Question

The Boeing 747 has a cruising altitude of 45,000 feet and cruising speed of 275 m/s. At this elevation, the temperature and pressure according to the US Standard Atmosphere (air properties as a function of altitude) are 220K and 1.8x104 Pa, respectively. The engines are steady state devices that can be modeled using the 1st Law of Thermodynamics with air (ideal gas) as the working fluid undergoing several processes.

a. The inlet area of the engines is 0.5 m2. What is the mass flow rate (per engine)?

b. The first stage (inlet) of the jet engine is a diffuser. If the exit of the diffuser is 0.6 m2, T2 = 250K and P2 = 25200 Pa, what is the air velocity after the diffuser process? (State 2 is the exit of the first stage and the entrance to the compressor)

c. The engine compressor is rated at 30 MW and the air entering the compressor is at 250K. What is the temperature at the exit of the compressor if the process is assumed to be adiabatic? For more accuracy, use the “ideal-gas properties of air” table (Table A17 in the provided Thermo property tables) for properties you may need.

d. The working fluid enters the combustor after the compression process. At the cruising speed, each engine consumes 1 L/s of jet fuel. What is the rate of heat release per engine if the volumetric energy density of jet fuel is 35 MJ/L?

e. Model the combustor as a heat exchanger in which the heat from combustion gets transferred to the working fluid as an outside heat source (not like the real combustor pictured above). What is the specific (intensive) enthalpy change using this model assuming there is no heat loss in the combustor?

f. Using the Table again, what is the specific enthalpy and temperature after combustion?

g. The turbine in the jet engine only needs to supply enough power to compress the air in the compressor. What is the temperature of the air at the exit of the turbine assuming this turbine process is adiabatic with negligible kinetic energy change?

