Area Ratio of Nozzles Calculator

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Rocket Propulsion

Components of Gas Turbine

Jet Propulsion

Thermodynamics and Governing Equations

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✖The Mach at Exit in rocketry refers to the Mach number of the exhaust gases as they exit the rocket engine nozzle.ⓘ Mach at Exit [M₂]			+10% -10%
✖The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%

✖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.ⓘ Area Ratio of Nozzles [∈]

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Formula

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Area Ratio of Nozzles

Formula

`"∈" = (1/"M"_{"2"})*sqrt(((1+("γ"-1)/2*"M"_{"2"}^2)/(1+("γ"-1)/2))^(("γ"+1)/("γ"-1)))`

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)))`

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Area Ratio of Nozzles Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
∈ = (1/M₂)*sqrt(((1+(γ-1)/2*M₂^2)/(1+(γ-1)/2))^((γ+1)/(γ-1)))
This formula uses 1 Functions, 3 Variables

Functions Used

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., sqrt(Number)

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Mach at Exit: 2.5 --> No Conversion Required
Specific Heat Ratio: 1.33 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∈ = (1/M₂)*sqrt(((1+(γ-1)/2*M₂^2)/(1+(γ-1)/2))^((γ+1)/(γ-1))) --> (1/2.5)*sqrt(((1+(1.33-1)/2*2.5^2)/(1+(1.33-1)/2))^((1.33+1)/(1.33-1)))

Evaluating ... ...

∈ = 2.84713043039901

STEP 3: Convert Result to Output's Unit

2.84713043039901 --> No Conversion Required

FINAL ANSWER

2.84713043039901 ≈ 2.84713 <-- Area Ratio of Nozzle

(Calculation completed in 00.004 seconds)

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< 3 Nozzle Shape Calculators

Area Ratio of Nozzles

Go 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)))

Characteristics Velocity

Go Characteristics Velocity = sqrt((([R]*Temperature at Chamber)/Specific Heat Ratio)*((Specific Heat Ratio+1)/2)^((Specific Heat Ratio+1)/(Specific Heat Ratio-1)))

Nozzle Thrust Coefficient

Go Thrust Coefficient = Rocket Thrust/(Nozzle Throat Area*Inlet Nozzle Pressure)

Area Ratio of Nozzles Formula

What is Area Ratio of Nozzles

Area Ratio of Nozzles is the ratio of the cross-sectional area of the nozzle exit to the cross-sectional area of the nozzle throat, it quantifies how much the nozzle diverges from the throat to the exit, a higher area ratio typically leads to higher expansion and exhaust velocities, which can increase thrust efficiency, especially in vacuum or high-altitude conditions.

How to Calculate Area Ratio of Nozzles?

Area Ratio of Nozzles calculator 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 calculate the Area Ratio of Nozzle, Area Ratio of Nozzles refers to the ratio of the cross-sectional area of the nozzle at its exit plane (the nozzle exit) to the cross-sectional area of the nozzle at its throat, it determines the degree of expansion of the exhaust gases as they flow through the nozzle. Area Ratio of Nozzle is denoted by ∈ symbol.

How to calculate Area Ratio of Nozzles using this online calculator? To use this online calculator for Area Ratio of Nozzles, enter Mach at Exit (M₂) & Specific Heat Ratio (γ) and hit the calculate button. Here is how the Area Ratio of Nozzles calculation can be explained with given input values -> 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))).

FAQ

What is Area Ratio of Nozzles?

Area Ratio of Nozzles refers to the ratio of the cross-sectional area of the nozzle at its exit plane (the nozzle exit) to the cross-sectional area of the nozzle at its throat, it determines the degree of expansion of the exhaust gases as they flow through the nozzle and is represented as ∈ = (1/M₂)*sqrt(((1+(γ-1)/2*M₂^2)/(1+(γ-1)/2))^((γ+1)/(γ-1))) or 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))). The Mach at Exit in rocketry refers to the Mach number of the exhaust gases as they exit the rocket engine nozzle & The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.

How to calculate Area Ratio of Nozzles?

Area Ratio of Nozzles refers to the ratio of the cross-sectional area of the nozzle at its exit plane (the nozzle exit) to the cross-sectional area of the nozzle at its throat, it determines the degree of expansion of the exhaust gases as they flow through the nozzle is calculated using 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 calculate Area Ratio of Nozzles, you need Mach at Exit (M₂) & Specific Heat Ratio (γ). With our tool, you need to enter the respective value for Mach at Exit & Specific Heat Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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