Exit Velocity given Mach Number and Exit Temperature Calculator

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Rocket Propulsion

Components of Gas Turbine

Jet Propulsion

Thermodynamics and Governing Equations

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✖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%
✖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 temperature is the degree of measure of heat at exit to the system.ⓘ Exit Temperature [T_exit]			+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 Mach Number and Exit Temperature [C_j]

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Formula

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Exit Velocity given Mach Number and Exit Temperature

Formula

`"C"_{"j"} = "M"*sqrt("Y"*"[R]"/"M"_{"molar"}*"T"_{"exit"})`

Example

`"118.0019m/s"="1.4"*sqrt("1.392758"*"[R]"/"44.01g/mol"*"27K")`

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Exit Velocity given Mach Number and Exit Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature)
C_j = M*sqrt(Y*[R]/M_molar*T_exit)
This formula uses 1 Constants, 1 Functions, 5 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.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
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 Temperature - (Measured in Kelvin) - Exit temperature is the degree of measure of heat at exit to the system.

STEP 1: Convert Input(s) to Base Unit

Mach Number: 1.4 --> 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 Temperature: 27 Kelvin --> 27 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_j = M*sqrt(Y*[R]/M_molar*T_exit) --> 1.4*sqrt(1.392758*[R]/0.04401*27)

Evaluating ... ...

C_j = 118.001942588727

STEP 3: Convert Result to Output's Unit

118.001942588727 Meter per Second --> No Conversion Required

FINAL ANSWER

118.001942588727 ≈ 118.0019 Meter per Second <-- Exit Velocity

(Calculation completed in 00.004 seconds)

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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 Mach Number and Exit Temperature Formula

Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature)
C_j = M*sqrt(Y*[R]/M_molar*T_exit)

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 Mach Number and Exit Temperature?

Exit Velocity given Mach Number and Exit Temperature calculator uses Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature) to calculate the Exit Velocity, Exit Velocity given Mach number and Exit Temperature formula is used to determine the velocity that is produced at the end of the rocket's nozzle or exhaust if we know the Mach number and the exit temperature. Exit Velocity is denoted by C_j symbol.

How to calculate Exit Velocity given Mach Number and Exit Temperature using this online calculator? To use this online calculator for Exit Velocity given Mach Number and Exit Temperature, enter Mach Number (M), Specific Heat Ratio (Y), Molar Mass (M_molar) & Exit Temperature (T_exit) and hit the calculate button. Here is how the Exit Velocity given Mach Number and Exit Temperature calculation can be explained with given input values -> 674.2968 = 1.4*sqrt(1.392758*[R]/0.04401*27).

FAQ

What is Exit Velocity given Mach Number and Exit Temperature?

Exit Velocity given Mach number and Exit Temperature formula is used to determine the velocity that is produced at the end of the rocket's nozzle or exhaust if we know the Mach number and the exit temperature and is represented as C_j = M*sqrt(Y*[R]/M_molar*T_exit) or Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature). Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound, 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 temperature is the degree of measure of heat at exit to the system.

How to calculate Exit Velocity given Mach Number and Exit Temperature?

Exit Velocity given Mach number and Exit Temperature formula is used to determine the velocity that is produced at the end of the rocket's nozzle or exhaust if we know the Mach number and the exit temperature is calculated using Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature). To calculate Exit Velocity given Mach Number and Exit Temperature, you need Mach Number (M), Specific Heat Ratio (Y), Molar Mass (M_molar) & Exit Temperature (T_exit). With our tool, you need to enter the respective value for Mach Number, Specific Heat Ratio, Molar Mass & Exit Temperature 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 Mach Number, Specific Heat Ratio, Molar Mass & Exit Temperature. We can use 2 other way(s) to calculate the same, which is/are as follows -

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