Area Ratio of Nozzles Calculator

✖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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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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Created by LOKESH

Sri Ramakrishna Engineering College (SREC), COIMBATORE

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Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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< Nozzles Calculators

Characteristics Velocity

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

Propulsion Efficiency

LaTeX Go Propulsion Efficiency = (2*(Vehicle Speed/Exhaust Speed))/(1+(Vehicle Speed/Exhaust Speed)^2)

Specific Volume at Throat

LaTeX Go Specific Volume = Inlet Volume*((Specific Heat Ratio+1)/2)^(1/(Specific Heat Ratio-1))

Specific Temperature at Throat

LaTeX Go Specific Temperature = (2*Temperature at Chamber)/(Specific Heat Ratio+1)

Area Ratio of Nozzles Formula

LaTeX Go

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 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 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 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 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 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 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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