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Pressure behind Expansion Fan Formula

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Pressure Behind Expansion Fan is the pressure in the downstream direction of the expansion fan. Check FAQs

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}}

P₂ - Pressure Behind Expansion Fan?P₁ - Pressure 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?

Pressure behind Expansion Fan Example

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

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

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

13.6106 = 40 \cdot {(\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}}

13.6106Pa = 40Pa \cdot {(\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}}

13.6106 = 40 \cdot {(\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 behind Expansion Fan Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

P 2 = 40Pa \cdot {(\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 2 = 40 \cdot {(\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 2 = 13.6106336593585Pa

LAST Step Rounding Answer

∴

P 2 = 13.6106Pa

Pressure behind Expansion Fan Formula Elements

Variables

Pressure Behind Expansion Fan

Pressure Behind Expansion Fan is the pressure in the downstream direction of the expansion fan.

Symbol: P₂

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Pressure Behind Expansion Fan

Pressure Ahead of Expansion Fan

Pressure Ahead of Expansion Fan is the pressure in the upstream direction of the expansion fan.

Symbol: P₁

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Pressure 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 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 behind Expansion Fan?

Pressure behind Expansion Fan evaluator uses Pressure Behind Expansion Fan = Pressure 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))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)) to evaluate the Pressure Behind Expansion Fan, The Pressure behind Expansion Fan formula is defined as the product of upstream static pressure ahead of expansion fan to the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan. Pressure Behind Expansion Fan is denoted by P₂ symbol.

How to evaluate Pressure behind Expansion Fan using this online evaluator? To use this online evaluator for Pressure behind Expansion Fan, enter Pressure Ahead of Expansion Fan (P₁), 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 behind Expansion Fan

What is the formula to find Pressure behind Expansion Fan?

The formula of Pressure behind Expansion Fan is expressed as Pressure Behind Expansion Fan = Pressure 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))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)). Here is an example- 13.4042 = 40*((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 behind Expansion Fan?

With Pressure Ahead of Expansion Fan (P₁), 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 behind Expansion Fan using the formula - Pressure Behind Expansion Fan = Pressure 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))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)).

Can the Pressure behind Expansion Fan be negative?

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

Which unit is used to measure Pressure behind Expansion Fan?

Pressure behind Expansion Fan is usually measured using the Pascal[Pa] for Pressure. Kilopascal[Pa], Bar[Pa], Pound Per Square Inch[Pa] are the few other units in which Pressure behind Expansion Fan can be measured.

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Pressure behind Expansion Fan Formula

Pressure behind Expansion Fan Example

Pressure behind Expansion Fan Solution

Pressure behind Expansion Fan Formula Elements

Other formulas in Expansion Waves category

How to Evaluate Pressure behind Expansion Fan?

FAQs on Pressure behind Expansion Fan

Variable Name