Exit Velocity given Molar Mass 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%
✖Molar Mass is the mass of a given substance divided by the amount of substance.ⓘ Molar Mass [M_molar]			+10% -10%
✖Exit Pressure is the pressure of the gases leaving the rocket nozzle.ⓘ Exit Pressure [P_exit]			+10% -10%
✖The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket.ⓘ Chamber Pressure [P_c]			+10% -10%

✖Exit Velocity is the speed at which exhaust gases exit the primary nozzle of a propulsion system, such as a rocket or jet engine.ⓘ Exit Velocity given Molar Mass [C_j]

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Formula

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Exit Velocity given Molar Mass

Formula

`"C"_{"j"} = sqrt(((2*"T"_{"c"}*"[R]"*"Y")/("M"_{"molar"})/("Y"-1))*(1-("P"_{"exit"}/"P"_{"c"})^(1-1/"Y")))`

Example

`"93.93211m/s"=sqrt(((2*"14K"*"[R]"*"1.392758")/("44.01g/mol")/("1.392758"-1))*(1-("2.1MPa"/"20MPa")^(1-1/"1.392758")))`

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Exit Velocity given Molar Mass Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
C_j = sqrt(((2*T_c*[R]*Y)/(M_molar)/(Y-1))*(1-(P_exit/P_c)^(1-1/Y)))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

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.
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.
Molar Mass - (Measured in Kilogram Per Mole) - Molar Mass is the mass of a given substance divided by the amount of substance.
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.

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
Molar Mass: 44.01 Gram Per Mole --> 0.04401 Kilogram Per Mole (Check conversion here)
Exit Pressure: 2.1 Megapascal --> 2100000 Pascal (Check conversion here)
Chamber Pressure: 20 Megapascal --> 20000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_j = sqrt(((2*T_c*[R]*Y)/(M_molar)/(Y-1))*(1-(P_exit/P_c)^(1-1/Y))) --> sqrt(((2*14*[R]*1.392758)/(0.04401)/(1.392758-1))*(1-(2100000/20000000)^(1-1/1.392758)))

Evaluating ... ...

C_j = 93.932105979307

STEP 3: Convert Result to Output's Unit

93.932105979307 Meter per Second --> No Conversion Required

FINAL ANSWER

93.932105979307 ≈ 93.93211 Meter per Second <-- Exit Velocity

(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]

Exit Velocity given Molar Mass Formula

What is Exit Velocity?

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

How to Calculate Exit Velocity given Molar Mass?

Exit Velocity given Molar Mass calculator uses 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))) to calculate the Exit Velocity, The Exit Velocity given Molar Mass formula can be used to determine the exit velocity through the nozzle when the value of Molar Mass is known. Exit Velocity is denoted by C_j symbol.

How to calculate Exit Velocity given Molar Mass using this online calculator? To use this online calculator for Exit Velocity given Molar Mass, enter Chamber Temperature (T_c), Specific Heat Ratio (Y), Molar Mass (M_molar), Exit Pressure (P_exit) & Chamber Pressure (P_c) and hit the calculate button. Here is how the Exit Velocity given Molar Mass calculation can be explained with given input values -> 93.93211 = sqrt(((2*14*[R]*1.392758)/(0.04401)/(1.392758-1))*(1-(2100000/20000000)^(1-1/1.392758))).

FAQ

What is Exit Velocity given Molar Mass?

The Exit Velocity given Molar Mass formula can be used to determine the exit velocity through the nozzle when the value of Molar Mass is known and is represented as C_j = sqrt(((2*T_c*[R]*Y)/(M_molar)/(Y-1))*(1-(P_exit/P_c)^(1-1/Y))) or 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))). 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, Molar Mass is the mass of a given substance divided by the amount of substance, 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.

How to calculate Exit Velocity given Molar Mass?

The Exit Velocity given Molar Mass formula can be used to determine the exit velocity through the nozzle when the value of Molar Mass is known is calculated using 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))). To calculate Exit Velocity given Molar Mass, you need Chamber Temperature (T_c), Specific Heat Ratio (Y), Molar Mass (M_molar), Exit Pressure (P_exit) & Chamber Pressure (P_c). With our tool, you need to enter the respective value for Chamber Temperature, Specific Heat Ratio, Molar Mass, Exit Pressure & Chamber Pressure 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 Chamber Temperature, Specific Heat Ratio, Molar Mass, Exit Pressure & Chamber Pressure. 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*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))

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