Max work output in Brayton cycle Calculator

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✖Compressor efficiency is the ratio of input kinetic energy to the work done.ⓘ Compressor Efficiency [η_c]			+10% -10%
✖The Temperature at Inlet of Compressor in Brayton cycle is entry temperature of the air.ⓘ Temperature at Inlet of Compressor in Brayton [T_B1]			+10% -10%
✖The Temperature at Inlet to Turbine in Brayton Cycle is the temperature of the air after heat addition and combustion.ⓘ Temperature at Inlet to Turbine in Brayton Cycle [T_B3]			+10% -10%
✖Turbine Efficiency shows how efficient the turbine is in the process.ⓘ Turbine Efficiency [η_turbine]			+10% -10%

✖Maximum Work done in Brayton Cycle is the maximum output that can be achieved at a certain pressure ratio.ⓘ Max work output in Brayton cycle [W_pmax]

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Formula

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Max work output in Brayton cycle

Formula

`("W"_{"p"}"max") = (1005*1/"η"_{"c"})*"T"_{"B1"}*(sqrt("T"_{"B3"}/"T"_{"B1"}*"η"_{"c"}*"η"_{"turbine"})-1)^2`

Example

`"102.8266KJ"=(1005*1/"0.3")*"290K"*(sqrt("550K"/"290K"*"0.3"*"0.8")-1)^2`

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Max work output in Brayton cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
W_pmax = (1005*1/η_c)*T_B1*(sqrt(T_B3/T_B1*η_c*η_turbine)-1)^2
This formula uses 1 Functions, 5 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

Maximum Work done in Brayton Cycle - (Measured in Joule) - Maximum Work done in Brayton Cycle is the maximum output that can be achieved at a certain pressure ratio.
Compressor Efficiency - Compressor efficiency is the ratio of input kinetic energy to the work done.
Temperature at Inlet of Compressor in Brayton - (Measured in Kelvin) - The Temperature at Inlet of Compressor in Brayton cycle is entry temperature of the air.
Temperature at Inlet to Turbine in Brayton Cycle - (Measured in Kelvin) - The Temperature at Inlet to Turbine in Brayton Cycle is the temperature of the air after heat addition and combustion.
Turbine Efficiency - Turbine Efficiency shows how efficient the turbine is in the process.

STEP 1: Convert Input(s) to Base Unit

Compressor Efficiency: 0.3 --> No Conversion Required
Temperature at Inlet of Compressor in Brayton: 290 Kelvin --> 290 Kelvin No Conversion Required
Temperature at Inlet to Turbine in Brayton Cycle: 550 Kelvin --> 550 Kelvin No Conversion Required
Turbine Efficiency: 0.8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_pmax = (1005*1/η_c)*T_B1*(sqrt(T_B3/T_B1*η_c*η_turbine)-1)^2 --> (1005*1/0.3)*290*(sqrt(550/290*0.3*0.8)-1)^2

Evaluating ... ...

W_pmax = 102826.550730392

STEP 3: Convert Result to Output's Unit

102826.550730392 Joule -->102.826550730392 Kilojoule (Check conversion here)

FINAL ANSWER

102.826550730392 ≈ 102.8266 Kilojoule <-- Maximum Work done in Brayton Cycle

(Calculation completed in 00.004 seconds)

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DIT UNIVERSITY (DITU), Dehradun

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< 19 Thermodynamics and Governing Equations Calculators

Max work output in Brayton cycle

Go 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

Choked Mass Flow Rate given specific heat ratio

Go Choked Mass Flow Rate = (Heat Capacity Ratio/(sqrt(Heat Capacity Ratio-1)))*((Heat Capacity Ratio+1)/2)^(-((Heat Capacity Ratio+1)/(2*Heat Capacity Ratio-2)))

Choked Mass Flow Rate

Go Choked Mass Flow Rate = (Mass Flow Rate*sqrt(Specific Heat Capacity at Constant Pressure*Temperature))/(Nozzle Throat Area*Throat Pressure)

Stagnation Velocity of Sound given Specific Heat at Constant Pressure

Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Specific Heat Capacity at Constant Pressure*Stagnation Temperature)

Specific Heat of mixed out gas

Go Specific Heat of Mixed Gas = (Specific Heat of Core Gas+Bypass Ratio*Specific Heat of Bypass Air)/(1+Bypass Ratio)

Stagnation Temperature

Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)

Stagnation Velocity of Sound

Go Stagnation Velocity of Sound = sqrt(Heat Capacity Ratio*[R]*Stagnation Temperature)

Speed of Sound

Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)

Stagnation Velocity of Sound given Stagnation Enthalpy

Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Stagnation Enthalpy)

Heat Capacity Ratio

Go Heat Capacity Ratio = Specific Heat Capacity at Constant Pressure/Specific Heat Capacity at Constant Volume

Efficiency of cycle

Go Efficiency of Cycle = (Turbine Work-Compressor Work)/Heat

Internal Energy of Perfect Gas at given Temperature

Go Internal Energy = Specific Heat Capacity at Constant Volume*Temperature

Enthalpy of Ideal Gas at given Temperature

Go Enthalpy = Specific Heat Capacity at Constant Pressure*Temperature

Stagnation enthalpy

Go Stagnation Enthalpy = Enthalpy+(Velocity of Fluid Flow^2)/2

Efficiency of Joule cycle

Go Efficiency of Joule Cycle = Net Work Output/Heat

Pressure Ratio

Go Pressure Ratio = Final Pressure/Initial Pressure

Work ratio in practical cycle

Go Work Ratio = 1-(Compressor Work/Turbine Work)

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Max work output in Brayton cycle Formula

What is the condition for maximum work in brayton cycle?

It occurs at an optimum pressure ratio, which is found by differentiating the work output equation with respect to pressure ratio.

How to Calculate Max work output in Brayton cycle?

Max work output in Brayton cycle calculator 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 calculate the Maximum Work done in Brayton Cycle, Max work output in Brayton cycle formula is defined as the maximum work that can be achieved from brayton cycle at a particular pressure ratio. Maximum Work done in Brayton Cycle is denoted by W_pmax symbol.

How to calculate Max work output in Brayton cycle using this online calculator? To use this online calculator 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. Here is how the Max work output in Brayton cycle calculation can be explained with given input values -> 0.102827 = (1005*1/0.3)*290*(sqrt(550/290*0.3*0.8)-1)^2.

FAQ

What is Max work output in Brayton cycle?

Max work output in Brayton cycle formula is defined as the maximum work that can be achieved from brayton cycle at a particular pressure ratio and is represented as W_pmax = (1005*1/η_c)*T_B1*(sqrt(T_B3/T_B1*η_c*η_turbine)-1)^2 or 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. Compressor efficiency is the ratio of input kinetic energy to the work done, The Temperature at Inlet of Compressor in Brayton cycle is entry temperature of the air, The Temperature at Inlet to Turbine in Brayton Cycle is the temperature of the air after heat addition and combustion & Turbine Efficiency shows how efficient the turbine is in the process.

How to calculate Max work output in Brayton cycle?

Max work output in Brayton cycle formula is defined as the maximum work that can be achieved from brayton cycle at a particular pressure ratio is calculated using 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 calculate Max work output in Brayton cycle, you need 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). With our tool, you need to enter the respective value for Compressor Efficiency, Temperature at Inlet of Compressor in Brayton, Temperature at Inlet to Turbine in Brayton Cycle & Turbine Efficiency 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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