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Rocket Exhaust Gas Velocity Formula

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Jet Velocity is the effective exhaust velocity. Check FAQs

V e = \sqrt{(\frac{2 \cdot γ}{γ - 1}) \cdot [R] \cdot T 1 \cdot (1 - {(\frac{p 2}{p 1})}^{\frac{γ - 1}{γ}})}

V_e - Jet Velocity?γ - Specific Heat Ratio?T₁ - Temperature at Chamber?p₂ - Nozzle Exit Pressure?p₁ - Pressure at Chamber?[R] - Universal gas constant?

Rocket Exhaust Gas Velocity Example

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Here is how the Rocket Exhaust Gas Velocity equation looks like with Values.

Here is how the Rocket Exhaust Gas Velocity equation looks like with Units.

Here is how the Rocket Exhaust Gas Velocity equation looks like.

118.6448 = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot 8.3145 \cdot 256 \cdot (1 - {(\frac{1.239}{1256})}^{\frac{1.33 - 1}{1.33}})}

118.6448m/s = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot 8.3145 \cdot 256K \cdot (1 - {(\frac{1.239MPa}{1256MPa})}^{\frac{1.33 - 1}{1.33}})}

118.6448 = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot 8.3145 \cdot 256 \cdot (1 - {(\frac{1.239}{1256})}^{\frac{1.33 - 1}{1.33}})}

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Rocket Exhaust Gas Velocity Solution

Follow our step by step solution on how to calculate Rocket Exhaust Gas Velocity?

FIRST Step Consider the formula

V e = \sqrt{(\frac{2 \cdot γ}{γ - 1}) \cdot [R] \cdot T 1 \cdot (1 - {(\frac{p 2}{p 1})}^{\frac{γ - 1}{γ}})}

Next Step Substitute values of Variables

∴

V e = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot [R] \cdot 256K \cdot (1 - {(\frac{1.239MPa}{1256MPa})}^{\frac{1.33 - 1}{1.33}})}

Next Step Substitute values of Constants

∴

V e = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot 8.3145 \cdot 256K \cdot (1 - {(\frac{1.239MPa}{1256MPa})}^{\frac{1.33 - 1}{1.33}})}

Next Step Convert Units

∴

V e = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot 8.3145 \cdot 256K \cdot (1 - {(\frac{1.2E+6Pa}{1.3E+9Pa})}^{\frac{1.33 - 1}{1.33}})}

Next Step Prepare to Evaluate

∴

V e = \sqrt{(\frac{2 \cdot 1.33}{1.33 - 1}) \cdot 8.3145 \cdot 256 \cdot (1 - {(\frac{1.2E+6}{1.3E+9})}^{\frac{1.33 - 1}{1.33}})}

Next Step Evaluate

∴

V e = 118.644770171364m/s

LAST Step Rounding Answer

∴

V e = 118.6448m/s

Rocket Exhaust Gas Velocity Formula Elements

Variables

Constants

Functions

Jet Velocity

Jet Velocity is the effective exhaust velocity.

Symbol: V_e

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Jet Velocity

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

Temperature at Chamber

Temperature at Chamber typically refers to the temperature inside a closed chamber or enclosure.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature at Chamber

Nozzle Exit Pressure

The Nozzle Exit Pressure in rocketry refers to the pressure of the exhaust gases at the exit of the rocket engine nozzle.

Symbol: p₂

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Nozzle Exit Pressure

Pressure at Chamber

Pressure at Chamber in rocketry refers to the pressure of the combustion gases inside the combustion chamber of the rocket engine.

Symbol: p₁

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Pressure at Chamber

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 in Theory Of Rockets category

Go Total Velocity Required to Place Satellite in Orbit

V T = \sqrt{\frac{[G.] \cdot M E \cdot (R E + 2 \cdot h)}{R E \cdot (R E + h)}}

Go Velocity Increment of Rocket

ΔV = V e \cdot \ln (\frac{m i}{m final})

Go Structural Mass Fraction

σ = \frac{m s}{m p + m s}

Go Payload Mass Fraction

λ = \frac{m d}{m p + m s}

How to Evaluate Rocket Exhaust Gas Velocity?

Rocket Exhaust Gas Velocity evaluator uses Jet Velocity = sqrt(((2*Specific Heat Ratio)/(Specific Heat Ratio-1))*[R]*Temperature at Chamber*(1-(Nozzle Exit Pressure/Pressure at Chamber)^((Specific Heat Ratio-1)/Specific Heat Ratio))) to evaluate the Jet Velocity, The Rocket Exhaust Gas Velocity, also known as exit velocity, of a rocket refers to the velocity of the exhaust gases as they leave the rocket engine nozzle, it represents the speed at which the expelled gases are ejected from the rocket, propelling it forward in accordance with Newton's third law of motion: for every action, there is an equal and opposite reaction. Jet Velocity is denoted by V_e symbol.

How to evaluate Rocket Exhaust Gas Velocity using this online evaluator? To use this online evaluator for Rocket Exhaust Gas Velocity, enter Specific Heat Ratio (γ), Temperature at Chamber (T₁), Nozzle Exit Pressure (p₂) & Pressure at Chamber (p₁) and hit the calculate button.

FAQs on Rocket Exhaust Gas Velocity

What is the formula to find Rocket Exhaust Gas Velocity?

The formula of Rocket Exhaust Gas Velocity is expressed as Jet Velocity = sqrt(((2*Specific Heat Ratio)/(Specific Heat Ratio-1))*[R]*Temperature at Chamber*(1-(Nozzle Exit Pressure/Pressure at Chamber)^((Specific Heat Ratio-1)/Specific Heat Ratio))). Here is an example- 118.6448 = sqrt(((2*1.33)/(1.33-1))*[R]*256*(1-(1239000/1256000000)^((1.33-1)/1.33))).

How to calculate Rocket Exhaust Gas Velocity?

With Specific Heat Ratio (γ), Temperature at Chamber (T₁), Nozzle Exit Pressure (p₂) & Pressure at Chamber (p₁) we can find Rocket Exhaust Gas Velocity using the formula - Jet Velocity = sqrt(((2*Specific Heat Ratio)/(Specific Heat Ratio-1))*[R]*Temperature at Chamber*(1-(Nozzle Exit Pressure/Pressure at Chamber)^((Specific Heat Ratio-1)/Specific Heat Ratio))). This formula also uses Universal gas constant and Square Root (sqrt) function(s).

Can the Rocket Exhaust Gas Velocity be negative?

Yes, the Rocket Exhaust Gas Velocity, measured in Speed can be negative.

Which unit is used to measure Rocket Exhaust Gas Velocity?

Rocket Exhaust Gas Velocity 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 Rocket Exhaust Gas Velocity can be measured.

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Rocket Exhaust Gas Velocity Formula

Rocket Exhaust Gas Velocity Example

Rocket Exhaust Gas Velocity Solution

Rocket Exhaust Gas Velocity Formula Elements

Other formulas in Theory Of Rockets category

How to Evaluate Rocket Exhaust Gas Velocity?

FAQs on Rocket Exhaust Gas Velocity

Variable Name