Thermodynamics

838 | Thermodynamicscritical ratio. Also illustrated on this figure is the effect of back pressure onthe nozzle exit pressure P e . We observe thatP e e P b for P b P*P* for P b 6 P*To summarize, for all back pressures lower than the critical pressure P*,the pressure at the exit plane of the converging nozzle P e is equal to P*, theMach number at the exit plane is unity, and the mass flow rate is the maximum(or choked) flow rate. Because the velocity of the flow is sonic at thethroat for the maximum flow rate, a back pressure lower than the criticalpressure cannot be sensed in the nozzle upstream flow and does not affectthe flow rate.The effects of the stagnation temperature T 0 and stagnation pressure P 0 onthe mass flow rate through a converging nozzle are illustrated in Fig. 17–22where the mass flow rate is plotted against the static-to-stagnation pressureratio at the throat P t /P 0 . An increase in P 0 (or a decrease in T 0 ) will increasethe mass flow rate through the converging nozzle; a decrease in P 0 (or anincrease in T 0 ) will decrease it. We could also conclude this by carefullyobserving Eqs. 17–24 and 17–25.A relation for the variation of flow area A through the nozzle relative tothroat area A* can be obtained by combining Eqs. 17–24 and 17–25 for thesame mass flow rate and stagnation properties of a particular fluid. ThisyieldsAA* 1 Ma ca 2k 1 ba1 k 11k12> 321k124Ma 2 bd2(17–26)Table A–32 gives values of A/A* as a function of the Mach number for air(k 1.4). There is one value of A/A* for each value of the Mach number,but there are two possible values of the Mach number for each value ofA/A*—one for subsonic flow and another for supersonic flow.⋅mMa t = 1 Ma t< 1Increase in P 0 ,decrease in T 0 ,or bothFIGURE 17–22The variation of the mass flow ratethrough a nozzle with inlet stagnationproperties.0P 0 , T 0Decrease in P 0 ,increase in T 0 ,or bothP*1.0 P tP 0P 0