Thermodynamics

Chapter 7 | 375(b) The required power input to the compressor is determined from the energybalance for steady-flow devices,E # in E # outm # h 1 W # a,in m # h 2aW # a,in m # 1h 2a h 1 2 10.2 kg>s231575.03 285.142 kJ>kg4 58.0 kWDiscussion Notice that in determining the power input to the compressor, weused h 2a instead of h 2s since h 2a is the actual enthalpy of the air as it exitsthe compressor. The quantity h 2s is a hypothetical enthalpy value that the airwould have if the process were isentropic.Isentropic Efficiency of NozzlesNozzles are essentially adiabatic devices and are used to accelerate a fluid.Therefore, the isentropic process serves as a suitable model for nozzles. Theisentropic efficiency of a nozzle is defined as the ratio of the actual kineticenergy of the fluid at the nozzle exit to the kinetic energy value at the exit ofan isentropic nozzle for the same inlet state and exit pressure. That is,Actual KE at nozzle exith N Isentropic KE at nozzle exit V 2a22V 2s(7–66)Note that the exit pressure is the same for both the actual and isentropicprocesses, but the exit state is different.Nozzles involve no work interactions, and the fluid experiences little orno change in its potential energy as it flows through the device. If, in addition,the inlet velocity of the fluid is small relative to the exit velocity, theenergy balance for this steady-flow device reduces toh 1 h 2a V 22a2Then the isentropic efficiency of the nozzle can be expressed in terms ofenthalpies ashh 1h 2ah 2sV 2 2a2Inlet stateV 2 2s212s2aP 1Actual processIsentropic processExitpressureP 2h N h 1 h 2a(7–67)h 1 h 2swhere h 2a and h 2s are the enthalpy values at the nozzle exit for the actualand isentropic processes, respectively (Fig. 7–54). Isentropic efficiencies ofnozzles are typically above 90 percent, and nozzle efficiencies above 95percent are not uncommon.s 2s = s 1FIGURE 7–54The h-s diagram of the actual andisentropic processes of an adiabaticnozzle.sEXAMPLE 7–16Effect of Efficiency on Nozzle Exit VelocityAir at 200 kPa and 950 K enters an adiabatic nozzle at low velocity and isdischarged at a pressure of 80 kPa. If the isentropic efficiency of the nozzleis 92 percent, determine (a) the maximum possible exit velocity, (b) the exittemperature, and (c) the actual exit velocity of the air. Assume constantspecific heats for air.