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Exit Velocity given Molar Mass Formula

GoExit Velocity given Mach Number and Exit Temperature Formula

GoExit Velocity given Molar Specific Heat Capacity 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 = \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}})}

C_j - Exit Velocity?T_c - Chamber Temperature?γ - Specific Heat Ratio?M_molar - Molar Mass?P_exit - Exit Pressure?P_c - Chamber Pressure?[R] - Universal gas constant?

Exit Velocity given Molar Mass Example

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Here is how the Exit Velocity given Molar Mass equation looks like with Values.

Here is how the Exit Velocity given Molar Mass equation looks like with Units.

Here is how the Exit Velocity given Molar Mass equation looks like.

248.87 = \sqrt{(\frac{2 \cdot 24.6 \cdot 8.3145 \cdot 1.33}{6.5} / (1.33 - 1)) \cdot (1 - {(\frac{2.1}{6.49})}^{1 - \frac{1}{1.33}})}

248.87m/s = \sqrt{(\frac{2 \cdot 24.6K \cdot 8.3145 \cdot 1.33}{6.5g/mol} / (1.33 - 1)) \cdot (1 - {(\frac{2.1MPa}{6.49MPa})}^{1 - \frac{1}{1.33}})}

248.87 = \sqrt{(\frac{2 \cdot 24.6 \cdot 8.3145 \cdot 1.33}{6.5} / (1.33 - 1)) \cdot (1 - {(\frac{2.1}{6.49})}^{1 - \frac{1}{1.33}})}

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Exit Velocity given Molar Mass Solution

Follow our step by step solution on how to calculate Exit Velocity given Molar Mass?

FIRST Step Consider the formula

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}})}

Next Step Substitute values of Variables

∴

C j = \sqrt{(\frac{2 \cdot 24.6K \cdot [R] \cdot 1.33}{6.5g/mol} / (1.33 - 1)) \cdot (1 - {(\frac{2.1MPa}{6.49MPa})}^{1 - \frac{1}{1.33}})}

Next Step Substitute values of Constants

∴

C j = \sqrt{(\frac{2 \cdot 24.6K \cdot 8.3145 \cdot 1.33}{6.5g/mol} / (1.33 - 1)) \cdot (1 - {(\frac{2.1MPa}{6.49MPa})}^{1 - \frac{1}{1.33}})}

Next Step Convert Units

∴

C j = \sqrt{(\frac{2 \cdot 24.6K \cdot 8.3145 \cdot 1.33}{0.0065kg/mol} / (1.33 - 1)) \cdot (1 - {(\frac{2.1E+6Pa}{6.5E+6Pa})}^{1 - \frac{1}{1.33}})}

Next Step Prepare to Evaluate

∴

C j = \sqrt{(\frac{2 \cdot 24.6 \cdot 8.3145 \cdot 1.33}{0.0065} / (1.33 - 1)) \cdot (1 - {(\frac{2.1E+6}{6.5E+6})}^{1 - \frac{1}{1.33}})}

Next Step Evaluate

∴

C j = 248.869960344833m/s

LAST Step Rounding Answer

∴

C j = 248.87m/s

Exit Velocity given Molar Mass 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

Chamber Temperature

Chamber Temperature refers to the temperature of the combustion chamber in a propulsion system, such as a rocket or jet engine.

Symbol: T_c

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Chamber Temperature

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 Pressure

Exit Pressure is the pressure of the gases leaving the rocket nozzle.

Symbol: P_exit

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Exit Pressure

Chamber Pressure

The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket.

Symbol: P_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Chamber Pressure

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 Mach Number and Exit Temperature

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

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}})}

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 Molar Mass?

Exit Velocity given Molar Mass evaluator 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 evaluate the Exit Velocity, Exit Velocity given Molar Mass formula is defined as a method to determine the speed at which exhaust gases exit a propulsion system, taking into account the molar mass of the gases and the thermodynamic properties of the system. Exit Velocity is denoted by C_j symbol.

How to evaluate Exit Velocity given Molar Mass using this online evaluator? To use this online evaluator for Exit Velocity given Molar Mass, enter Chamber Temperature (T_c), Specific Heat Ratio (γ), Molar Mass (M_molar), Exit Pressure (P_exit) & Chamber Pressure (P_c) and hit the calculate button.

FAQs on Exit Velocity given Molar Mass

What is the formula to find Exit Velocity given Molar Mass?

The formula of Exit Velocity given Molar Mass is expressed as 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))). Here is an example- 249.017 = sqrt(((2*24.6*[R]*1.33)/(0.0065)/(1.33-1))*(1-(2100000/6490000)^(1-1/1.33))).

How to calculate Exit Velocity given Molar Mass?

With Chamber Temperature (T_c), Specific Heat Ratio (γ), Molar Mass (M_molar), Exit Pressure (P_exit) & Chamber Pressure (P_c) we can find Exit Velocity given Molar Mass using the formula - 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))). 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=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)))

Can the Exit Velocity given Molar Mass be negative?

No, the Exit Velocity given Molar Mass, measured in Speed cannot be negative.

Which unit is used to measure Exit Velocity given Molar Mass?

Exit Velocity given Molar Mass 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 Molar Mass can be measured.

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Exit Velocity given Molar Mass Formula

​GoExit Velocity given Mach Number and Exit Temperature Formula

​GoExit Velocity given Molar Specific Heat Capacity Formula

Exit Velocity given Molar Mass Example

Exit Velocity given Molar Mass Solution

Exit Velocity given Molar Mass Formula Elements

Other Formulas to find Exit Velocity

Other formulas in Thrust and Power Generation category

How to Evaluate Exit Velocity given Molar Mass?

FAQs on Exit Velocity given Molar Mass

Variable Name

GoExit Velocity given Mach Number and Exit Temperature Formula

GoExit Velocity given Molar Specific Heat Capacity Formula