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

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Temperature Behind Oblique Shock signifies the temperature of a fluid or airflow after passing through an oblique shock wave. Check FAQs

T s2 = T s1 \cdot (\frac{1 + (\frac{2 \cdot γ o}{γ o + 1}) \cdot ({M n1}^{2} - 1)}{(γ o + 1) \cdot \frac{{M n1}^{2}}{2 + (γ o - 1) \cdot {M n1}^{2}}})

T_s2 - Temperature Behind Oblique Shock?T_s1 - Temperature Ahead of Oblique Shock?γ_o - Specific Heat Ratio Oblique Shock?M_n1 - Upstream Mach Normal to Oblique Shock?

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

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

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

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

400.9287 = 288 \cdot (\frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.606}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}})

400.9287K = 288K \cdot (\frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.606}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}})

400.9287 = 288 \cdot (\frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.606}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}})

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

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

FIRST Step Consider the formula

T s2 = T s1 \cdot (\frac{1 + (\frac{2 \cdot γ o}{γ o + 1}) \cdot ({M n1}^{2} - 1)}{(γ o + 1) \cdot \frac{{M n1}^{2}}{2 + (γ o - 1) \cdot {M n1}^{2}}})

Next Step Substitute values of Variables

∴

T s2 = 288K \cdot (\frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.606}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}})

Next Step Prepare to Evaluate

∴

T s2 = 288 \cdot (\frac{1 + (\frac{2 \cdot 1.4}{1.4 + 1}) \cdot ({1.606}^{2} - 1)}{(1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}})

Next Step Evaluate

∴

T s2 = 400.928747600831K

LAST Step Rounding Answer

∴

T s2 = 400.9287K

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

Variables

Temperature Behind Oblique Shock

Temperature Behind Oblique Shock signifies the temperature of a fluid or airflow after passing through an oblique shock wave.

Symbol: T_s2

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature Behind Oblique Shock

Temperature Ahead of Oblique Shock

Temperature Ahead of Oblique Shock refers to the temperature of a fluid or airflow before encountering an oblique shock wave.

Symbol: T_s1

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature Ahead of Oblique Shock

Specific Heat Ratio Oblique Shock

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

Symbol: γ_o

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Specific Heat Ratio Oblique Shock

Upstream Mach Normal to Oblique Shock

Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

Symbol: M_n1

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Upstream Mach Normal to Oblique Shock

Other formulas in Oblique Shock category

Go Component of Upstream Mach Normal to Oblique Shock

M n1 = M 1 \cdot \sin (β)

Go Component of Downstream Mach Normal to Oblique Shock

M n2 = M 2 \cdot \sin (β - θ)

Go Flow Deflection Angle due to Oblique Shock

θ = a \tan (\frac{2 \cdot \cot (β) \cdot ({(M 1 \cdot \sin (β))}^{2} - 1)}{{M 1}^{2} \cdot (γ o + \cos (2 \cdot β)) + 2})

Go Density Ratio across Oblique Shock

ρ r = (γ o + 1) \cdot \frac{{M n1}^{2}}{2 + (γ o - 1) \cdot {M n1}^{2}}

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

Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number evaluator uses Temperature Behind Oblique Shock = Temperature Ahead of Oblique Shock*((1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))) to evaluate the Temperature Behind Oblique Shock, The Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number formula calculates the temperature of the fluid immediately after encountering an oblique shock wave, given the initial temperature and Mach number of the flow. Temperature Behind Oblique Shock is denoted by T_s2 symbol.

How to evaluate Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number using this online evaluator? To use this online evaluator for Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number, enter Temperature Ahead of Oblique Shock (T_s1), Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) and hit the calculate button.

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

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

The formula of Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number is expressed as Temperature Behind Oblique Shock = Temperature Ahead of Oblique Shock*((1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))). Here is an example- 400.9287 = 288*((1+((2*1.4)/(1.4+1))*(1.606^2-1))/((1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2))).

How to calculate Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number?

With Temperature Ahead of Oblique Shock (T_s1), Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) we can find Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number using the formula - Temperature Behind Oblique Shock = Temperature Ahead of Oblique Shock*((1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))).

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

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

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

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

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

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

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

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

Other formulas in Oblique Shock category

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

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

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