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Temperature Ratio across Expansion Fan Formula

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Temperature Ratio Across Expansion Fan is the ratio of downstream temperature to upstream temperature across the expansion fan. Check FAQs

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}}

T_e,r - Temperature Ratio Across 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 Ratio across Expansion Fan Example

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

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

Here is how the Temperature Ratio across Expansion Fan equation looks like.

0.7309 = \frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}}

0.7309 = \frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}}

0.7309 = \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 Ratio across Expansion Fan Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

T e,r = \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 e,r = \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 e,r = 0.73090692124105

LAST Step Rounding Answer

∴

T e,r = 0.7309

Temperature Ratio across Expansion Fan Formula Elements

Variables

Temperature Ratio Across Expansion Fan

Temperature Ratio Across Expansion Fan is the ratio of downstream temperature to upstream temperature across the expansion fan.

Symbol: T_e,r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Temperature Ratio Across 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 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 Temperature behind Expansion Fan

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}})

Go Forward Mach Angle of Expansion Fan

μ 1 = a r \sin (\frac{1}{M e1})

How to Evaluate Temperature Ratio across Expansion Fan?

Temperature Ratio across Expansion Fan evaluator uses Temperature Ratio Across 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 Ratio Across Expansion Fan, The Temperature Ratio across Expansion Fan formula is defined as the ratio of static to stagnation temperature downstream of the expansion fan to the static to stagnation temperature upstream of the expansion fan. Temperature Ratio Across Expansion Fan is denoted by T_e,r symbol.

How to evaluate Temperature Ratio across Expansion Fan using this online evaluator? To use this online evaluator for Temperature Ratio across Expansion Fan, enter 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 Ratio across Expansion Fan

What is the formula to find Temperature Ratio across Expansion Fan?

The formula of Temperature Ratio across Expansion Fan is expressed as Temperature Ratio Across 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- 0.731707 = (1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2).

How to calculate Temperature Ratio across Expansion Fan?

With 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 Ratio across Expansion Fan using the formula - Temperature Ratio Across 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).

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Temperature Ratio across Expansion Fan Formula

Temperature Ratio across Expansion Fan Example

Temperature Ratio across Expansion Fan Solution

Temperature Ratio across Expansion Fan Formula Elements

Other formulas in Expansion Waves category

How to Evaluate Temperature Ratio across Expansion Fan?

FAQs on Temperature Ratio across Expansion Fan

Variable Name