Rocket Exit Temperature Calculator

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Rocket Propulsion

Components of Gas Turbine

Jet Propulsion

Thermodynamics and Governing Equations

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✖Chamber Temperature refers to the temperature of the combustion chamber in a propulsion system, such as a rocket or jet engine.ⓘ Chamber Temperature [T_c]			+10% -10%
✖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%

✖Exit temperature is the degree of measure of heat at exit to the system.ⓘ Rocket Exit Temperature [T_exit]

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Formula

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Rocket Exit Temperature

Formula

`"T"_{"exit"} = "T"_{"c"}*(1+("Y"-1)/2*"M"^2)^-1`

Example

`"10.10901K"="14K"*(1+("1.392758"-1)/2*("1.4")^2)^-1`

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Rocket Exit Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1
T_exit = T_c*(1+(Y-1)/2*M^2)^-1
This formula uses 4 Variables

Variables Used

Exit Temperature - (Measured in Kelvin) - Exit temperature is the degree of measure of heat at exit to the system.
Chamber Temperature - (Measured in Kelvin) - Chamber Temperature refers to the temperature of the combustion chamber in a propulsion system, such as a rocket or jet engine.
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

Chamber Temperature: 14 Kelvin --> 14 Kelvin No Conversion Required
Specific Heat Ratio: 1.392758 --> No Conversion Required
Mach Number: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_exit = T_c*(1+(Y-1)/2*M^2)^-1 --> 14*(1+(1.392758-1)/2*1.4^2)^-1

Evaluating ... ...

T_exit = 10.1090124127408

STEP 3: Convert Result to Output's Unit

10.1090124127408 Kelvin --> No Conversion Required

FINAL ANSWER

10.1090124127408 ≈ 10.10901 Kelvin <-- Exit Temperature

(Calculation completed in 00.004 seconds)

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Created by Shreyash

Rajiv Gandhi Institute of Technology (RGIT), Mumbai

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National Institute Of Technology (NIT), Hamirpur

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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]

Rocket Exit Temperature Formula

Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1
T_exit = T_c*(1+(Y-1)/2*M^2)^-1

What is exit temperature?

Exit temperature in simple terms is the temperature at the exit of the rocket's nozzle. When exhaust gases flow from the combustion chamber to the nozzle, they experience a temperature change relative to the total temperature of the combustion chamber and its Mach number.

How to Calculate Rocket Exit Temperature?

Rocket Exit Temperature calculator uses Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1 to calculate the Exit Temperature, The Rocket Exit Temperature formula defines the exit temperature at an exhaust, given that we know the total temperature and Mach number. Exit Temperature is denoted by T_exit symbol.

How to calculate Rocket Exit Temperature using this online calculator? To use this online calculator for Rocket Exit Temperature, enter Chamber Temperature (T_c), Specific Heat Ratio (Y) & Mach Number (M) and hit the calculate button. Here is how the Rocket Exit Temperature calculation can be explained with given input values -> 10.10901 = 14*(1+(1.392758-1)/2*1.4^2)^-1.

FAQ

What is Rocket Exit Temperature?

The Rocket Exit Temperature formula defines the exit temperature at an exhaust, given that we know the total temperature and Mach number and is represented as T_exit = T_c*(1+(Y-1)/2*M^2)^-1 or Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1. Chamber Temperature refers to the temperature of the combustion chamber in a propulsion system, such as a rocket or jet engine, 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 Rocket Exit Temperature?

The Rocket Exit Temperature formula defines the exit temperature at an exhaust, given that we know the total temperature and Mach number is calculated using Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1. To calculate Rocket Exit Temperature, you need Chamber Temperature (T_c), Specific Heat Ratio (Y) & Mach Number (M). With our tool, you need to enter the respective value for Chamber Temperature, 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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