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Area Ratio of Nozzles Formula

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The Area Ratio of Nozzle refers to the ratio of the cross-sectional area of the exit (throat) of the nozzle to the cross-sectional area of the exit (exit plane) of the nozzle. Check FAQs

∈ = (\frac{1}{M 2}) \cdot \sqrt{{(\frac{1 + \frac{γ - 1}{2} \cdot {M 2}^{2}}{1 + \frac{γ - 1}{2}})}^{\frac{γ + 1}{γ - 1}}}

∈ - Area Ratio of Nozzle?M₂ - Mach at Exit?γ - Specific Heat Ratio?

Area Ratio of Nozzles Example

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

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

Here is how the Area Ratio of Nozzles equation looks like.

2.8471 = (\frac{1}{2.5}) \cdot \sqrt{{(\frac{1 + \frac{1.33 - 1}{2} \cdot {2.5}^{2}}{1 + \frac{1.33 - 1}{2}})}^{\frac{1.33 + 1}{1.33 - 1}}}

2.8471 = (\frac{1}{2.5}) \cdot \sqrt{{(\frac{1 + \frac{1.33 - 1}{2} \cdot {2.5}^{2}}{1 + \frac{1.33 - 1}{2}})}^{\frac{1.33 + 1}{1.33 - 1}}}

2.8471 = (\frac{1}{2.5}) \cdot \sqrt{{(\frac{1 + \frac{1.33 - 1}{2} \cdot {2.5}^{2}}{1 + \frac{1.33 - 1}{2}})}^{\frac{1.33 + 1}{1.33 - 1}}}

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Area Ratio of Nozzles Solution

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

FIRST Step Consider the formula

∈ = (\frac{1}{M 2}) \cdot \sqrt{{(\frac{1 + \frac{γ - 1}{2} \cdot {M 2}^{2}}{1 + \frac{γ - 1}{2}})}^{\frac{γ + 1}{γ - 1}}}

Next Step Substitute values of Variables

∴

∈ = (\frac{1}{2.5}) \cdot \sqrt{{(\frac{1 + \frac{1.33 - 1}{2} \cdot {2.5}^{2}}{1 + \frac{1.33 - 1}{2}})}^{\frac{1.33 + 1}{1.33 - 1}}}

Next Step Prepare to Evaluate

∴

∈ = (\frac{1}{2.5}) \cdot \sqrt{{(\frac{1 + \frac{1.33 - 1}{2} \cdot {2.5}^{2}}{1 + \frac{1.33 - 1}{2}})}^{\frac{1.33 + 1}{1.33 - 1}}}

Next Step Evaluate

∴

∈ = 2.84713043039901

LAST Step Rounding Answer

∴

∈ = 2.8471

Area Ratio of Nozzles Formula Elements

Variables

Functions

Area Ratio of Nozzle

The Area Ratio of Nozzle refers to the ratio of the cross-sectional area of the exit (throat) of the nozzle to the cross-sectional area of the exit (exit plane) of the nozzle.

Symbol: ∈

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Area Ratio of Nozzle

Mach at Exit

The Mach at Exit in rocketry refers to the Mach number of the exhaust gases as they exit the rocket engine nozzle.

Symbol: M₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach at Exit

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Nozzles category

Go Propulsion Efficiency

η prop = \frac{2 \cdot (\frac{v 0}{v 9})}{1 + {(\frac{v 0}{v 9})}^{2}}

Go Specific Volume at Throat

V t = V 1 \cdot {(\frac{γ + 1}{2})}^{\frac{1}{γ - 1}}

Go Specific Temperature at Throat

T t = \frac{2 \cdot T 1}{γ + 1}

Go Characteristics Velocity

C ✸ = \sqrt{(\frac{[R] \cdot T 1}{γ}) \cdot {(\frac{γ + 1}{2})}^{\frac{γ + 1}{γ - 1}}}

How to Evaluate Area Ratio of Nozzles?

Area Ratio of Nozzles evaluator uses Area Ratio of Nozzle = (1/Mach at Exit)*sqrt(((1+(Specific Heat Ratio-1)/2*Mach at Exit^2)/(1+(Specific Heat Ratio-1)/2))^((Specific Heat Ratio+1)/(Specific Heat Ratio-1))) to evaluate the Area Ratio of Nozzle, Area Ratio of Nozzles formula is defined as a relationship that describes the ratio of the cross-sectional areas of a nozzle, which is crucial for optimizing the performance and efficiency of rocket propulsion systems. Area Ratio of Nozzle is denoted by ∈ symbol.

How to evaluate Area Ratio of Nozzles using this online evaluator? To use this online evaluator for Area Ratio of Nozzles, enter Mach at Exit (M₂) & Specific Heat Ratio (γ) and hit the calculate button.

FAQs on Area Ratio of Nozzles

What is the formula to find Area Ratio of Nozzles?

The formula of Area Ratio of Nozzles is expressed as Area Ratio of Nozzle = (1/Mach at Exit)*sqrt(((1+(Specific Heat Ratio-1)/2*Mach at Exit^2)/(1+(Specific Heat Ratio-1)/2))^((Specific Heat Ratio+1)/(Specific Heat Ratio-1))). Here is an example- 2.84713 = (1/2.5)*sqrt(((1+(1.33-1)/2*2.5^2)/(1+(1.33-1)/2))^((1.33+1)/(1.33-1))).

How to calculate Area Ratio of Nozzles?

With Mach at Exit (M₂) & Specific Heat Ratio (γ) we can find Area Ratio of Nozzles using the formula - Area Ratio of Nozzle = (1/Mach at Exit)*sqrt(((1+(Specific Heat Ratio-1)/2*Mach at Exit^2)/(1+(Specific Heat Ratio-1)/2))^((Specific Heat Ratio+1)/(Specific Heat Ratio-1))). This formula also uses Square Root (sqrt) function(s).

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Area Ratio of Nozzles Formula

Area Ratio of Nozzles Example

Area Ratio of Nozzles Solution

Area Ratio of Nozzles Formula Elements

Other formulas in Nozzles category

How to Evaluate Area Ratio of Nozzles?

FAQs on Area Ratio of Nozzles

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