Exit Velocity given Molar Specific Heat Capacity Calculator

✖Total Temperature is the sum of the static temperature and the dynamic temperature.ⓘ Total Temperature [T_tot]			+10% -10%
✖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.ⓘ Molar Specific Heat Capacity at Constant Pressure [C_{p molar}]			+10% -10%
✖Exit Pressure is the pressure of the gases leaving the rocket nozzle.ⓘ Exit Pressure [P_exit]			+10% -10%
✖The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket.ⓘ Chamber Pressure [P_c]			+10% -10%
✖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%

✖Exit Velocity is the speed at which exhaust gases exit the primary nozzle of a propulsion system, such as a rocket or jet engine.ⓘ Exit Velocity given Molar Specific Heat Capacity [C_j]

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Exit Velocity given Molar Specific Heat Capacity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))
C_j = sqrt(2*T_tot*C_{p molar}*(1-(P_exit/P_c)^(1-1/γ)))
This formula uses 1 Functions, 6 Variables

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

Exit Velocity - (Measured in Meter per Second) - Exit Velocity is the speed at which exhaust gases exit the primary nozzle of a propulsion system, such as a rocket or jet engine.
Total Temperature - (Measured in Kelvin) - Total Temperature is the sum of the static temperature and the dynamic temperature.
Molar Specific Heat Capacity at Constant Pressure - (Measured in Joule Per Kelvin Per Mole) - 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.
Exit Pressure - (Measured in Pascal) - Exit Pressure is the pressure of the gases leaving the rocket nozzle.
Chamber Pressure - (Measured in Pascal) - The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket.
Specific Heat Ratio - The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.

STEP 1: Convert Input(s) to Base Unit

Total Temperature: 590 Kelvin --> 590 Kelvin No Conversion Required
Molar Specific Heat Capacity at Constant Pressure: 213.6 Joule Per Kelvin Per Mole --> 213.6 Joule Per Kelvin Per Mole No Conversion Required
Exit Pressure: 2.1 Megapascal --> 2100000 Pascal (Check conversion here)
Chamber Pressure: 6.49 Megapascal --> 6490000 Pascal (Check conversion here)
Specific Heat Ratio: 1.33 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_j = sqrt(2*T_tot*C_{p molar}*(1-(P_exit/P_c)^(1-1/γ))) --> sqrt(2*590*213.6*(1-(2100000/6490000)^(1-1/1.33)))

Evaluating ... ...

C_j = 248.086019107038

STEP 3: Convert Result to Output's Unit

248.086019107038 Meter per Second --> No Conversion Required

FINAL ANSWER

248.086019107038 ≈ 248.086 Meter per Second <-- Exit Velocity

(Calculation completed in 00.004 seconds)

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Rajiv Gandhi Institute of Technology (RGIT), Mumbai

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Exit Velocity given Molar Specific Heat Capacity Formula

LaTeX Go

Exit Velocity

The velocity produced at the outlet of the rocket engine through the nozzle is called as the exit velocity. This parameter is useful to examine the rocket's performance.

How to Calculate Exit Velocity given Molar Specific Heat Capacity?

Exit Velocity given Molar Specific Heat Capacity calculator 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 calculate 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 calculate Exit Velocity given Molar Specific Heat Capacity using this online calculator? To use this online calculator 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. Here is how the Exit Velocity given Molar Specific Heat Capacity calculation can be explained with given input values -> 248.1441 = sqrt(2*590*213.6*(1-(2100000/6490000)^(1-1/1.33))).

FAQ

What is Exit Velocity given Molar Specific Heat Capacity?

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 and is represented as C_j = sqrt(2*T_tot*C_{p molar}*(1-(P_exit/P_c)^(1-1/γ))) or Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))). Total Temperature is the sum of the static temperature and the dynamic temperature, 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, Exit Pressure is the pressure of the gases leaving the rocket nozzle, The Chamber Pressure is the amount of pressure generated inside the combustion chamber of a rocket & The specific heat ratio describes the ratio of specific heats of a gas at constant pressure to that at constant volume.

How to calculate Exit Velocity given Molar Specific Heat Capacity?

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 is calculated using Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio))). To calculate Exit Velocity given Molar Specific Heat Capacity, you need 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). With our tool, you need to enter the respective value for Total Temperature, Molar Specific Heat Capacity at Constant Pressure, Exit Pressure, Chamber Pressure & Specific Heat Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Exit Velocity?

In this formula, Exit Velocity uses Total Temperature, Molar Specific Heat Capacity at Constant Pressure, Exit Pressure, Chamber Pressure & Specific Heat Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)))

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