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Temperature behind Expansion Fan Formula

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Temperature behind expansion fan is the temperature in the downstream direction of the expansion fan. Check FAQs

T 2 = T 1 \cdot (\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})

T₂ - Temperature Behind Expansion Fan?T₁ - Temperature Ahead of Expansion Fan?γ_e - Specific Heat Ratio Expansion Wave?M_e1 - Mach Number Ahead of Expansion Fan?M_e2 - Mach Number Behind Expansion Fan?

Temperature behind Expansion Fan Example

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Here is how the Temperature behind Expansion Fan equation looks like with Values.

Here is how the Temperature behind Expansion Fan equation looks like with Units.

Here is how the Temperature behind Expansion Fan equation looks like.

288.065 = 394.12 \cdot (\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})

288.065K = 394.12K \cdot (\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})

288.065 = 394.12 \cdot (\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})

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Temperature behind Expansion Fan Solution

Follow our step by step solution on how to calculate Temperature behind Expansion Fan?

FIRST Step Consider the formula

T 2 = T 1 \cdot (\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})

Next Step Substitute values of Variables

∴

T 2 = 394.12K \cdot (\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})

Next Step Prepare to Evaluate

∴

T 2 = 394.12 \cdot (\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})

Next Step Evaluate

∴

T 2 = 288.065035799523K

LAST Step Rounding Answer

∴

T 2 = 288.065K

Temperature behind Expansion Fan Formula Elements

Variables

Temperature Behind Expansion Fan

Temperature behind expansion fan is the temperature in the downstream direction of the expansion fan.

Symbol: T₂

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature Behind Expansion Fan

Temperature Ahead of Expansion Fan

Temperature ahead of expansion fan is the temperature in the upstream direction of the expansion fan.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature Ahead of Expansion Fan

Specific Heat Ratio Expansion Wave

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

Symbol: γ_e

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Specific Heat Ratio Expansion Wave

Mach Number Ahead of Expansion Fan

Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.

Symbol: M_e1

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Ahead of Expansion Fan

Mach Number Behind Expansion Fan

Mach Number Behind Expansion Fan is the Mach number of downstream flow across the expansion fan.

Symbol: M_e2

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Behind Expansion Fan

Other formulas in Expansion Waves category

Go Pressure Ratio across Expansion Fan

P e,r = {(\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})}^{\frac{γ e}{γ e - 1}}

Go Temperature Ratio across Expansion Fan

T e,r = \frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}}

Go Pressure behind Expansion Fan

P 2 = P 1 \cdot {(\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})}^{\frac{γ e}{γ e - 1}}

Go Forward Mach Angle of Expansion Fan

μ 1 = a r \sin (\frac{1}{M e1})

How to Evaluate Temperature behind Expansion Fan?

Temperature behind Expansion Fan evaluator uses Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)) to evaluate the Temperature Behind Expansion Fan, The Temperature behind Expansion Fan formula is derived from the ideal gas law and the concept of isentropic flow. It relates the temperature change to the Mach number through the specific heat ratio. Temperature Behind Expansion Fan is denoted by T₂ symbol.

How to evaluate Temperature behind Expansion Fan using this online evaluator? To use this online evaluator for Temperature behind Expansion Fan, enter Temperature Ahead of Expansion Fan (T₁), Specific Heat Ratio Expansion Wave (γ_e), Mach Number Ahead of Expansion Fan (M_e1) & Mach Number Behind Expansion Fan (M_e2) and hit the calculate button.

FAQs on Temperature behind Expansion Fan

What is the formula to find Temperature behind Expansion Fan?

The formula of Temperature behind Expansion Fan is expressed as Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)). Here is an example- 288.3805 = 394.12*((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2)).

How to calculate Temperature behind Expansion Fan?

With Temperature Ahead of Expansion Fan (T₁), Specific Heat Ratio Expansion Wave (γ_e), Mach Number Ahead of Expansion Fan (M_e1) & Mach Number Behind Expansion Fan (M_e2) we can find Temperature behind Expansion Fan using the formula - Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)).

Can the Temperature behind Expansion Fan be negative?

Yes, the Temperature behind Expansion Fan, measured in Temperature can be negative.

Which unit is used to measure Temperature behind Expansion Fan?

Temperature behind Expansion Fan is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Temperature behind Expansion Fan can be measured.

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Temperature behind Expansion Fan Formula

Temperature behind Expansion Fan Example

Temperature behind Expansion Fan Solution

Temperature behind Expansion Fan Formula Elements

Other formulas in Expansion Waves category

How to Evaluate Temperature behind Expansion Fan?

FAQs on Temperature behind Expansion Fan

Variable Name