Thermodynamics

Chapter 17 | 869The maximum value of stagnation temperature T* 0 occurs at Ma 1, and itsvalue can be determined from Table A–34 or from Eq. 17–65. At Ma 1 0.1702 we read T 0 /T* 0 0.1291. Therefore,T* 0 T 010.1291 553.2 K0.1291 4285 KThe stagnation temperature ratio at the exit state and the Mach number correspondingto it are, from Table A–34,T 02T* 0 1598 K4285 K 0.3729 S Ma 2 0.3142The Rayleigh flow relations corresponding to the inlet and exit Mach numbersare (Table A–34):Ma 1 0.1702: T 1T* 0.1541 P 1P* 2.3065 V 1V* 0.0668Ma 2 0.3142: T 2T* 0.4389 P 2P* 2.1086 V 2V* 0.2082Then the exit temperature, pressure, and velocity are determined to beT 2T 1 T 2>T*T 1 >T* 0.43890.1541 2.848 S T 2 2.848T 1 2.848 1550 K2 1566 KP 2 P 2/P*P 1 P 1 /P* 2.10862.3065 0.9142 S P 2 0.9142P 1 0.9142 1480 kPa2 439 kPaV 2 V 2>V*V 1 V 1 >V* 0.20820.0668 3.117 S V 2 3.117V 1 3.117 180 m>s2 249 m/sDiscussion Note that the temperature and velocity increase and pressuredecreases during this subsonic Rayleigh flow with heating, as expected. Thisproblem can also be solved using appropriate relations instead of tabulatedvalues, which can likewise be coded for convenient computer solutions.17–7 ■ STEAM NOZZLESWe have seen in Chapter 3 that water vapor at moderate or high pressuresdeviates considerably from ideal-gas behavior, and thus most of the relationsdeveloped in this chapter are not applicable to the flow of steamthrough the nozzles or blade passages encountered in steam turbines. Giventhat the steam properties such as enthalpy are functions of pressure as wellas temperature and that no simple property relations exist, an accurate analysisof steam flow through the nozzles is no easy matter. Often it becomesnecessary to use steam tables, an h-s diagram, or a computer program forthe properties of steam.A further complication in the expansion of steam through nozzles occursas the steam expands into the saturation region, as shown in Fig. 17–59. Asthe steam expands in the nozzle, its pressure and temperature drop, and