Mass Flow Rate through Engine Calculator

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Rocket Propulsion

Components of Gas Turbine

Jet Propulsion

Thermodynamics and Governing Equations

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✖Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%
✖The area is the amount of two-dimensional space taken up by an object.ⓘ Area [A]			+10% -10%
✖Total Pressure is the sum of all the forces that the gas molecules exert on the walls of their container.ⓘ Total Pressure [P_t]			+10% -10%
✖The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ Specific Heat Ratio [Y]			+10% -10%
✖Molar Mass is the mass of a given substance divided by the amount of substance.ⓘ Molar Mass [M_molar]			+10% -10%
✖Total Temperature is the sum of the static temperature and the dynamic temperature.ⓘ Total Temperature [T_t]			+10% -10%

✖Mass Flow Rate represents the amount of mass passing through a system per unit of time.ⓘ Mass Flow Rate through Engine [m_a]

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Formula

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Mass Flow Rate through Engine

Formula

`"m"_{"a"} = "M"*"A"*"P"_{"t"}*sqrt("Y"*"M"_{"molar"}/("T"_{"t"}*"[R]"))*(1+("Y"-1)*"M"^2/2)^(-("Y"+1)/(2*"Y"-2))`

Example

`"460.4282kg/s"="1.4"*"50m²"*"0.004MPa"*sqrt("1.392758"*"44.01g/mol"/("375K"*"[R]"))*(1+("1.392758"-1)*("1.4")^2/2)^(-("1.392758"+1)/(2*"1.392758"-2))`

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Mass Flow Rate through Engine Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Flow Rate = Mach Number*Area*Total Pressure*sqrt(Specific Heat Ratio*Molar Mass/(Total Temperature*[R]))*(1+(Specific Heat Ratio-1)*Mach Number^2/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))
m_a = M*A*P_t*sqrt(Y*M_molar/(T_t*[R]))*(1+(Y-1)*M^2/2)^(-(Y+1)/(2*Y-2))
This formula uses 1 Constants, 1 Functions, 7 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

Mass Flow Rate - (Measured in Kilogram per Second) - Mass Flow Rate represents the amount of mass passing through a system per unit of time.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
Area - (Measured in Square Meter) - The area is the amount of two-dimensional space taken up by an object.
Total Pressure - (Measured in Pascal) - Total Pressure is the sum of all the forces that the gas molecules exert on the walls of their container.
Specific Heat Ratio - The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Molar Mass - (Measured in Kilogram Per Mole) - Molar Mass is the mass of a given substance divided by the amount of substance.
Total Temperature - (Measured in Kelvin) - Total Temperature is the sum of the static temperature and the dynamic temperature.

STEP 1: Convert Input(s) to Base Unit

Mach Number: 1.4 --> No Conversion Required
Area: 50 Square Meter --> 50 Square Meter No Conversion Required
Total Pressure: 0.004 Megapascal --> 4000 Pascal (Check conversion here)
Specific Heat Ratio: 1.392758 --> No Conversion Required
Molar Mass: 44.01 Gram Per Mole --> 0.04401 Kilogram Per Mole (Check conversion here)
Total Temperature: 375 Kelvin --> 375 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m_a = M*A*P_t*sqrt(Y*M_molar/(T_t*[R]))*(1+(Y-1)*M^2/2)^(-(Y+1)/(2*Y-2)) --> 1.4*50*4000*sqrt(1.392758*0.04401/(375*[R]))*(1+(1.392758-1)*1.4^2/2)^(-(1.392758+1)/(2*1.392758-2))

Evaluating ... ...

m_a = 460.428167323859

STEP 3: Convert Result to Output's Unit

460.428167323859 Kilogram per Second --> No Conversion Required

FINAL ANSWER

460.428167323859 ≈ 460.4282 Kilogram per Second <-- Mass Flow Rate

(Calculation completed in 00.004 seconds)

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Rajiv Gandhi Institute of Technology (RGIT), Mumbai

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< 14 Rocket Propulsion Calculators

Mass Flow Rate through Engine

Go Mass Flow Rate = Mach Number*Area*Total Pressure*sqrt(Specific Heat Ratio*Molar Mass/(Total Temperature*[R]))*(1+(Specific Heat Ratio-1)*Mach Number^2/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))

Exit Velocity given Molar Mass

Go 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)))

Compressible Area Ratio

Go Area Ratio = ((Specific Heat Ratio+1)/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2))*((1+(Specific Heat Ratio-1)/2*Mach Number^2)^((Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)))/Mach Number

Exit Velocity given Molar Specific Heat Capacity

Go Exit Velocity = sqrt(2*Total Temperature*Molar Specific Heat Capacity at Constant Pressure*(1-(Exit Pressure/Chamber Pressure)^(1-1/Specific Heat Ratio)))

Rocket Exit Pressure

Go Exit Pressure = Chamber Pressure*((1+(Specific Heat Ratio-1)/2*Mach Number^2)^-(Specific Heat Ratio/(Specific Heat Ratio-1)))

