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

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Temperature Behind Normal Shock is defined as the downstream temperature across the shock. Check FAQs

T 2 = T 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}}})

T₂ - Temperature Behind Normal Shock?T₁ - Temperature Ahead of Normal Shock?γ - Specific Heat Ratio?M₁ - Mach Number Ahead of Normal Shock?

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

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

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

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

391.6411 = 298.15 \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}}})

391.6411K = 298.15K \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}}})

391.6411 = 298.15 \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 Temperature behind Normal Shock for given Upstream Temperature and Mach Number Solution

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

FIRST Step Consider the formula

T 2 = T 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

∴

T 2 = 298.15K \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

∴

T 2 = 298.15 \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

∴

T 2 = 391.641137299502K

LAST Step Rounding Answer

∴

T 2 = 391.6411K

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

Variables

Temperature Behind Normal Shock

Temperature Behind Normal Shock is defined as the downstream temperature across the shock.

Symbol: T₂

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature Behind Normal Shock

Temperature Ahead of Normal Shock

Temperature Ahead of Normal Shock signifies the temperature of a fluid before encountering a normal shock wave.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature 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 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 Temperature behind Normal Shock for given Upstream Temperature and Mach Number?

Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number evaluator uses Temperature Behind Normal Shock = Temperature 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 Temperature Behind Normal Shock, The Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number computes the temperature of a fluid behind a normal shock wave based on the provided upstream temperature and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in temperature resulting from the shock wave passage. Temperature Behind Normal Shock is denoted by T₂ symbol.

How to evaluate Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number using this online evaluator? To use this online evaluator for Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number, enter Temperature Ahead of Normal Shock (T₁), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button.

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

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

The formula of Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number is expressed as Temperature Behind Normal Shock = Temperature 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- 391.6411 = 298.15*((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 Temperature behind Normal Shock for given Upstream Temperature and Mach Number?

With Temperature Ahead of Normal Shock (T₁), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) we can find Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number using the formula - Temperature Behind Normal Shock = Temperature 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))).

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

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

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

Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number can be measured.

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

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

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

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

Other formulas in Downstream Shock Waves category

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

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

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