other Formulas to find Enthalpy Behind Normal Shock

Other formulas in Downstream Shock Waves category

How to Evaluate Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number?

FAQs on Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number

Variable Name

GoEnthalpy behind Normal Shock from Normal Shock Energy Equation Formula