Thermodynamics

824 | ThermodynamicsFIGURE 17–1Aircraft and jet engines involve highspeeds, and thus the kinetic energyterm should always be consideredwhen analyzing them.(a) Photo courtesy of NASA,http://lisar.larc.nasa.gov/IMAGES/SMALL/EL-1999-00108.jpeg, and (b) Figure courtesy of Prattand Whitney. Used by permission.h 1h 2VControl1 Vvolume2h 01 h 02 = h 01FIGURE 17–2Steady flow of a fluid through anadiabatic duct.17–1 ■ STAGNATION PROPERTIESWhen analyzing control volumes, we find it very convenient to combine theinternal energy and the flow energy of a fluid into a single term, enthalpy,defined per unit mass as h u Pv. Whenever the kinetic and potentialenergies of the fluid are negligible, as is often the case, the enthalpy representsthe total energy of a fluid. For high-speed flows, such as thoseencountered in jet engines (Fig. 17–1), the potential energy of the fluid isstill negligible, but the kinetic energy is not. In such cases, it is convenientto combine the enthalpy and the kinetic energy of the fluid into a singleterm called stagnation (or total) enthalpy h 0 , defined per unit mass as(17–1)When the potential energy of the fluid is negligible, the stagnation enthalpyrepresents the total energy of a flowing fluid stream per unit mass. Thus itsimplifies the thermodynamic analysis of high-speed flows.Throughout this chapter the ordinary enthalpy h is referred to as the staticenthalpy, whenever necessary, to distinguish it from the stagnationenthalpy. Notice that the stagnation enthalpy is a combination property of afluid, just like the static enthalpy, and these two enthalpies become identicalwhen the kinetic energy of the fluid is negligible.Consider the steady flow of a fluid through a duct such as a nozzle, diffuser,or some other flow passage where the flow takes place adiabaticallyand with no shaft or electrical work, as shown in Fig. 17–2. Assuming thefluid experiences little or no change in its elevation and its potential energy,the energy balance relation (E . in E. out ) for this single-stream steady-flowsystem reduces toorh 0 h V 22 1kJ>kg2h 1 V 2 12 h 2 V 2 22(17–2)h 01 h 02(17–3)That is, in the absence of any heat and work interactions and any changes inpotential energy, the stagnation enthalpy of a fluid remains constant duringa steady-flow process. Flows through nozzles and diffusers usually satisfythese conditions, and any increase in fluid velocity in these devices createsan equivalent decrease in the static enthalpy of the fluid.If the fluid were brought to a complete stop, then the velocity at state 2would be zero and Eq. 17–2 would becomeh 1 V 2 12 h 2 h 02Thus the stagnation enthalpy represents the enthalpy of a fluid when it isbrought to rest adiabatically.During a stagnation process, the kinetic energy of a fluid is converted toenthalpy (internal energy flow energy), which results in an increase in thefluid temperature and pressure (Fig. 17–3). The properties of a fluid at thestagnation state are called stagnation properties (stagnation temperature,