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Ideal Turbine Work given Pressure Ratio Formula

GoTurbine Work given Enthalpy Formula

GoTurbine Work in Gas Turbine given Temperature Formula

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Turbine Work represents the work done by a turbine in converting the thermal energy of a fluid into mechanical energy. Check FAQs

W T = C p \cdot T 3 \cdot (\frac{{P r}^{\frac{γ - 1}{γ}} - 1}{{P r}^{\frac{γ - 1}{γ}}})

W_T - Turbine Work?C_p - Specific heat at constant pressure?T₃ - Turbine Inlet Temperature?P_r - Turbine Pressure Ratio?γ - Heat Capacity Ratio?

Ideal Turbine Work given Pressure Ratio Example

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Here is how the Ideal Turbine Work given Pressure Ratio equation looks like with Values.

Here is how the Ideal Turbine Work given Pressure Ratio equation looks like with Units.

Here is how the Ideal Turbine Work given Pressure Ratio equation looks like.

873.4321 = 1.248 \cdot 1300 \cdot (\frac{{14.96}^{\frac{1.4 - 1}{1.4}} - 1}{{14.96}^{\frac{1.4 - 1}{1.4}}})

873.4321KJ = 1.248kJ/kg*K \cdot 1300K \cdot (\frac{{14.96}^{\frac{1.4 - 1}{1.4}} - 1}{{14.96}^{\frac{1.4 - 1}{1.4}}})

873.4321 = 1.248 \cdot 1300 \cdot (\frac{{14.96}^{\frac{1.4 - 1}{1.4}} - 1}{{14.96}^{\frac{1.4 - 1}{1.4}}})

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Ideal Turbine Work given Pressure Ratio Solution

Follow our step by step solution on how to calculate Ideal Turbine Work given Pressure Ratio?

FIRST Step Consider the formula

W T = C p \cdot T 3 \cdot (\frac{{P r}^{\frac{γ - 1}{γ}} - 1}{{P r}^{\frac{γ - 1}{γ}}})

Next Step Substitute values of Variables

∴

W T = 1.248kJ/kg*K \cdot 1300K \cdot (\frac{{14.96}^{\frac{1.4 - 1}{1.4}} - 1}{{14.96}^{\frac{1.4 - 1}{1.4}}})

Next Step Convert Units

∴

W T = 1248J/(kg*K) \cdot 1300K \cdot (\frac{{14.96}^{\frac{1.4 - 1}{1.4}} - 1}{{14.96}^{\frac{1.4 - 1}{1.4}}})

Next Step Prepare to Evaluate

∴

W T = 1248 \cdot 1300 \cdot (\frac{{14.96}^{\frac{1.4 - 1}{1.4}} - 1}{{14.96}^{\frac{1.4 - 1}{1.4}}})

Next Step Evaluate

∴

W T = 873432.11385659J

Next Step Convert to Output's Unit

∴

W T = 873.43211385659KJ

LAST Step Rounding Answer

∴

W T = 873.4321KJ

Ideal Turbine Work given Pressure Ratio Formula Elements

Variables

Turbine Work

Turbine Work represents the work done by a turbine in converting the thermal energy of a fluid into mechanical energy.

Symbol: W_T

Measurement: EnergyUnit: KJ

Note: Value should be greater than 0.

Formulas to find Turbine Work

Specific heat at constant pressure

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.

Symbol: C_p

Measurement: Specific Heat CapacityUnit: kJ/kg*K

Note: Value can be positive or negative.

Formulas to find Specific heat at constant pressure

Turbine Inlet Temperature

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.

Symbol: T₃

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Turbine Inlet Temperature

Turbine Pressure Ratio

Turbine Pressure Ratio refers to the ratio of the pressure at the turbine inlet to the pressure at the turbine outlet.

Symbol: P_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Turbine Pressure Ratio

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.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Heat Capacity Ratio

Other Formulas to find Turbine Work

Go Turbine Work given Enthalpy

W T = h 3 - h 4

Go Turbine Work in Gas Turbine given Temperature

W T = C p \cdot (T 3 - T 4)

Other formulas in Turbine category

Go Degree of Reaction for Turbine

R = \frac{ΔE rotor drop}{ΔE stage drop}

Go Efficiency of turbine in actual gas turbine cycle

η T = \frac{T 3 - T 4}{T 3 - T 4,s}

Go Efficiency of Turbine in actual Gas Turbine Cycle given Enthalpy

η T = \frac{h 3 - h 4}{h 3 - h4 s}

How to Evaluate Ideal Turbine Work given Pressure Ratio?

Ideal Turbine Work given Pressure Ratio evaluator 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 evaluate 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 evaluate Ideal Turbine Work given Pressure Ratio using this online evaluator? To use this online evaluator 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.

FAQs on Ideal Turbine Work given Pressure Ratio

What is the formula to find Ideal Turbine Work given Pressure Ratio?

The formula of Ideal Turbine Work given Pressure Ratio is expressed as 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))). Here is an example- 0.650036 = 1248*1300*((14.96^((1.4-1)/1.4)-1)/(14.96^((1.4-1)/1.4))).

How to calculate Ideal Turbine Work given Pressure Ratio?

With Specific heat at constant pressure (C_p), Turbine Inlet Temperature (T₃), Turbine Pressure Ratio (P_r) & Heat Capacity Ratio (γ) we can find Ideal Turbine Work given Pressure Ratio using the formula - 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))).

What are the other ways to Calculate Turbine Work?

Here are the different ways to Calculate Turbine Work-

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

Can the Ideal Turbine Work given Pressure Ratio be negative?

No, the Ideal Turbine Work given Pressure Ratio, measured in Energy cannot be negative.

Which unit is used to measure Ideal Turbine Work given Pressure Ratio?

Ideal Turbine Work given Pressure Ratio is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Ideal Turbine Work given Pressure Ratio can be measured.

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Ideal Turbine Work given Pressure Ratio Formula

​GoTurbine Work given Enthalpy Formula

​GoTurbine Work in Gas Turbine given Temperature Formula

Ideal Turbine Work given Pressure Ratio Example

Ideal Turbine Work given Pressure Ratio Solution

Ideal Turbine Work given Pressure Ratio Formula Elements

Other Formulas to find Turbine Work

Other formulas in Turbine category

How to Evaluate Ideal Turbine Work given Pressure Ratio?

FAQs on Ideal Turbine Work given Pressure Ratio

Variable Name

GoTurbine Work given Enthalpy Formula

GoTurbine Work in Gas Turbine given Temperature Formula