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Exit Velocity given Mach Number and Exit Temperature Formula

GoExit Velocity given Molar Specific Heat Capacity Formula

GoExit Velocity given Molar Mass Formula

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Exit Velocity is the speed at which exhaust gases exit the primary nozzle of a propulsion system, such as a rocket or jet engine. Check FAQs

C j = M \cdot \sqrt{γ \cdot \frac{[R]}{M molar} \cdot T exit}

C_j - Exit Velocity?M - Mach Number?γ - Specific Heat Ratio?M_molar - Molar Mass?T_exit - Exit Temperature?[R] - Universal gas constant?

Exit Velocity given Mach Number and Exit Temperature Example

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Here is how the Exit Velocity given Mach Number and Exit Temperature equation looks like with Values.

Here is how the Exit Velocity given Mach Number and Exit Temperature equation looks like with Units.

Here is how the Exit Velocity given Mach Number and Exit Temperature equation looks like.

248.3706 = 1.4 \cdot \sqrt{1.33 \cdot \frac{8.3145}{6.5} \cdot 18.5}

248.3706m/s = 1.4 \cdot \sqrt{1.33 \cdot \frac{8.3145}{6.5g/mol} \cdot 18.5K}

248.3706 = 1.4 \cdot \sqrt{1.33 \cdot \frac{8.3145}{6.5} \cdot 18.5}

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Exit Velocity given Mach Number and Exit Temperature Solution

Follow our step by step solution on how to calculate Exit Velocity given Mach Number and Exit Temperature?

FIRST Step Consider the formula

C j = M \cdot \sqrt{γ \cdot \frac{[R]}{M molar} \cdot T exit}

Next Step Substitute values of Variables

∴

C j = 1.4 \cdot \sqrt{1.33 \cdot \frac{[R]}{6.5g/mol} \cdot 18.5K}

Next Step Substitute values of Constants

∴

C j = 1.4 \cdot \sqrt{1.33 \cdot \frac{8.3145}{6.5g/mol} \cdot 18.5K}

Next Step Convert Units

∴

C j = 1.4 \cdot \sqrt{1.33 \cdot \frac{8.3145}{0.0065kg/mol} \cdot 18.5K}

Next Step Prepare to Evaluate

∴

C j = 1.4 \cdot \sqrt{1.33 \cdot \frac{8.3145}{0.0065} \cdot 18.5}

Next Step Evaluate

∴

C j = 248.370570327279m/s

LAST Step Rounding Answer

∴

C j = 248.3706m/s

Exit Velocity given Mach Number and Exit Temperature Formula Elements

Variables

Constants

Functions

Exit Velocity

Exit Velocity is the speed at which exhaust gases exit the primary nozzle of a propulsion system, such as a rocket or jet engine.

Symbol: C_j

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Exit Velocity

Mach Number

Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Specific Heat Ratio

The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Specific Heat Ratio

Molar Mass

Molar Mass is the mass of a given substance divided by the amount of substance.

Symbol: M_molar

Measurement: Molar MassUnit: g/mol

Note: Value can be positive or negative.

Formulas to find Molar Mass

Exit Temperature

Exit temperature is the degree of measure of heat at exit to the system.

Symbol: T_exit

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Exit Temperature

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

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.

Syntax: sqrt(Number)

Other Formulas to find Exit Velocity

Go Exit Velocity given Molar Specific Heat Capacity

C j = \sqrt{2 \cdot T tot \cdot C p molar \cdot (1 - {(\frac{P exit}{P c})}^{1 - \frac{1}{γ}})}

Go Exit Velocity given Molar Mass

C j = \sqrt{(\frac{2 \cdot T c \cdot [R] \cdot γ}{M molar} / (γ - 1)) \cdot (1 - {(\frac{P exit}{P c})}^{1 - \frac{1}{γ}})}

Other formulas in Thrust and Power Generation category

Go Power required to produce Exhaust Jet Velocity

P = \frac{1}{2} \cdot m a \cdot {C j}^{2}

Go Thrust given Exhaust Velocity and Mass Flow Rate

F = m a \cdot C j

Go Thrust given Mass and Acceleration of Rocket

F = m \cdot a

Go Acceleration of Rocket

a = \frac{F}{m}

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

Exit Velocity given Mach Number and Exit Temperature evaluator uses Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature) to evaluate 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 evaluate Exit Velocity given Mach Number and Exit Temperature using this online evaluator? To use this online evaluator for Exit Velocity given Mach Number and Exit Temperature, enter Mach Number (M), Specific Heat Ratio (γ), Molar Mass (M_molar) & Exit Temperature (T_exit) and hit the calculate button.

FAQs on Exit Velocity given Mach Number and Exit Temperature

What is the formula to find Exit Velocity given Mach Number and Exit Temperature?

The formula of Exit Velocity given Mach Number and Exit Temperature is expressed as Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature). Here is an example- 244.9912 = 1.4*sqrt(1.33*[R]/0.0065*18.5).

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

With Mach Number (M), Specific Heat Ratio (γ), Molar Mass (M_molar) & Exit Temperature (T_exit) we can find Exit Velocity given Mach Number and Exit Temperature using the formula - Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature). This formula also uses Universal gas constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Exit Velocity?

Here are the different ways to Calculate Exit Velocity-

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)))

Can the Exit Velocity given Mach Number and Exit Temperature be negative?

No, the Exit Velocity given Mach Number and Exit Temperature, measured in Speed cannot be negative.

Which unit is used to measure Exit Velocity given Mach Number and Exit Temperature?

Exit Velocity given Mach Number and Exit Temperature is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Exit Velocity given Mach Number and Exit Temperature can be measured.

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: Value
: Unit

Exit Velocity given Mach Number and Exit Temperature Formula

​GoExit Velocity given Molar Specific Heat Capacity Formula

​GoExit Velocity given Molar Mass Formula

Exit Velocity given Mach Number and Exit Temperature Example

Exit Velocity given Mach Number and Exit Temperature Solution

Exit Velocity given Mach Number and Exit Temperature Formula Elements

Other Formulas to find Exit Velocity

Other formulas in Thrust and Power Generation category

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

FAQs on Exit Velocity given Mach Number and Exit Temperature

Variable Name

GoExit Velocity given Molar Specific Heat Capacity Formula

GoExit Velocity given Molar Mass Formula