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Exit Velocity given Molar Specific Heat Capacity Formula

GoExit Velocity given Mach Number and Exit Temperature 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 = \sqrt{2 \cdot T tot \cdot C p molar \cdot (1 - {(\frac{P exit}{P c})}^{1 - \frac{1}{γ}})}

C_j - Exit Velocity?T_tot - Total Temperature?C_{p molar} - Molar Specific Heat Capacity at Constant Pressure?P_exit - Exit Pressure?P_c - Chamber Pressure?γ - Specific Heat Ratio?

Exit Velocity given Molar Specific Heat Capacity Example

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Here is how the Exit Velocity given Molar Specific Heat Capacity equation looks like with Values.

Here is how the Exit Velocity given Molar Specific Heat Capacity equation looks like with Units.

Here is how the Exit Velocity given Molar Specific Heat Capacity equation looks like.

248.086 = \sqrt{2 \cdot 590 \cdot 213.6 \cdot (1 - {(\frac{2.1}{6.49})}^{1 - \frac{1}{1.33}})}

248.086m/s = \sqrt{2 \cdot 590K \cdot 213.6J/K*mol \cdot (1 - {(\frac{2.1MPa}{6.49MPa})}^{1 - \frac{1}{1.33}})}

248.086 = \sqrt{2 \cdot 590 \cdot 213.6 \cdot (1 - {(\frac{2.1}{6.49})}^{1 - \frac{1}{1.33}})}

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Exit Velocity given Molar Specific Heat Capacity Solution

Follow our step by step solution on how to calculate Exit Velocity given Molar Specific Heat Capacity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C j = \sqrt{2 \cdot 590K \cdot 213.6J/K*mol \cdot (1 - {(\frac{2.1MPa}{6.49MPa})}^{1 - \frac{1}{1.33}})}

Next Step Convert Units

∴

C j = \sqrt{2 \cdot 590K \cdot 213.6J/K*mol \cdot (1 - {(\frac{2.1E+6Pa}{6.5E+6Pa})}^{1 - \frac{1}{1.33}})}

Next Step Prepare to Evaluate

∴

C j = \sqrt{2 \cdot 590 \cdot 213.6 \cdot (1 - {(\frac{2.1E+6}{6.5E+6})}^{1 - \frac{1}{1.33}})}

Next Step Evaluate

∴

C j = 248.086019107038m/s

LAST Step Rounding Answer

∴

C j = 248.086m/s

Exit Velocity given Molar Specific Heat Capacity Formula Elements

Variables

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

Total Temperature

Total Temperature is the sum of the static temperature and the dynamic temperature.

Symbol: T_tot

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Total Temperature

Molar Specific Heat Capacity at Constant Pressure

Molar Specific Heat Capacity at Constant Pressure, (of a gas) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.

Symbol: C_{p molar}

Measurement: Molar Specific Heat Capacity at Constant PressureUnit: J/K*mol

Note: Value should be greater than 0.

Formulas to find Molar Specific Heat Capacity at Constant Pressure

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

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

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 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 Molar Specific Heat Capacity?

Exit Velocity given Molar Specific Heat Capacity evaluator uses Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))) to evaluate the Exit Velocity, The Exit Velocity given Molar Specific Heat Capacity formula can be used to determine the exit velocity through the nozzle when the value of specific heat capacity at constant pressure is known. Exit Velocity is denoted by C_j symbol.

How to evaluate Exit Velocity given Molar Specific Heat Capacity using this online evaluator? To use this online evaluator for Exit Velocity given Molar Specific Heat Capacity, enter Total Temperature (T_tot), Molar Specific Heat Capacity at Constant Pressure (C_{p molar}), Exit Pressure (P_exit), Chamber Pressure (P_c) & Specific Heat Ratio (γ) and hit the calculate button.

FAQs on Exit Velocity given Molar Specific Heat Capacity

What is the formula to find Exit Velocity given Molar Specific Heat Capacity?

The formula of Exit Velocity given Molar Specific Heat Capacity is expressed as Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))). Here is an example- 248.1441 = sqrt(2*590*213.6*(1-(2100000/6490000)^(1-1/1.33))).

How to calculate Exit Velocity given Molar Specific Heat Capacity?

With Total Temperature (T_tot), Molar Specific Heat Capacity at Constant Pressure (C_{p molar}), Exit Pressure (P_exit), Chamber Pressure (P_c) & Specific Heat Ratio (γ) we can find Exit Velocity given Molar Specific Heat Capacity using the formula - Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))). This formula also uses 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*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 Molar Specific Heat Capacity be negative?

No, the Exit Velocity given Molar Specific Heat Capacity, measured in Speed cannot be negative.

Which unit is used to measure Exit Velocity given Molar Specific Heat Capacity?

Exit Velocity given Molar Specific Heat Capacity 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 Specific Heat Capacity can be measured.

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Exit Velocity given Molar Specific Heat Capacity Formula

​GoExit Velocity given Mach Number and Exit Temperature Formula

​GoExit Velocity given Molar Mass Formula

Exit Velocity given Molar Specific Heat Capacity Example

Exit Velocity given Molar Specific Heat Capacity Solution

Exit Velocity given Molar Specific Heat Capacity Formula Elements

Other Formulas to find Exit Velocity

Other formulas in Thrust and Power Generation category

How to Evaluate Exit Velocity given Molar Specific Heat Capacity?

FAQs on Exit Velocity given Molar Specific Heat Capacity

Variable Name

GoExit Velocity given Mach Number and Exit Temperature Formula

GoExit Velocity given Molar Mass Formula