Exit Velocity given Mach Number and Exit Temperature

Go Exit Velocity = Mach Number*sqrt(Specific Heat Ratio*[R]/Molar Mass*Exit Temperature)

Rocket Exit Temperature

Go Exit Temperature = Chamber Temperature*(1+(Specific Heat Ratio-1)/2*Mach Number^2)^-1

Total Impulse

Go Total impulse = int(Thrust,x,Initial time,Final time)

Power required to produce Exhaust Jet Velocity given Mass of Rocket and Acceleration

Go Power Required = (Mass of Rocket*Acceleration*Effective Exhaust Velocity)/2

Power required to produce Exhaust Jet Velocity

Go Power Required = 1/2*Mass Flow Rate*Exit Velocity^2

Thrust given Exhaust Velocity and Mass Flow Rate

Go Thrust = Mass Flow Rate*Exit Velocity

Thrust given Mass and Acceleration of Rocket

Go Thrust = Mass of Rocket*Acceleration

Acceleration of Rocket

Go Acceleration = Thrust/Mass of Rocket

Photon Propulsion Thrust

Go Thrust = 1000*Power in Jet/[c]

Mass Flow Rate through Engine Formula

What is Mass Flow Rate?

The amount of mass that flows through an area in a given amount of time is known as the mass flow rate. It is a measurement of the velocity at which gases and liquids pass through a specified area. It is an important factor that determines the amount of thrust produced.

Condition for Maximum mass flow rate

Maximum mass flow rate occurs when the Mach number is equal to one. This condition is known as choking and it is an important factor to determine the characteristics and limit of an engine.

How to Calculate Mass Flow Rate through Engine?

Mass Flow Rate through Engine calculator uses Mass Flow Rate = Mach Number*Area*Total Pressure*sqrt(Specific Heat Ratio*Molar Mass/(Total Temperature*[R]))*(1+(Specific Heat Ratio-1)*Mach Number^2/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)) to calculate the Mass Flow Rate, Mass Flow Rate through Engine formula is used to determine the amount of mass flowing through the nozzle from an exhaust of a rocket engine given that we know the flow area, total pressure and temperature of the flow, the Mach number, the ratio of specific heats of the gas, and the gas constant. Mass Flow Rate is denoted by m_a symbol.

How to calculate Mass Flow Rate through Engine using this online calculator? To use this online calculator for Mass Flow Rate through Engine, enter Mach Number (M), Area (A), Total Pressure (P_t), Specific Heat Ratio (Y), Molar Mass (M_molar) & Total Temperature (T_t) and hit the calculate button. Here is how the Mass Flow Rate through Engine calculation can be explained with given input values -> 2.518388 = 1.4*50*4000*sqrt(1.392758*0.04401/(375*[R]))*(1+(1.392758-1)*1.4^2/2)^(-(1.392758+1)/(2*1.392758-2)).

FAQ

What is Mass Flow Rate through Engine?

Mass Flow Rate through Engine formula is used to determine the amount of mass flowing through the nozzle from an exhaust of a rocket engine given that we know the flow area, total pressure and temperature of the flow, the Mach number, the ratio of specific heats of the gas, and the gas constant and is represented as m_a = M*A*P_t*sqrt(Y*M_molar/(T_t*[R]))*(1+(Y-1)*M^2/2)^(-(Y+1)/(2*Y-2)) or Mass Flow Rate = Mach Number*Area*Total Pressure*sqrt(Specific Heat Ratio*Molar Mass/(Total Temperature*[R]))*(1+(Specific Heat Ratio-1)*Mach Number^2/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)). Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound, The area is the amount of two-dimensional space taken up by an object, Total Pressure is the sum of all the forces that the gas molecules exert on the walls of their container, The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume, Molar Mass is the mass of a given substance divided by the amount of substance & Total Temperature is the sum of the static temperature and the dynamic temperature.

How to calculate Mass Flow Rate through Engine?

Mass Flow Rate through Engine formula is used to determine the amount of mass flowing through the nozzle from an exhaust of a rocket engine given that we know the flow area, total pressure and temperature of the flow, the Mach number, the ratio of specific heats of the gas, and the gas constant is calculated using Mass Flow Rate = Mach Number*Area*Total Pressure*sqrt(Specific Heat Ratio*Molar Mass/(Total Temperature*[R]))*(1+(Specific Heat Ratio-1)*Mach Number^2/2)^(-(Specific Heat Ratio+1)/(2*Specific Heat Ratio-2)). To calculate Mass Flow Rate through Engine, you need Mach Number (M), Area (A), Total Pressure (P_t), Specific Heat Ratio (Y), Molar Mass (M_molar) & Total Temperature (T_t). With our tool, you need to enter the respective value for Mach Number, Area, Total Pressure, Specific Heat Ratio, Molar Mass & Total Temperature 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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