Exit Velocity given Molar Specific Heat Capacity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))
Cj = sqrt(2*Tt*Cp molar*(1-(Pexit/Pc)^(1-1/Y)))
This formula uses 1 Functions, 6 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
Exit Velocity - (Measured in Meter per Second) - Exit Velocity is the speed at which exhaust gases exit the primary nozzle of a propulsion system, such as a rocket or jet engine.
Total Temperature - (Measured in Kelvin) - Total Temperature is the sum of the static temperature and the dynamic temperature.
Molar Specific Heat Capacity at Constant Pressure - (Measured in Joule Per Kelvin Per Mole) - Molar Specific Heat Capacity at Constant Pressure, (of a gas) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.
Exit Pressure - (Measured in Pascal) - Exit Pressure is the pressure of the gases leaving the rocket nozzle.
Chamber Pressure - (Measured in Pascal) - The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket.
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.
STEP 1: Convert Input(s) to Base Unit
Total Temperature: 375 Kelvin --> 375 Kelvin No Conversion Required
Molar Specific Heat Capacity at Constant Pressure: 122 Joule Per Kelvin Per Mole --> 122 Joule Per Kelvin Per Mole No Conversion Required
Exit Pressure: 2.1 Megapascal --> 2100000 Pascal (Check conversion here)
Chamber Pressure: 20 Megapascal --> 20000000 Pascal (Check conversion here)
Specific Heat Ratio: 1.392758 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cj = sqrt(2*Tt*Cp molar*(1-(Pexit/Pc)^(1-1/Y))) --> sqrt(2*375*122*(1-(2100000/20000000)^(1-1/1.392758)))
Evaluating ... ...
Cj = 207.457371762512
STEP 3: Convert Result to Output's Unit
207.457371762512 Meter per Second --> No Conversion Required
FINAL ANSWER
207.457371762512 207.4574 Meter per Second <-- Exit Velocity
(Calculation completed in 00.004 seconds)

Credits

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Rajiv Gandhi Institute of Technology (RGIT), Mumbai
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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]

Exit Velocity given Molar Specific Heat Capacity Formula

Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))
Cj = sqrt(2*Tt*Cp molar*(1-(Pexit/Pc)^(1-1/Y)))

Exit Velocity

The velocity produced at the outlet of the rocket engine through the nozzle is called as the exit velocity. This parameter is useful to examine the rocket's performance.

How to Calculate Exit Velocity given Molar Specific Heat Capacity?

Exit Velocity given Molar Specific Heat Capacity calculator uses Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))) to calculate the Exit Velocity, The Exit Velocity given Molar Specific Heat Capacity formula can be used to determine the exit velocity through the nozzle when the value of specific heat capacity at constant pressure is known. Exit Velocity is denoted by Cj symbol.

How to calculate Exit Velocity given Molar Specific Heat Capacity using this online calculator? To use this online calculator for Exit Velocity given Molar Specific Heat Capacity, enter Total Temperature (Tt), Molar Specific Heat Capacity at Constant Pressure (Cp molar), Exit Pressure (Pexit), Chamber Pressure (Pc) & Specific Heat Ratio (Y) and hit the calculate button. Here is how the Exit Velocity given Molar Specific Heat Capacity calculation can be explained with given input values -> 207.4574 = sqrt(2*375*122*(1-(2100000/20000000)^(1-1/1.392758))).

FAQ

What is Exit Velocity given Molar Specific Heat Capacity?
The Exit Velocity given Molar Specific Heat Capacity formula can be used to determine the exit velocity through the nozzle when the value of specific heat capacity at constant pressure is known and is represented as Cj = sqrt(2*Tt*Cp molar*(1-(Pexit/Pc)^(1-1/Y))) or Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))). Total Temperature is the sum of the static temperature and the dynamic temperature, Molar Specific Heat Capacity at Constant Pressure, (of a gas) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure, Exit Pressure is the pressure of the gases leaving the rocket nozzle, The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket & 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.
How to calculate Exit Velocity given Molar Specific Heat Capacity?
The Exit Velocity given Molar Specific Heat Capacity formula can be used to determine the exit velocity through the nozzle when the value of specific heat capacity at constant pressure is known is calculated using Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))). To calculate Exit Velocity given Molar Specific Heat Capacity, you need Total Temperature (Tt), Molar Specific Heat Capacity at Constant Pressure (Cp molar), Exit Pressure (Pexit), Chamber Pressure (Pc) & Specific Heat Ratio (Y). With our tool, you need to enter the respective value for Total Temperature, Molar Specific Heat Capacity at Constant Pressure, Exit Pressure, Chamber Pressure & Specific Heat Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Exit Velocity?
In this formula, Exit Velocity uses Total Temperature, Molar Specific Heat Capacity at Constant Pressure, Exit Pressure, Chamber Pressure & Specific Heat Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature)
  • 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)))
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