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Propellant Mass Flow Rate Formula

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The Propellant Mass Flow Rate refers to the amount of mass that flows through a given point in the rocket propulsion system per unit time. Check FAQs

ṁ = (A t \cdot P 1 \cdot γ) \cdot \frac{\sqrt{{(\frac{2}{γ + 1})}^{\frac{γ + 1}{γ - 1}}}}{\sqrt{γ \cdot [R] \cdot T 1}}

ṁ - Propellant Mass Flow Rate?A_t - Nozzle Throat Area?P₁ - Inlet Nozzle Pressure?γ - Specific Heat Ratio?T₁ - Temperature at Chamber?[R] - Universal gas constant?

Propellant Mass Flow Rate Example

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

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

Here is how the Propellant Mass Flow Rate equation looks like.

11.3282 = (0.21 \cdot 0.0037 \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot 8.3145 \cdot 256}}

11.3282kg/s = (0.21m² \cdot 0.0037MPa \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot 8.3145 \cdot 256K}}

11.3282 = (0.21 \cdot 0.0037 \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot 8.3145 \cdot 256}}

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Propellant Mass Flow Rate Solution

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

FIRST Step Consider the formula

ṁ = (A t \cdot P 1 \cdot γ) \cdot \frac{\sqrt{{(\frac{2}{γ + 1})}^{\frac{γ + 1}{γ - 1}}}}{\sqrt{γ \cdot [R] \cdot T 1}}

Next Step Substitute values of Variables

∴

ṁ = (0.21m² \cdot 0.0037MPa \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot [R] \cdot 256K}}

Next Step Substitute values of Constants

∴

ṁ = (0.21m² \cdot 0.0037MPa \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot 8.3145 \cdot 256K}}

Next Step Convert Units

∴

ṁ = (0.21m² \cdot 3700Pa \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot 8.3145 \cdot 256K}}

Next Step Prepare to Evaluate

∴

ṁ = (0.21 \cdot 3700 \cdot 1.33) \cdot \frac{\sqrt{{(\frac{2}{1.33 + 1})}^{\frac{1.33 + 1}{1.33 - 1}}}}{\sqrt{1.33 \cdot 8.3145 \cdot 256}}

Next Step Evaluate

∴

ṁ = 11.328154115397kg/s

LAST Step Rounding Answer

∴

ṁ = 11.3282kg/s

Propellant Mass Flow Rate Formula Elements

Variables

Constants

Functions

Propellant Mass Flow Rate

The Propellant Mass Flow Rate refers to the amount of mass that flows through a given point in the rocket propulsion system per unit time.

Symbol: ṁ

Measurement: Mass Flow RateUnit: kg/s

Note: Value should be greater than 0.

Formulas to find Propellant Mass Flow Rate

Nozzle Throat Area

The nozzle throat area refers to the cross-sectional area of the narrowest part of a propulsion nozzle, known as the throat.

Symbol: A_t

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Nozzle Throat Area

Inlet Nozzle Pressure

Inlet Nozzle Pressure represents the pressure of the incoming air or propellant before it enters the combustion chamber or the turbine section.

Symbol: P₁

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Inlet Nozzle 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

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

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 Propellents category

Go Propellant Mixture Ratio

r = \frac{ṁ o}{ṁ f}

Go Oxidizer Mass Flow Rate

ṁ o = \frac{r \cdot ṁ}{r + 1}

Go Fuel Mass Flow rate

ṁ f = \frac{ṁ}{r + 1}

How to Evaluate Propellant Mass Flow Rate?

Propellant Mass Flow Rate evaluator uses Propellant Mass Flow Rate = (Nozzle Throat Area*Inlet Nozzle Pressure*Specific Heat Ratio)*sqrt((2/(Specific Heat Ratio+1))^((Specific Heat Ratio+1)/(Specific Heat Ratio-1)))/sqrt(Specific Heat Ratio*[R]*Temperature at Chamber) to evaluate the Propellant Mass Flow Rate, Propellant Mass Flow Rate formula is defined as a measure of the mass of propellant consumed per unit time in rocket propulsion systems, which is crucial for determining thrust and overall performance of the rocket engine. Propellant Mass Flow Rate is denoted by ṁ symbol.

How to evaluate Propellant Mass Flow Rate using this online evaluator? To use this online evaluator for Propellant Mass Flow Rate, enter Nozzle Throat Area (A_t), Inlet Nozzle Pressure (P₁), Specific Heat Ratio (γ) & Temperature at Chamber (T₁) and hit the calculate button.

FAQs on Propellant Mass Flow Rate

What is the formula to find Propellant Mass Flow Rate?

The formula of Propellant Mass Flow Rate is expressed as Propellant Mass Flow Rate = (Nozzle Throat Area*Inlet Nozzle Pressure*Specific Heat Ratio)*sqrt((2/(Specific Heat Ratio+1))^((Specific Heat Ratio+1)/(Specific Heat Ratio-1)))/sqrt(Specific Heat Ratio*[R]*Temperature at Chamber). Here is an example- 11.32815 = (0.21*3700*1.33)*sqrt((2/(1.33+1))^((1.33+1)/(1.33-1)))/sqrt(1.33*[R]*256).

How to calculate Propellant Mass Flow Rate?

With Nozzle Throat Area (A_t), Inlet Nozzle Pressure (P₁), Specific Heat Ratio (γ) & Temperature at Chamber (T₁) we can find Propellant Mass Flow Rate using the formula - Propellant Mass Flow Rate = (Nozzle Throat Area*Inlet Nozzle Pressure*Specific Heat Ratio)*sqrt((2/(Specific Heat Ratio+1))^((Specific Heat Ratio+1)/(Specific Heat Ratio-1)))/sqrt(Specific Heat Ratio*[R]*Temperature at Chamber). This formula also uses Universal gas constant and Square Root (sqrt) function(s).

Can the Propellant Mass Flow Rate be negative?

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

Which unit is used to measure Propellant Mass Flow Rate?

Propellant Mass Flow Rate 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 Propellant Mass Flow Rate can be measured.

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Propellant Mass Flow Rate Formula

Propellant Mass Flow Rate Example

Propellant Mass Flow Rate Solution

Propellant Mass Flow Rate Formula Elements

Other formulas in Propellents category

How to Evaluate Propellant Mass Flow Rate?

FAQs on Propellant Mass Flow Rate

Variable Name