Work of Turbine Calculator

Mass flow rate

Specific heat (Cp)

Turbine inlet temperature

Turbine outlet temperature

Turbine power output

Apply isentropic efficiency

Bring the ideal answer down to the real shaft output.

Subtract compressor work

See the net shaft power left after the compressor takes its share.

Estimate from a pressure ratio

Work out the ideal isentropic outlet temperature and work.

Engine architecture

Turbojet or turbofan

Turboshaft or turboprop

Industrial or power generation

Turbine power output

Specific work (per kg of gas): kJ/kg
Temperature drop (K)

In a turboshaft or turboprop, a free power turbine downstream of the gas generator turns the leftover energy into shaft torque for a rotor, propeller, or gearbox.

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Show the performance chart and grid

Plot power against the temperature drop and mass flow.

Turbine power (MW) by mass flow and temperature drop
Drop (K)	3 kg/s	5 kg/s	7 kg/s
200	0.69	1.15	1.61
400	1.38	2.3	3.22
600	2.07	3.45	4.83

The turbine is the part of a gas turbine engine where actual work is done. The hot pressurised gases produced in the combustor flow through the turbine and expand, releasing energy. Some of this energy turns the compressor which is mounted on the same shaft while the rest powers whatever load the engine is designed to drive - whether it be a propeller, helicopter rotor, generator or jet thrust exiting from the tail. This calculator can calculate the power extracted by the turbine from the gas stream and also supports an inverse calculation: leave any field blank to have its value determined.

What is meant by turbine work?

The turbine work refers to the mechanical energy that is extracted by the turbine from the gas flow during the expansion and cooling of the gas. As this process approximates an ideal gas expansion process, this amount of energy corresponds to the temperature change experienced by the gas before it flows through the turbine and after it has flowed through the turbine. Multiplying the temperature change by the mass flow rate and the specific heat capacity of the gas gives the power. If this is expressed per kilogram of gas instead of per second of gas, then one obtains the specific work.

Formula for turbine work:

For an ideal gas, the power output of a turbine is equal to the product of mass flow rate, specific heat and temperature change.

W_t = \dot{m}\,C_p\,(T_{in} - T_{out})

W_t is the power in watts, m-dot is the mass flow rate, C_p is the specific heat capacity at constant pressure, T_in and T_out are the inlet and outlet temperatures respectively. Absolute temperatures are used so that the temperature difference makes physical sense. The calculator accepts Kelvin, Celsius or Fahrenheit and converts them for you since the temperature difference in Kelvin has the same numerical value as the temperature difference in Celsius.

An example calculation:

Suppose you are sizing a gas turbine for a helicopter turboshaft. The power turbine receives five kilograms of hot gas per second with an inlet temperature of 1300 K, and the outlet temperature is 900 K, with a specific heat capacity of 1150 J/(kg·K). Plugging these values in:

W_t = 5 \times 1{,}150 \times (1{,}300 - 900) = 2{,}300{,}000\ \text{W} = 2.3\ \text{MW}

So after subtracting the energy required by the gas turbine compressor to maintain its rotation, there is still 2.3 megawatts of power being transferred into the rotor system.

Specific work:

If you remove the mass flow, you get the specific work, i.e. the energy extracted per kilogram of gas:

w_t = C_p\,(T_{in} - T_{out})

With the same values, specific work w_t is equal to 1.150 multiplied by 400, which is 460,000 J/kg, or 460 kJ/kg. This value is used in normal analysis to compare different turbine designs and allows for avoiding disturbances due to the size of the engine when assessing it.

Symbol	Meaning	Example
W_t	Turbine power output	2.3 MW
m-dot	Mass flow rate	5 kg/s
C_p	Specific heat at constant pressure	1,150 J/(kg K)
T_in	Turbine inlet temperature	1,300 K
T_out	Turbine outlet temperature	900 K
w_t	Specific work	460 kJ/kg

Other applications of the same equation

This formula fulfills different tasks in various engine types. In turbojet or propeller turbines the high-pressure turbine has only one task: it produces the exact power required for the compressor. If the power is too low, the motor speed will drop. In turboshaft and turboprop engines an additional free-running turbine stage is added to use the remaining energy to drive the rotor, propeller or transmission. Industrial gas turbines let the gas expand as far as possible in order to drive a generator; combined-cycle plants direct the still hot exhaust gases into a steam cycle, which increases the overall efficiency by more than 60%.

What factors affect the outcome?

Four input values determine the result and their effects are varied. The turbine inlet temperature is a critical factor as the higher the operating temperature, the more power will be gained. Modern engines reach temperatures of 1600 to 1900 K which is also why the first blades are made from single crystal casting and have cooling channels. The mass flow affects the power linearly; doubling the air mass flow doubles the power. The temperature drop is the other half of the equation but too much expansion in too few stages can hurt efficiency. The effect of specific heat is less pronounced and increases with increasing temperature, dependent on gas composition.

Some important notes

Please use absolute temperatures; the calculator will convert from Celsius or Fahrenheit before calculation. If specific heat (C_p) is not known, 1.150 J/(kg K) can be used as a reasonable starting point for combustion gases, while air at room temperature is closer to 1.005. Note that direct application of the formula gives ideal values; actual turbine efficiencies are between 85% and 92%, so enable the efficiency option to adjust the values to match the actual shaft output level. If you're doing a full engine cycle analysis, this will give you the total power available from the turbine; use the "Net Output" option to subtract out the compressor's demand and see how much power is available for useful work.

Frequently asked questions

What is the difference between turbine work and turbine power?

Although these terms are often used synonymously, they are not identical. This calculator outputs power in watts or kilowatts which is the energy per unit time. The specific work, given in joules per kg, is the energy of the gas per mass unit; it is determined by the same equation without considering the mass flow rate.

How is the pressure ratio related to temperature change?

For an ideal expansion, the ratio of exit to inlet temperature is equal to the power of (gamma minus one) divided by gamma where gamma for hot combustion gases is approximately 1.33. A real turbine does not achieve this ideal state so actual temperature drop will be less than the isentropic temperature drop. With pressure ratio option enabled, you can display the ideal exit temperature and work under given expansion conditions.

Why is turbine inlet temperature important?

A 100 K increase in inlet temperature increases thermal efficiency by about 2% to 3%, which is why manufacturers invest so much in cooling and blade materials. In the best engines, the inlet temperature exceeds the melting point of the alloy used, and blades can only withstand these temperatures with air cooling and ceramic coatings.

Does the turbine section do more work than the compressor section?

It must be, otherwise the engine cannot run. The remaining power is what makes the engine work; in turboshaft engines this comes from shaft power, in turbojet engines from jet speed, and in turbofan engines from both. Use the "Net Output" option to subtract compressor requirements and find out how much power remains.

What specific heat capacity should I use?

For the combustion gases inside a turbine 1.150 J/(kg K) is a good standard value to use. Air at ambient temperature is about 1.005 but the exact value depends on the temperature and gas composition so tables of actual mixtures are best.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

NASA Glenn Research Center: Turbine Work
Derivation of turbine work from the enthalpy drop across the turbine.
Wikipedia: Brayton cycle
The thermodynamic cycle behind gas turbine engines.