Compressible Area Ratio Calculator

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Rocket Propulsion

Components of Gas Turbine

Jet Propulsion

Thermodynamics and Governing Equations

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✖The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ Specific Heat Ratio [Y]			+10% -10%
✖Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%

✖Area Ratio is defined as the Area ratio of the exit area to that of the throat area.ⓘ Compressible Area Ratio [A_r]

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Formula

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Compressible Area Ratio

Formula

`"A"_{"r"} = (("Y"+1)/2)^(-("Y"+1)/(2*"Y"-2))*((1+("Y"-1)/2*"M"^2)^(("Y"+1)/(2*"Y"-2)))/"M"`

Example

`"1.115458"=(("1.392758"+1)/2)^(-("1.392758"+1)/(2*"1.392758"-2))*((1+("1.392758"-1)/2*("1.4")^2)^(("1.392758"+1)/(2*"1.392758"-2)))/"1.4"`

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Compressible Area Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
A_r = ((Y+1)/2)^(-(Y+1)/(2*Y-2))*((1+(Y-1)/2*M^2)^((Y+1)/(2*Y-2)))/M
This formula uses 3 Variables

Variables Used

Area Ratio - Area Ratio is defined as the Area ratio of the exit area to that of the throat area.
Specific Heat Ratio - The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.392758 --> No Conversion Required
Mach Number: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_r = ((Y+1)/2)^(-(Y+1)/(2*Y-2))*((1+(Y-1)/2*M^2)^((Y+1)/(2*Y-2)))/M --> ((1.392758+1)/2)^(-(1.392758+1)/(2*1.392758-2))*((1+(1.392758-1)/2*1.4^2)^((1.392758+1)/(2*1.392758-2)))/1.4

Evaluating ... ...

A_r = 1.11545751111788

STEP 3: Convert Result to Output's Unit

1.11545751111788 --> No Conversion Required

FINAL ANSWER

1.11545751111788 ≈ 1.115458 <-- Area Ratio

(Calculation completed in 00.004 seconds)

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Created by Shreyash

Rajiv Gandhi Institute of Technology (RGIT), Mumbai

Shreyash has created this Calculator and 10+ more calculators!

Verified by Akshat Nama

Indian Institute of Information Technology, Design And Manufacturing (IIITDM ), Jabalpur

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< 14 Rocket Propulsion Calculators

Mass Flow Rate through Engine

Go Mass Flow Rate = Mach Number*Area*Total Pressure*sqrt(Specific Heat Ratio*Molar Mass/(Total Temperature*[R]))*(1+(Specific Heat Ratio-1)*Mach Number^2/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))

Exit Velocity given Molar Mass

Go Exit Velocity = sqrt(((2*Chamber Temperature*[R]*Specific Heat Ratio)/(Molar Mass)/(Specific Heat Ratio-1))*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))

Compressible Area Ratio

Go 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

Exit Velocity given Molar Specific Heat Capacity

Go Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))

Rocket Exit Pressure

Go Exit Pressure = Chamber Pressure*((1+(Specific Heat Ratio-1)/2*Mach Number^2)^-(Specific Heat Ratio/(Specific Heat Ratio-1)))

Exit Velocity given Mach Number and Exit Temperature

Go Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature)

Rocket Exit Temperature

Go Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1

Total Impulse

Go Total impulse = int(Thrust,x,Initial time,Final time)

Power required to produce Exhaust Jet Velocity given Mass of Rocket and Acceleration

Go Power Required = (Mass of Rocket*Acceleration*Effective Exhaust Velocity)/2

Power required to produce Exhaust Jet Velocity

Go Power Required = 1/2*Mass Flow Rate*Exit Velocity^2

Thrust given Exhaust Velocity and Mass Flow Rate

Go Thrust = Mass Flow Rate*Exit Velocity

Thrust given Mass and Acceleration of Rocket

Go Thrust = Mass of Rocket*Acceleration

Acceleration of Rocket

Go Acceleration = Thrust/Mass of Rocket

Photon Propulsion Thrust

Go Thrust = 1000*Power in Jet/[c]

Compressible Area Ratio Formula

What does Compressible Area Ratio of a rocket nozzle signify?

The area ratio of the exit area to that of the throat area is called as the Compressible Area Ratio.

Throat of the nozzle

The optimum mass flow rate through the system happens when the flow is constricted at the smallest area. For example, a nozzle that can change its area is useful to maximize the mass flow rate. Such type of region where maximum mass flow rate occurs is called as the throat of the nozzle.

How to Calculate Compressible Area Ratio?

Compressible Area Ratio calculator 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 calculate 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 calculate Compressible Area Ratio using this online calculator? To use this online calculator for Compressible Area Ratio, enter Specific Heat Ratio (Y) & Mach Number (M) and hit the calculate button. Here is how the Compressible Area Ratio calculation can be explained with given input values -> 1.115458 = ((1.392758+1)/2)^(-(1.392758+1)/(2*1.392758-2))*((1+(1.392758-1)/2*1.4^2)^((1.392758+1)/(2*1.392758-2)))/1.4.

FAQ

What is Compressible 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 and is represented as A_r = ((Y+1)/2)^(-(Y+1)/(2*Y-2))*((1+(Y-1)/2*M^2)^((Y+1)/(2*Y-2)))/M or 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. The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume & Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Compressible 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 is calculated using 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 calculate Compressible Area Ratio, you need Specific Heat Ratio (Y) & Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio & Mach Number 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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