Thermodynamics

524 | ThermodynamicsProcess 4-5 (isentropic expansion of an ideal gas in a turbine): Neglectingthe kinetic energy changes across the compressor and the turbine andassuming the turbine work to be equal to the compressor work, we find thetemperature and pressure at the turbine exit to bew comp,in w turb,outh 3 h 2 h 4 h 5c p 1T 3 T 2 2 c p 1T 4 T 5 2T 5 T 4 T 3 T 2 2460 927 480 2013 RP 5 P 4 a T k>1k125b 180 psia2a 2013 R 1.4>11.412T 4 2460 R b 39.7 psia(b) To find the air velocity at the nozzle exit, we need to first determine thenozzle exit temperature and then apply the steady-flow energy equation.Process 5-6 (isentropic expansion of an ideal gas in a nozzle):T 6 T 5 a P 1k12>k6b 12013 R2a 5 psia 11.412>1.4P 5 39.7 psia b 1114 R0h 6 V 622 h 5 V 5220 c p 1T 6 T 5 2 V 2 62V 6 22c p 1T 5 T 6 2 B2 10.240 Btu>lbm # R2312013 11142 R4 a25,037 ft 2 >s 21 Btu>lbm b 3288 ft/s¡(c) The propulsive efficiency of a turbojet engine is the ratio of the propulsivepower developed W . P to the total heat transfer rate to the working fluid:W # P m # 1V exit V inlet 2V aircraft 1100 lbm>s2313288 8502 ft>s4 1850 ft>s2a 1 Btu>lbm25,037 ft 2 >s 2 b 8276 Btu>s1or 11,707 hp2Q # in m # 1h 4 h 3 2 m # c p 1T 4 T 3 2 1100 lbm>s2 10.240 Btu>lbm # R2312460 9272 R4 36,794 Btu>sh P W# PQ # 8276 Btu>sin36,794 Btu>s 22.5%That is, 22.5 percent of the energy input is used to propel the aircraft andto overcome the drag force exerted by the atmospheric air.