Isentropic Efficiencies of Steady-flow Devices

A standard for efficiencies We have the Carnot cycle for cyclic devices.We have the Carnot cycle for cyclic devices. Need something for discreet devices.Need something for discreet devices. Most designed to work adiabatically.Most designed to work adiabatically. –Best is always reversible. Therefore, isentropic efficiencies are used.Therefore, isentropic efficiencies are used. –Under isentropic conditions for the same inlet state and same outlet pressure.

Isentropic efficiency of a turbine Defined as: Actual turbine work/Isentropic turbine work.Defined as: Actual turbine work/Isentropic turbine work. –both at same inlet state and exit pressure. Usually ignore kinetic and potential energy changes.Usually ignore kinetic and potential energy changes. So work is just the change in enthalpy.So work is just the change in enthalpy. –That is if it is adiabatic.

Adiabatic turbine

Adiabatic compressor Isentropic efficiency is inverted If the compressor is cooled, use isothermal efficiency: For a pump, the isentropic efficiency is:

Adiabatic nozzles – Actual KE at exit / Isentropic KE at exit If KE’s in are small and no work or Q: h 1 -h 2 = KE 2 Therefore: Which is the same as that of a turbine.

Remember that the 2s state is always hypothetical and is at the same pressure as the 2a state for all three devices.