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Mass Flow Rate through Engine Formula

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Mass Flow Rate represents the amount of mass passing through a system per unit of time. Check FAQs

m a = M \cdot A \cdot P t \cdot \sqrt{γ \cdot \frac{M molar}{T tot \cdot [R]}} \cdot {(1 + (γ - 1) \cdot \frac{M^{2}}{2})}^{- \frac{γ + 1}{2 \cdot γ - 2}}

m_a - Mass Flow Rate?M - Mach Number?A - Area?P_t - Total Pressure?γ - Specific Heat Ratio?M_molar - Molar Mass?T_tot - Total Temperature?[R] - Universal gas constant?

Mass Flow Rate through Engine Example

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Here is how the Mass Flow Rate through Engine equation looks like with Values.

Here is how the Mass Flow Rate through Engine equation looks like with Units.

Here is how the Mass Flow Rate through Engine equation looks like.

23.4985 = 1.4 \cdot 8.5 \cdot 0.004 \cdot \sqrt{1.33 \cdot \frac{6.5}{590 \cdot 8.3145}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

23.4985kg/s = 1.4 \cdot 8.5m² \cdot 0.004MPa \cdot \sqrt{1.33 \cdot \frac{6.5g/mol}{590K \cdot 8.3145}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

23.4985 = 1.4 \cdot 8.5 \cdot 0.004 \cdot \sqrt{1.33 \cdot \frac{6.5}{590 \cdot 8.3145}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

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Mass Flow Rate through Engine Solution

Follow our step by step solution on how to calculate Mass Flow Rate through Engine?

FIRST Step Consider the formula

m a = M \cdot A \cdot P t \cdot \sqrt{γ \cdot \frac{M molar}{T tot \cdot [R]}} \cdot {(1 + (γ - 1) \cdot \frac{M^{2}}{2})}^{- \frac{γ + 1}{2 \cdot γ - 2}}

Next Step Substitute values of Variables

∴

m a = 1.4 \cdot 8.5m² \cdot 0.004MPa \cdot \sqrt{1.33 \cdot \frac{6.5g/mol}{590K \cdot [R]}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

Next Step Substitute values of Constants

∴

m a = 1.4 \cdot 8.5m² \cdot 0.004MPa \cdot \sqrt{1.33 \cdot \frac{6.5g/mol}{590K \cdot 8.3145}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

Next Step Convert Units

∴

m a = 1.4 \cdot 8.5m² \cdot 4000Pa \cdot \sqrt{1.33 \cdot \frac{0.0065kg/mol}{590K \cdot 8.3145}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

Next Step Prepare to Evaluate

∴

m a = 1.4 \cdot 8.5 \cdot 4000 \cdot \sqrt{1.33 \cdot \frac{0.0065}{590 \cdot 8.3145}} \cdot {(1 + (1.33 - 1) \cdot \frac{{1.4}^{2}}{2})}^{- \frac{1.33 + 1}{2 \cdot 1.33 - 2}}

Next Step Evaluate

∴

m a = 23.4984808798025kg/s

LAST Step Rounding Answer

∴

m a = 23.4985kg/s

Mass Flow Rate through Engine Formula Elements

Variables

Constants

Functions

Mass Flow Rate

Mass Flow Rate represents the amount of mass passing through a system per unit of time.

Symbol: m_a

Measurement: Mass Flow RateUnit: kg/s

Note: Value should be greater than 0.

Formulas to find Mass Flow Rate

Mach Number

Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Area

The area is the amount of two-dimensional space taken up by an object.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area

Total Pressure

Total Pressure is the sum of all the forces that the gas molecules exert on the walls of their container.

Symbol: P_t

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Total 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

Molar Mass

Molar Mass is the mass of a given substance divided by the amount of substance.

Symbol: M_molar

Measurement: Molar MassUnit: g/mol

Note: Value can be positive or negative.

Formulas to find Molar Mass

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

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 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

How to Evaluate Mass Flow Rate through Engine?

Mass Flow Rate through Engine evaluator 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 evaluate 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 evaluate Mass Flow Rate through Engine using this online evaluator? To use this online evaluator for Mass Flow Rate through Engine, enter Mach Number (M), Area (A), Total Pressure (P_t), Specific Heat Ratio (γ), Molar Mass (M_molar) & Total Temperature (T_tot) and hit the calculate button.

FAQs on Mass Flow Rate through Engine

What is the formula to find Mass Flow Rate through Engine?

The formula of Mass Flow Rate through Engine is expressed as 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)). Here is an example- 23.49848 = 1.4*8.5*4000*sqrt(1.33*0.0065/(590*[R]))*(1+(1.33-1)*1.4^2/2)^(-(1.33+1)/(2*1.33-2)).

How to calculate Mass Flow Rate through Engine?

With Mach Number (M), Area (A), Total Pressure (P_t), Specific Heat Ratio (γ), Molar Mass (M_molar) & Total Temperature (T_tot) we can find Mass Flow Rate through Engine using the formula - 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)). This formula also uses Universal gas constant and Square Root (sqrt) function(s).

Can the Mass Flow Rate through Engine be negative?

No, the Mass Flow Rate through Engine, measured in Mass Flow Rate cannot be negative.

Which unit is used to measure Mass Flow Rate through Engine?

Mass Flow Rate through Engine is usually measured using the Kilogram per Second[kg/s] for Mass Flow Rate. Gram per Second[kg/s], Gram per Hour[kg/s], Milligram per Minute[kg/s] are the few other units in which Mass Flow Rate through Engine can be measured.

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Mass Flow Rate through Engine Formula

Mass Flow Rate through Engine Example

Mass Flow Rate through Engine Solution

Mass Flow Rate through Engine Formula Elements

Other formulas in Thrust and Power Generation category

How to Evaluate Mass Flow Rate through Engine?

FAQs on Mass Flow Rate through Engine

Variable Name