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Compressible Area Ratio Formula

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Area Ratio is defined as the Area ratio of the exit area to that of the throat area. Check FAQs

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

A_r - Area Ratio?γ - Specific Heat Ratio?M - Mach Number?

Compressible Area Ratio Example

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Here is how the Compressible Area Ratio equation looks like with Values.

Here is how the Compressible Area Ratio equation looks like with Units.

Here is how the Compressible Area Ratio equation looks like.

1.1203 = {(\frac{1.33 + 1}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}} \cdot \frac{{(1 + \frac{1.33 - 1}{2} \cdot {1.4}^{2})}^{\frac{1.33 + 1}{2 \cdot 1.33 - 2}}}{1.4}

1.1203 = {(\frac{1.33 + 1}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}} \cdot \frac{{(1 + \frac{1.33 - 1}{2} \cdot {1.4}^{2})}^{\frac{1.33 + 1}{2 \cdot 1.33 - 2}}}{1.4}

1.1203 = {(\frac{1.33 + 1}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}} \cdot \frac{{(1 + \frac{1.33 - 1}{2} \cdot {1.4}^{2})}^{\frac{1.33 + 1}{2 \cdot 1.33 - 2}}}{1.4}

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Compressible Area Ratio Solution

Follow our step by step solution on how to calculate Compressible Area Ratio?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A r = {(\frac{1.33 + 1}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}} \cdot \frac{{(1 + \frac{1.33 - 1}{2} \cdot {1.4}^{2})}^{\frac{1.33 + 1}{2 \cdot 1.33 - 2}}}{1.4}

Next Step Prepare to Evaluate

∴

A r = {(\frac{1.33 + 1}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}} \cdot \frac{{(1 + \frac{1.33 - 1}{2} \cdot {1.4}^{2})}^{\frac{1.33 + 1}{2 \cdot 1.33 - 2}}}{1.4}

Next Step Evaluate

∴

A r = 1.12028343696668

LAST Step Rounding Answer

∴

A r = 1.1203

Compressible Area Ratio Formula Elements

Variables

Area Ratio

Area Ratio is defined as the Area ratio of the exit area to that of the throat area.

Symbol: A_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Area Ratio

Specific Heat Ratio

The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Specific Heat Ratio

Mach Number

Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Other formulas in Thrust and Power Generation category

Go Power required to produce Exhaust Jet Velocity

P = \frac{1}{2} \cdot m a \cdot {C j}^{2}

Go Thrust given Exhaust Velocity and Mass Flow Rate

F = m a \cdot C j

Go Thrust given Mass and Acceleration of Rocket

F = m \cdot a

Go Acceleration of Rocket

a = \frac{F}{m}

How to Evaluate Compressible Area Ratio?

Compressible Area Ratio evaluator uses Area Ratio = ((Specific Heat Ratio+1)/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))*((1+(Specific Heat Ratio-1)/2*Mach Number^2)^((Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)))/Mach Number to evaluate the Area Ratio, The Compressible Area Ratio can be defined as the Area ratio of the exit area to that of the throat area. The value to be computed depends on the specific heat ratio and Mach number. Area Ratio is denoted by A_r symbol.

How to evaluate Compressible Area Ratio using this online evaluator? To use this online evaluator for Compressible Area Ratio, enter Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button.

FAQs on Compressible Area Ratio

What is the formula to find Compressible Area Ratio?

The formula of Compressible Area Ratio is expressed as Area Ratio = ((Specific Heat Ratio+1)/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))*((1+(Specific Heat Ratio-1)/2*Mach Number^2)^((Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)))/Mach Number. Here is an example- 1.120283 = ((1.33+1)/2)^(-(1.33+1)/(2*1.33-2))*((1+(1.33-1)/2*1.4^2)^((1.33+1)/(2*1.33-2)))/1.4.

How to calculate Compressible Area Ratio?

With Specific Heat Ratio (γ) & Mach Number (M) we can find Compressible Area Ratio using the formula - Area Ratio = ((Specific Heat Ratio+1)/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))*((1+(Specific Heat Ratio-1)/2*Mach Number^2)^((Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)))/Mach Number.

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Compressible Area Ratio Formula

Compressible Area Ratio Example

Compressible Area Ratio Solution

Compressible Area Ratio Formula Elements

Other formulas in Thrust and Power Generation category

How to Evaluate Compressible Area Ratio?

FAQs on Compressible Area Ratio

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