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Max work output in Brayton cycle Formula

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Maximum Work done in Brayton Cycle is the maximum output that can be achieved at a certain pressure ratio. Check FAQs

W p max = (1005 \cdot \frac{1}{η c}) \cdot T B1 \cdot {(\sqrt{\frac{T B3}{T B1} \cdot η c \cdot η turbine} - 1)}^{2}

W_pmax - Maximum Work done in Brayton Cycle?η_c - Compressor Efficiency?T_B1 - Temperature at Inlet of Compressor in Brayton?T_B3 - Temperature at Inlet to Turbine in Brayton Cycle?η_turbine - Turbine Efficiency?

Max work output in Brayton cycle Example

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Here is how the Max work output in Brayton cycle equation looks like with Values.

Here is how the Max work output in Brayton cycle equation looks like with Units.

Here is how the Max work output in Brayton cycle equation looks like.

102.8266 = (1005 \cdot \frac{1}{0.3}) \cdot 290 \cdot {(\sqrt{\frac{550}{290} \cdot 0.3 \cdot 0.8} - 1)}^{2}

102.8266KJ = (1005 \cdot \frac{1}{0.3}) \cdot 290K \cdot {(\sqrt{\frac{550K}{290K} \cdot 0.3 \cdot 0.8} - 1)}^{2}

102.8266 = (1005 \cdot \frac{1}{0.3}) \cdot 290 \cdot {(\sqrt{\frac{550}{290} \cdot 0.3 \cdot 0.8} - 1)}^{2}

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Max work output in Brayton cycle Solution

Follow our step by step solution on how to calculate Max work output in Brayton cycle?

FIRST Step Consider the formula

W p max = (1005 \cdot \frac{1}{η c}) \cdot T B1 \cdot {(\sqrt{\frac{T B3}{T B1} \cdot η c \cdot η turbine} - 1)}^{2}

Next Step Substitute values of Variables

∴

W p max = (1005 \cdot \frac{1}{0.3}) \cdot 290K \cdot {(\sqrt{\frac{550K}{290K} \cdot 0.3 \cdot 0.8} - 1)}^{2}

Next Step Prepare to Evaluate

∴

W p max = (1005 \cdot \frac{1}{0.3}) \cdot 290 \cdot {(\sqrt{\frac{550}{290} \cdot 0.3 \cdot 0.8} - 1)}^{2}

Next Step Evaluate

∴

W p max = 102826.550730392J

Next Step Convert to Output's Unit

∴

W p max = 102.826550730392KJ

LAST Step Rounding Answer

∴

W p max = 102.8266KJ

Max work output in Brayton cycle Formula Elements

Variables

Functions

Maximum Work done in Brayton Cycle

Maximum Work done in Brayton Cycle is the maximum output that can be achieved at a certain pressure ratio.

Symbol: W_pmax

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Maximum Work done in Brayton Cycle

Compressor Efficiency

Compressor efficiency is the ratio of input kinetic energy to the work done.

Symbol: η_c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Compressor Efficiency

Temperature at Inlet of Compressor in Brayton

The Temperature at Inlet of Compressor in Brayton cycle is entry temperature of the air.

Symbol: T_B1

Measurement: TemperatureUnit: K

Note: Value should be greater than 10.

Formulas to find Temperature at Inlet of Compressor in Brayton

Temperature at Inlet to Turbine in Brayton Cycle

The Temperature at Inlet to Turbine in Brayton Cycle is the temperature of the air after heat addition and combustion.

Symbol: T_B3

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature at Inlet to Turbine in Brayton Cycle

Turbine Efficiency

Turbine Efficiency shows how efficient the turbine is in the process.

Symbol: η_turbine

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Turbine Efficiency

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 Thermodynamics and Governing Equations category

Go Heat Capacity Ratio

γ = \frac{C p}{C v}

Go Internal Energy of Perfect Gas at given Temperature

U = C v \cdot T

Go Enthalpy of Ideal Gas at given Temperature

h = C p \cdot T

Go Stagnation Velocity of Sound

a o = \sqrt{γ \cdot [R] \cdot T 0}

How to Evaluate Max work output in Brayton cycle?

Max work output in Brayton cycle evaluator uses Maximum Work done in Brayton Cycle = (1005*1/Compressor Efficiency)*Temperature at Inlet of Compressor in Brayton*(sqrt(Temperature at Inlet to Turbine in Brayton Cycle/Temperature at Inlet of Compressor in Brayton*Compressor Efficiency*Turbine Efficiency)-1)^2 to evaluate the Maximum Work done in Brayton Cycle, Max work output in Brayton cycle formula is defined as a representation of the maximum work that can be extracted from a Brayton cycle, highlighting the efficiency of the cycle in converting thermal energy into mechanical work. Maximum Work done in Brayton Cycle is denoted by W_pmax symbol.

How to evaluate Max work output in Brayton cycle using this online evaluator? To use this online evaluator for Max work output in Brayton cycle, enter Compressor Efficiency (η_c), Temperature at Inlet of Compressor in Brayton (T_B1), Temperature at Inlet to Turbine in Brayton Cycle (T_B3) & Turbine Efficiency (η_turbine) and hit the calculate button.

FAQs on Max work output in Brayton cycle

What is the formula to find Max work output in Brayton cycle?

The formula of Max work output in Brayton cycle is expressed as Maximum Work done in Brayton Cycle = (1005*1/Compressor Efficiency)*Temperature at Inlet of Compressor in Brayton*(sqrt(Temperature at Inlet to Turbine in Brayton Cycle/Temperature at Inlet of Compressor in Brayton*Compressor Efficiency*Turbine Efficiency)-1)^2. Here is an example- 0.102827 = (1005*1/0.3)*290*(sqrt(550/290*0.3*0.8)-1)^2.

How to calculate Max work output in Brayton cycle?

With Compressor Efficiency (η_c), Temperature at Inlet of Compressor in Brayton (T_B1), Temperature at Inlet to Turbine in Brayton Cycle (T_B3) & Turbine Efficiency (η_turbine) we can find Max work output in Brayton cycle using the formula - Maximum Work done in Brayton Cycle = (1005*1/Compressor Efficiency)*Temperature at Inlet of Compressor in Brayton*(sqrt(Temperature at Inlet to Turbine in Brayton Cycle/Temperature at Inlet of Compressor in Brayton*Compressor Efficiency*Turbine Efficiency)-1)^2. This formula also uses Square Root (sqrt) function(s).

Can the Max work output in Brayton cycle be negative?

Yes, the Max work output in Brayton cycle, measured in Energy can be negative.

Which unit is used to measure Max work output in Brayton cycle?

Max work output in Brayton cycle is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Max work output in Brayton cycle can be measured.

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