## Compressible Area Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area Ratio = (((Specific Heat Ratio Dynamic+1)/2)^(-(Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))*((((1+(Specific Heat Ratio Dynamic-1)*Mach Number^2/2)^((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))/Mach Number))
Ar = (((κ+1)/2)^(-(κ+1)/(2*κ-2)))*((((1+(κ-1)*M^2/2)^((κ+1)/(2*κ-2)))/M))
This formula uses 3 Variables
Variables Used
Area Ratio - Area Ratio is the ratio of the waterline length times the beam to the total projected propeller area.
Specific Heat Ratio Dynamic - The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at 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 Dynamic: 1.392758 --> No Conversion Required
Mach Number: 8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ar = (((κ+1)/2)^(-(κ+1)/(2*κ-2)))*((((1+(κ-1)*M^2/2)^((κ+1)/(2*κ-2)))/M)) --> (((1.392758+1)/2)^(-(1.392758+1)/(2*1.392758-2)))*((((1+(1.392758-1)*8^2/2)^((1.392758+1)/(2*1.392758-2)))/8))
Evaluating ... ...
Ar = 203.935246391495
STEP 3: Convert Result to Output's Unit
203.935246391495 --> No Conversion Required
FINAL ANSWER
203.935246391495 <-- Area Ratio
(Calculation completed in 00.000 seconds)
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## Credits

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
Akshat Nama has verified this Calculator and 10 more calculators!

## < 15 Rocket Propulsion Calculators

Mass Flow Rate through Engine
Mass Flowrate = Area*Total Pressure*((Specific Heat Ratio Dynamic/(Total Temperature*Universal Gas Constant))^0.5)*Mach Number*(1+(Specific Heat Ratio Dynamic-1)* Mach Number^2/2)^(-((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))
Compressible Area Ratio
Area Ratio = (((Specific Heat Ratio Dynamic+1)/2)^(-(Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))*((((1+(Specific Heat Ratio Dynamic-1)*Mach Number^2/2)^((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))/Mach Number))
Exit Velocity given Molar Mass
Exit velocity = sqrt(((2*Inlet Temperature*Universal Gas Constant*Specific Heat Ratio Dynamic)/(Molar Mass)/(Specific Heat Ratio Dynamic-1))*((1-(Exit pressure/Inlet Pressure)^(1-(1/Specific Heat Ratio Dynamic)))))
Exit Velocity given Specific Heat Capacity
Exit velocity = sqrt((2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure)*(1-(Exit pressure/Inlet Pressure)^(1-(1/Specific Heat Ratio Dynamic))))
Exit Pressure
Exit pressure = Inlet Pressure*(((1+(Specific Heat Ratio Dynamic-1)/2*Mach Number^2))^-((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1)))
Tsiolkovsky Rocket Equation
Change in Rocket Velocity = Specific Impulse*[g]*ln(Wet mass/Dry mass)
Exit Velocity given Mach number and Exit Temperature
Exit velocity = Mach Number*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5
Exit Temperature
Exit Temperature = (Total Temperature)*(1+((Specific Heat Ratio Dynamic-1)/2)*(Mach Number^2))^-1
Power required to produce Exhaust Jet Velocity given Mass of Rocket and Acceleration
Power required = (Mass of Rocket*Acceleration*Rocket Exhaust Velocity)/2
Rocket Mass Ratio
Rocket Mass ratio = e^(Change in Rocket Velocity/Rocket Exhaust Velocity)
Power required to produce Exhaust Jet Velocity
Power required = 1/2*Air Flow Rate*Jet velocity of aircraft^2
Thrust given exhaust velocity and mass flow rate
Thrust = Air Flow Rate*Jet velocity of aircraft
Photon propulsion thrust
Thrust = 1000*Power in jet/Velocity of light
Thrust given mass and acceleration of rocket
Thrust = Mass*Acceleration
Acceleration of rocket
Acceleration = Thrust/Mass

## Compressible Area Ratio Formula

Area Ratio = (((Specific Heat Ratio Dynamic+1)/2)^(-(Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))*((((1+(Specific Heat Ratio Dynamic-1)*Mach Number^2/2)^((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))/Mach Number))
Ar = (((κ+1)/2)^(-(κ+1)/(2*κ-2)))*((((1+(κ-1)*M^2/2)^((κ+1)/(2*κ-2)))/M))

## 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 Dynamic+1)/2)^(-(Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))*((((1+(Specific Heat Ratio Dynamic-1)*Mach Number^2/2)^((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-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 Ar symbol.

How to calculate Compressible Area Ratio using this online calculator? To use this online calculator for Compressible Area Ratio, enter Specific Heat Ratio Dynamic (κ) & Mach Number (M) and hit the calculate button. Here is how the Compressible Area Ratio calculation can be explained with given input values -> 203.9352 = (((1.392758+1)/2)^(-(1.392758+1)/(2*1.392758-2)))*((((1+(1.392758-1)*8^2/2)^((1.392758+1)/(2*1.392758-2)))/8)).

### 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 Ar = (((κ+1)/2)^(-(κ+1)/(2*κ-2)))*((((1+(κ-1)*M^2/2)^((κ+1)/(2*κ-2)))/M)) or Area Ratio = (((Specific Heat Ratio Dynamic+1)/2)^(-(Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))*((((1+(Specific Heat Ratio Dynamic-1)*Mach Number^2/2)^((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))/Mach Number)). The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at 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 Dynamic+1)/2)^(-(Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))*((((1+(Specific Heat Ratio Dynamic-1)*Mach Number^2/2)^((Specific Heat Ratio Dynamic+1)/(2*Specific Heat Ratio Dynamic-2)))/Mach Number)). To calculate Compressible Area Ratio, you need Specific Heat Ratio Dynamic (κ) & Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio Dynamic & 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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