Ideal Turbine Work given Pressure Ratio Calculator

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Components of Gas Turbine

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Thermodynamics and Governing Equations

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✖Specific heat at constant pressure is the energy required to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant.ⓘ Specific heat at constant pressure [C_p]			+10% -10%
✖Turbine Inlet Temperature refers to the temperature of the fluid entering a turbine, such as the hot gases from combustion in a gas turbine engine.ⓘ Turbine Inlet Temperature [T₃]			+10% -10%
✖Turbine Pressure Ratio refers to the ratio of the pressure at the turbine inlet to the pressure at the turbine outlet.ⓘ Turbine Pressure Ratio [P_r]			+10% -10%
✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Heat Capacity Ratio [γ]			+10% -10%

✖Turbine Work represents the work done by a turbine in converting the thermal energy of a fluid into mechanical energy.ⓘ Ideal Turbine Work given Pressure Ratio [W_T]

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Formula

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Ideal Turbine Work given Pressure Ratio

Formula

`"W"_{"T"} = "C"_{"p"}*"T"_{"3"}*(("P"_{"r"}^(("γ"-1)/"γ")-1)/("P"_{"r"}^(("γ"-1)/"γ")))`

Example

`"873.4321KJ"="1.248kJ/kg*K"*"1300K"*((("14.96")^(("1.4"-1)/"1.4")-1)/(("14.96")^(("1.4"-1)/"1.4")))`

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Ideal Turbine Work given Pressure Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Turbine Work = Specific heat at constant pressure*Turbine Inlet Temperature*((Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)/(Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)))
W_T = C_p*T₃*((P_r^((γ-1)/γ)-1)/(P_r^((γ-1)/γ)))
This formula uses 5 Variables

Variables Used

Turbine Work - (Measured in Joule) - Turbine Work represents the work done by a turbine in converting the thermal energy of a fluid into mechanical energy.
Specific heat at constant pressure - (Measured in Joule per Kilogram per K) - Specific heat at constant pressure is the energy required to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant.
Turbine Inlet Temperature - (Measured in Kelvin) - Turbine Inlet Temperature refers to the temperature of the fluid entering a turbine, such as the hot gases from combustion in a gas turbine engine.
Turbine Pressure Ratio - Turbine Pressure Ratio refers to the ratio of the pressure at the turbine inlet to the pressure at the turbine outlet.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

STEP 1: Convert Input(s) to Base Unit

Specific heat at constant pressure: 1.248 Kilojoule per Kilogram per K --> 1248 Joule per Kilogram per K (Check conversion here)
Turbine Inlet Temperature: 1300 Kelvin --> 1300 Kelvin No Conversion Required
Turbine Pressure Ratio: 14.96 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_T = C_p*T₃*((P_r^((γ-1)/γ)-1)/(P_r^((γ-1)/γ))) --> 1248*1300*((14.96^((1.4-1)/1.4)-1)/(14.96^((1.4-1)/1.4)))

Evaluating ... ...

W_T = 873432.11385659

STEP 3: Convert Result to Output's Unit

873432.11385659 Joule -->873.43211385659 Kilojoule (Check conversion here)

FINAL ANSWER

873.43211385659 ≈ 873.4321 Kilojoule <-- Turbine Work

(Calculation completed in 00.009 seconds)

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Home » Physics » Aeroengines » Components of Gas Turbine » Turbine » Ideal Turbine Work given Pressure Ratio

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Institute of Aeronautical Engineering (IARE), Hyderabad

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< 6 Turbine Calculators

Ideal Turbine Work given Pressure Ratio

Go Turbine Work = Specific heat at constant pressure*Turbine Inlet Temperature*((Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)/(Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)))

Efficiency of turbine in actual gas turbine cycle

Go Efficiency of Turbine = (Turbine Inlet Temperature-Turbine Exit Temperature)/(Turbine Inlet Temperature-Isentropic Turbine Exit Temperature)

Efficiency of Turbine in actual Gas Turbine Cycle given Enthalpy

Go Efficiency of Turbine = (Turbine Inlet Enthalpy-Turbine Exit Enthalpy)/(Turbine Inlet Enthalpy-Isentropic Turbine Exit Enthalpy)

Turbine Work in Gas Turbine given Temperature

Go Turbine Work = Specific heat at constant pressure*(Turbine Inlet Temperature-Turbine Exit Temperature)

Degree of Reaction for Turbine

Go Degree of Reaction = (Enthalpy Drop in Rotor)/(Enthalpy Drop in Stage)

Turbine Work given Enthalpy

Go Turbine Work = Turbine Inlet Enthalpy-Turbine Exit Enthalpy

Ideal Turbine Work given Pressure Ratio Formula

What is work done?

Work done is a process, where energy given as input to the system is utilized to perform some useful work.

How to Calculate Ideal Turbine Work given Pressure Ratio?

Ideal Turbine Work given Pressure Ratio calculator uses Turbine Work = Specific heat at constant pressure*Turbine Inlet Temperature*((Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)/(Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))) to calculate the Turbine Work, Ideal Turbine Work given Pressure Ratio formula is defined as the work done by a turbine in expanding the gases ideally (isentropically). Turbine Work is denoted by W_T symbol.

How to calculate Ideal Turbine Work given Pressure Ratio using this online calculator? To use this online calculator for Ideal Turbine Work given Pressure Ratio, enter Specific heat at constant pressure (C_p), Turbine Inlet Temperature (T₃), Turbine Pressure Ratio (P_r) & Heat Capacity Ratio (γ) and hit the calculate button. Here is how the Ideal Turbine Work given Pressure Ratio calculation can be explained with given input values -> 0.650036 = 1248*1300*((14.96^((1.4-1)/1.4)-1)/(14.96^((1.4-1)/1.4))).

FAQ

What is Ideal Turbine Work given Pressure Ratio?

Ideal Turbine Work given Pressure Ratio formula is defined as the work done by a turbine in expanding the gases ideally (isentropically) and is represented as W_T = C_p*T₃*((P_r^((γ-1)/γ)-1)/(P_r^((γ-1)/γ))) or Turbine Work = Specific heat at constant pressure*Turbine Inlet Temperature*((Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)/(Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))). Specific heat at constant pressure is the energy required to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant, Turbine Inlet Temperature refers to the temperature of the fluid entering a turbine, such as the hot gases from combustion in a gas turbine engine, Turbine Pressure Ratio refers to the ratio of the pressure at the turbine inlet to the pressure at the turbine outlet & The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

How to calculate Ideal Turbine Work given Pressure Ratio?

Ideal Turbine Work given Pressure Ratio formula is defined as the work done by a turbine in expanding the gases ideally (isentropically) is calculated using Turbine Work = Specific heat at constant pressure*Turbine Inlet Temperature*((Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)/(Turbine Pressure Ratio^((Heat Capacity Ratio-1)/Heat Capacity Ratio))). To calculate Ideal Turbine Work given Pressure Ratio, you need Specific heat at constant pressure (C_p), Turbine Inlet Temperature (T₃), Turbine Pressure Ratio (P_r) & Heat Capacity Ratio (γ). With our tool, you need to enter the respective value for Specific heat at constant pressure, Turbine Inlet Temperature, Turbine Pressure Ratio & Heat Capacity Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Turbine Work?

In this formula, Turbine Work uses Specific heat at constant pressure, Turbine Inlet Temperature, Turbine Pressure Ratio & Heat Capacity Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -

Turbine Work = Turbine Inlet Enthalpy-Turbine Exit Enthalpy
Turbine Work = Specific heat at constant pressure*(Turbine Inlet Temperature-Turbine Exit Temperature)

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