1. 7–12 ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES
Chapter 7

2. Isentropic Efficiency
The more closely the actual process approximates the idealized isentropic process, the better the device performs.
A parameter that expresses quantitatively how efficiently an actual device approximates an idealized one is the isentropic efficiency, which is a measure of the deviation of actual processes from the corresponding idealized ones.

3. Isentropic Efficiency of Turbines

7. Isentropic Efficiencies of Compressors and Pumps
When the changes in kinetic and potential energies of the gas being compressed
are negligible, the work input to an adiabatic compressor becomes
equal to the change in enthalpy,
When the changes in potential and kinetic energies of a liquid are negligible,
the isentropic efficiency of a pump will be

8. Isothermal efficiency of a Compressor
Sometimes compressors are cooled intentionally by utilizing fins or a water jacket placed around the casing to reduce the work input requirements
where wt and wa are the required work inputs to the compressor for the reversible isothermal and actual cases, respectively.

12. Isentropic Efficiency of Nozzles
Nozzles are essentially adiabatic devices and are used to accelerate a fluid.
The isentropic efficiency of a nozzle is
Nozzles involve no work
the fluid experiences little or no change in its potential energy as it flows through the device.
If the inlet velocity of the fluid is small relative to the exit velocity,
Then
the energy balance for this steady-flow device reduces to
Then the isentropic efficiency of the nozzle

14. Note that

15. But << Then it can be ignored

17. 7–173 Air enters a two-stage compressor at 100 kPa and 27°C and is compressed to 900 kPa. The pressure ratio across each stage is the same, and the air is cooled to the initial temperature between the two stages. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of 0.02 kg/s. What would your answer be if only one stage of compression were used?

18. Recall: for two stage compressors the pressure ratio for minimum work we found

19. Compare 4.44 and 5.26 KW

20. 7–210 Consider the turbocharger of an internal combustion engine
7–210 Consider the turbocharger of an internal combustion engine. The exhaust gases enter the turbine at 450°C at a rate of 0.02 kg/s and leave at 400°C. Air enters the compressor at 70°C and 95 kPa at a rate of kg/s and leaves at 135 kPa. The mechanical efficiency between the turbine and the compressor is 95 percent (5 percent of turbine work is lost during its transmission to the compressor). Using air properties for the exhaust gases, determine (a) the air temperature at the compressor exit and (b) the isentropic efficiency of the Compressor

23. 7–175 Steam at 6 MPa and 500°C enters a two-stage adiabatic
turbine at a rate of 15 kg/s. Ten percent of the steam is
extracted at the end of the first stage at a pressure of 1.2 MPa
for other use. The remainder of the steam is further expanded
in the second stage and leaves the turbine at 20 kPa. Determine
the power output of the turbine, assuming (a) the
process is reversible and (b) the turbine has an isentropic efficiency
of 88 percent.

24. We take the entire turbine, including the connection part between the two stages, as the system, which is a control volume since mass crosses the boundary. Noting that one fluid stream enters the turbine and two fluid streams leave, the energy balance for this steady-flow system can be expressed in the rate form as

25. Substituting all h’s to find the power output of the turbine