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Pressure Ratio across Expansion Fan Formula

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Pressure Ratio Across Expansion Fan is the ratio of downstream and upstream pressure across expansion fan. Check FAQs

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}}

P_e,r - Pressure 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?

Pressure Ratio across Expansion Fan Example

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

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

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

0.3403 = {(\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})}^{\frac{1.41}{1.41 - 1}}

0.3403 = {(\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})}^{\frac{1.41}{1.41 - 1}}

0.3403 = {(\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})}^{\frac{1.41}{1.41 - 1}}

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Pressure Ratio across Expansion Fan Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

P e,r = {(\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})}^{\frac{1.41}{1.41 - 1}}

Next Step Prepare to Evaluate

∴

P e,r = {(\frac{1 + 0.5 \cdot (1.41 - 1) \cdot 5^{2}}{1 + 0.5 \cdot (1.41 - 1) \cdot 6^{2}})}^{\frac{1.41}{1.41 - 1}}

Next Step Evaluate

∴

P e,r = 0.340265841483963

LAST Step Rounding Answer

∴

P e,r = 0.3403

Pressure Ratio across Expansion Fan Formula Elements

Variables

Pressure Ratio Across Expansion Fan

Pressure Ratio Across Expansion Fan is the ratio of downstream and upstream pressure across expansion fan.

Symbol: P_e,r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Pressure 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 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 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 Pressure Ratio across Expansion Fan?

Pressure Ratio across Expansion Fan evaluator uses Pressure 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))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)) to evaluate the Pressure Ratio Across Expansion Fan, The Pressure Ratio across Expansion Fan is a measure of the change in pressure experienced by a fluid as it passes through the fan. Expansion fans are regions in a fluid flow where the flow velocity decreases, and pressure increases due to an expansion in the flow area. Pressure Ratio Across Expansion Fan is denoted by P_e,r symbol.

How to evaluate Pressure Ratio across Expansion Fan using this online evaluator? To use this online evaluator for Pressure 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 Pressure Ratio across Expansion Fan

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

The formula of Pressure Ratio across Expansion Fan is expressed as Pressure 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))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)). Here is an example- 0.335105 = ((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2))^((1.41)/(1.41-1)).

How to calculate Pressure 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 Pressure Ratio across Expansion Fan using the formula - Pressure 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))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)).

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Pressure Ratio across Expansion Fan Formula

Pressure Ratio across Expansion Fan Example

Pressure Ratio across Expansion Fan Solution

Pressure Ratio across Expansion Fan Formula Elements

Other formulas in Expansion Waves category

How to Evaluate Pressure Ratio across Expansion Fan?

FAQs on Pressure Ratio across Expansion Fan

Variable Name