Rocket Exhaust Gas Velocity Calculator

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Rocket Propulsion

Components of Gas Turbine

Jet Propulsion

Thermodynamics and Governing Equations

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✖The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Temperature at Chamber typically refers to the temperature inside a closed chamber or enclosure.ⓘ Temperature at Chamber [T₁]			+10% -10%
✖The Nozzle Exit Pressure in rocketry refers to the pressure of the exhaust gases at the exit of the rocket engine nozzle.ⓘ Nozzle Exit Pressure [p₂]			+10% -10%
✖Pressure at Chamber in rocketry refers to the pressure of the combustion gases inside the combustion chamber of the rocket engine.ⓘ Pressure at Chamber [p₁]			+10% -10%

✖Jet Velocity is the effective exhaust velocity.ⓘ Rocket Exhaust Gas Velocity [V_e]

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Formula

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Rocket Exhaust Gas Velocity

Formula

`"V"_{"e"} = sqrt(((2*"γ")/("γ"-1))*"[R]"*"T"_{"1"}*(1-("p"_{"2"}/"p"_{"1"})^(("γ"-1)/"γ")))`

Example

`"78.16306m/s"=sqrt(((2*"1.33")/("1.33"-1))*"[R]"*"256K"*(1-("1.24MPa"/"7.31MPa")^(("1.33"-1)/"1.33")))`

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Rocket Exhaust Gas Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
V_e = sqrt(((2*γ)/(γ-1))*[R]*T₁*(1-(p₂/p₁)^((γ-1)/γ)))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

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., sqrt(Number)

Variables Used

Jet Velocity - (Measured in Meter per Second) - Jet Velocity is the effective exhaust 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.
Temperature at Chamber - (Measured in Kelvin) - Temperature at Chamber typically refers to the temperature inside a closed chamber or enclosure.
Nozzle Exit Pressure - (Measured in Pascal) - The Nozzle Exit Pressure in rocketry refers to the pressure of the exhaust gases at the exit of the rocket engine nozzle.
Pressure at Chamber - (Measured in Pascal) - Pressure at Chamber in rocketry refers to the pressure of the combustion gases inside the combustion chamber of the rocket engine.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.33 --> No Conversion Required
Temperature at Chamber: 256 Kelvin --> 256 Kelvin No Conversion Required
Nozzle Exit Pressure: 1.24 Megapascal --> 1240000 Pascal (Check conversion here)
Pressure at Chamber: 7.31 Megapascal --> 7310000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_e = sqrt(((2*γ)/(γ-1))*[R]*T₁*(1-(p₂/p₁)^((γ-1)/γ))) --> sqrt(((2*1.33)/(1.33-1))*[R]*256*(1-(1240000/7310000)^((1.33-1)/1.33)))

Evaluating ... ...

V_e = 78.1630556389623

STEP 3: Convert Result to Output's Unit

78.1630556389623 Meter per Second --> No Conversion Required

FINAL ANSWER

78.1630556389623 ≈ 78.16306 Meter per Second <-- Jet Velocity

(Calculation completed in 00.007 seconds)

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Sri Ramakrishna Engineering College (SREC), COIMBATORE

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Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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< 9 Theory Of Rockets Calculators

Rocket Exhaust Gas Velocity

Go 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)))

Total Velocity Required to Place Satellite in Orbit

Go Total Velocity of Rocket = sqrt(([G.]*Mass Of Earth*(Radius of Earth+2*Height of Satellite))/(Radius of Earth*(Radius of Earth+Height of Satellite)))

Effective Exhaust Velocity of Rocket

Go Effective Exhaust Velocity = Jet Velocity+(Nozzle Exit Pressure-Atmospheric Pressure)*Exit Area/Propellant Mass Flow Rate

Throat Velocity of Nozzle

Go Throat Velocity = sqrt((2*Specific Heat Ratio)/(Specific Heat Ratio+1)*[R]*Temperature at Chamber)

Velocity Increment of Rocket

Go Velocity Increment of Rocket = Jet Velocity of Rocket*ln(Initial Mass of Rocket/Final Mass of Rocket)

Structural Mass Fraction

Go Structural Mass Fraction = Structural Mass/(Propellant Mass+Structural Mass)

Payload Mass Fraction

Go Payload Mass Fraction = Payload Mass/(Propellant Mass+Structural Mass)

Propellent Mass Fraction

Go Propellant Mass Fraction = Propellant Mass/Initial Mass

Mass Ratio of Rocket

Go Mass Ratio = Final Mass/Initial Mass

Rocket Exhaust Gas Velocity Formula

what is Jet Velocity ?

The jet velocity is a crucial parameter in rocket propulsion systems because it directly affects the thrust generated by the engine. Higher exit velocities result in greater thrust, allowing the rocket to accelerate more quickly and achieve higher speeds. The efficiency of a rocket engine is often assessed based on its exit velocity, as engines with higher velocities relative to the rocket's mass tend to produce more efficient propulsion systems.

How to Calculate Rocket Exhaust Gas Velocity?

Rocket Exhaust Gas Velocity calculator 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 calculate 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 calculate Rocket Exhaust Gas Velocity using this online calculator? To use this online calculator 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. Here is how the Rocket Exhaust Gas Velocity calculation can be explained with given input values -> 78.16306 = sqrt(((2*1.33)/(1.33-1))*[R]*256*(1-(1240000/7310000)^((1.33-1)/1.33))).

FAQ

What is Rocket Exhaust Gas 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 and is represented as V_e = sqrt(((2*γ)/(γ-1))*[R]*T₁*(1-(p₂/p₁)^((γ-1)/γ))) or 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))). The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume, Temperature at Chamber typically refers to the temperature inside a closed chamber or enclosure, The Nozzle Exit Pressure in rocketry refers to the pressure of the exhaust gases at the exit of the rocket engine nozzle & Pressure at Chamber in rocketry refers to the pressure of the combustion gases inside the combustion chamber of the rocket engine.

How to calculate Rocket Exhaust Gas 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 is calculated using 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 calculate Rocket Exhaust Gas Velocity, you need Specific Heat Ratio (γ), Temperature at Chamber (T₁), Nozzle Exit Pressure (p₂) & Pressure at Chamber (p₁). With our tool, you need to enter the respective value for Specific Heat Ratio, Temperature at Chamber, Nozzle Exit Pressure & Pressure at Chamber and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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