## 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
2.84713043039901 2.84713 <-- Area Ratio of Nozzle
(Calculation completed in 00.004 seconds)
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## Credits

Created by LOKESH
Sri Ramakrishna Engineering College (SREC), COIMBATORE
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Verified by Harsh Raj
Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal
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## < 3 Nozzle Shape Calculators

Area Ratio of Nozzles
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
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
Thrust Coefficient = Rocket Thrust/(Nozzle Throat Area*Inlet Nozzle Pressure)

## Area Ratio of Nozzles 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)))
= (1/M2)*sqrt(((1+(γ-1)/2*M2^2)/(1+(γ-1)/2))^((γ+1)/(γ-1)))

## 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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