Exit Velocity given Mach number and Exit Temperature Calculator

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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 [k]			+10% -10%
✖Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joulekelvin−1mole−1.ⓘ Universal Gas Constant [R]			+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 velocity of the flow at state 2 or exit.ⓘ Exit Velocity given Mach number and Exit Temperature [c₂]

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Formula

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Exit Velocity given Mach number and Exit Temperature

Formula

`"c"_{"2"} = "M"*("k"*"R"*"T"_{"exit"})^0.5`

Example

`"151.6131m/s"="8"*("1.6"*"8.314"*"27K")^0.5`

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Exit Velocity given Mach number and Exit Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Exit velocity = Mach Number*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5
c₂ = M*(k*R*T_exit)^0.5
This formula uses 5 Variables

Variables Used

Exit velocity - (Measured in Meter per Second) - Exit velocity is the velocity of the flow at state 2 or exit.
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.
Universal Gas Constant - Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1.
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: 8 --> No Conversion Required
Specific Heat Ratio: 1.6 --> No Conversion Required
Universal Gas Constant: 8.314 --> No Conversion Required
Exit Temperature: 27 Kelvin --> 27 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c₂ = M*(k*R*T_exit)^0.5 --> 8*(1.6*8.314*27)^0.5

Evaluating ... ...

c₂ = 151.613149825469

STEP 3: Convert Result to Output's Unit

151.613149825469 Meter per Second --> No Conversion Required

FINAL ANSWER

151.613149825469 Meter per Second <-- Exit velocity

(Calculation completed in 00.016 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!

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Go 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

Go 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

Go 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

Go Exit velocity = sqrt((2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure)*(1-(Exit pressure/Inlet Pressure)^(1-(1/Specific Heat Ratio Dynamic))))

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Go 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

Go Change in Rocket Velocity = Specific Impulse*[g]*ln(Wet mass/Dry mass)

Exit Velocity given Mach number and Exit Temperature

Go Exit velocity = Mach Number*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5

Exit Temperature

Go 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

Go Power required = (Mass of Rocket*Acceleration*Rocket Exhaust Velocity)/2

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Go Rocket Mass ratio = e^(Change in Rocket Velocity/Rocket Exhaust Velocity)

Power required to produce Exhaust Jet Velocity

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Thrust given mass and acceleration of rocket

Go Thrust = Mass*Acceleration

Acceleration of rocket

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Exit Velocity given Mach number and Exit Temperature Formula

Exit velocity = Mach Number*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5
c₂ = M*(k*R*T_exit)^0.5

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*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5 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 c₂ 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 (k), Universal Gas Constant (R) & 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 -> 151.6131 = 8*(1.6*8.314*27)^0.5.

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 c₂ = M*(k*R*T_exit)^0.5 or Exit velocity = Mach Number*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5. 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, Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1 & 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*(Specific Heat Ratio*Universal Gas Constant*Exit Temperature)^0.5. To calculate Exit Velocity given Mach number and Exit Temperature, you need Mach Number (M), Specific Heat Ratio (k), Universal Gas Constant (R) & Exit Temperature (T_exit). With our tool, you need to enter the respective value for Mach Number, Specific Heat Ratio, Universal Gas Constant & 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, Universal Gas Constant & 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/Inlet Pressure)^(1-(1/Specific Heat Ratio Dynamic))))
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)))))

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