Ideal-gas properties of air Th K kJ/kg P. kJ/kg Vi k /kg.K 200 199.97 0.3363 142.56 1707.0 1.29559 210 209.97 0.3987 149.69 1512.0 1.34444 220 219.97 0.4690 156.82 1346.0 1.39105 230 230.02 0.5477 164.00 1205.0 1.43557 240 240.02 0.6355 171.13 1084.0 1.47824 250 250.05 0.7329 178.28 979.0 1.51917 260 260.09 0.8405 185.45 887.8 1.55848 270 270.11 0.9590 192.60 808.0 1.59634 280 280.13 1.0889 199.75 738.0 1.63279 285 285.14 1.1584 203.33 706.1 1.65055 290 290.16 1.2311 206.91 676.1 1.66802 295 295.17 1.3068 210.49 647.9 1.68515 298 298.18 1.3543 212.64 631.9 1.69528 300 300.19 1.3860 214.07 621.2 1.70203 305 305.22 1.4686 217.67 596.0 1.71865 310 310.24 1.5546 221.25 572.3 1.73498 315 315.27 1.6442 224.85 549.8 1.75106 320 320.29 1.7375 228.42 528.6 1.76690 325 325.31 1.8345 232.02 508.4 1.78249 330 330.34 1.9352 235.61 489.4 1.79783 340 340.42 2.149 242.82 454.1 1.82790 350 350.49 2.379 250.02 422.2 1.85708 360 360.58 2.626 257.24 393.4 1.88543 370 370.67 2.892 264.46 367.2 1.91313 380 380.77 3.176 271.69 343.4 1.94001 390 390.88 3.481 278.93 321.5 1.96633 400 400.98 3.806 286.16 301.6 1.99194 410 411.12 4.153 293.43 283.3 2.01699 420 421.26 4.522 300.69 266.6 2.04142 430 431.434.915 307.99 251.1 2.06533 440 441.61 5.332 315.30 236.8 2.08870 450 451.80 5.775 322.62 223.6 2.11161 460 462.02 6.245 329.97 211.4 2.13407 470 472.24 6.742 337.32 200.1 2.15604 480 482.497.268 344.70 189.5 2.17760 490 492.74 7.824 352.08 179.7 2.19876 500 503.02 8.411 359.49 170.6 2.21952 510 513.32 9.031 366.92 162.1 2.23993 520 523.63 9.684 374.36 154.1 2.25997 530 533.98 10.37 381.84 146.7 2.27967 540 544.35 11.10 389.34 139.7 2.29906 550 555.74 11.86 396.86 133.1 2.31809 560 565.17 12.66 404.42 127.0 2.33685 570 575.59 13.50 411.97 121.2 2.35531 Th K kJ/kg P, kJ/kg V, kJ/kg. 580 586.04 14.38 419.55 115.7 2.37348 590 596.52 15.31 427.15 110.6 2.39140 600 607.02 16.28 434.78 105.8 610 617.53 17.30 442.42 101.2 2.42644 620 628.07 18.36 450.09 96.92 2.44356 630 638.63 19.84 457.78 92.84 2.46048 640 649.22 20.64 465.50 88.99 2.47716 650 659.84 21.86 473.25 85.34 2.49364 660 670.47 23.13 481.01 81.89 2.50985 670 681.14 24.46 488.81 78.61 2.52589 680 691.82 25.85 496.62 75.50 2.54175 690 702.52 27.29 504.45 72.56 2.55731 700 713.27 28.80 512.33 69.76 2.57277 710 724.04 30.38 520.23 67.07 2.58810 720 734.82 32.02 528.14 64.53 2.60319 730 745.62 33.72 536.07 62.13 2.61803 740 756.44 35.50 544.02 59.82 2.63280 767.29 37.35 551.99 57.63 778.18 39.27 560.01 55.54 2.66176 780 800.03 43.35 576.12 51.64 2.69013 800 821.95 47.75 592.30 48.08 2.71787 843.98 52.59 608.59 44.84 2.74504 840 866.08 57.60 624.95 41.85 2.77170 860 888.27 63.09 641.40 39.12 2.79783 880 910.56 68.98 657.95 36.61 2.82344 900 932.93 75.29 674.58 34.31 2.84856 920 955.38 82.05 691.28 32.18 2.87324 940 977.92 89.28 708.08 30.22 2.89748 960 1000.55 97.00 725.02 28.40 2.92128 980 1023.25 105.2 741.98 26.73 2.94468 1000 1046.04 114.0 758.94 25.17 2.96770 1020 1068.89 123.4 776.10 23.72 2.99034 1040 1091.85 133.3 793.36 23.29 3.01260 1060 1114.86 143. 9 810.62 21.14 3.03449 1080 1137.89 155.2 827.88 19.98 3.05608 1100 1161.07 167.1 845.33 18.896 3.07732 1120 1184.28 179.7 862.79 17.886 3.09825 1140 1207.57 193.1 880.35 16.946 3.11883 1160 1230.92 207.2 897.91 16.064 3.13916 1180 1254.34 222.2 915.57 15.241 3.15916 1200 1277.79 238.0 933.33 14.470 3.17888 1220 1301.31 254.7 951.09 13.747 3.19834 1240 1324.93 272.3 968.95 13.069 3.21751 20

Answer 1

ANSWER of The Boeing 747 han a cruining altitude 45.000 feed & cruining speed of 275m/s. => Cruising Altitude = 45000 feet. = 13716 meter T= Book P= 1.8xio pa. Rair = 287.5/kg k. the height = RT 1 = Pair Saran at 1.88 104 Parsa: 284 X220 = 0.285 teglms. Denega A Boeing (447) eine (fur) : 6 C TS Noucle. 24 BUYn1 section Turlaine I comprenor Diffurer

a) 1. 0.5m²) aialet (Inlet Area So, mann How rate mt = SAV meso 28SXO'S*25. mas 0.885*0*5*2* = 39.198 kglace. m=39.198 teglsee stage of the jet engine on a b) The first deffuren. At the exit of diffuner 9 = 250k- P2 = 25900 pa Syze 25000 250*287 5. = 0.35 kglms) Area at exit of diffurer Pr Az = 0.6m2. m₂ = S2 A2 V₂ = mi 39.198 = Ves 251X0:6.

I ve 186.00mloec. The 30 mul engine compreanol an rated at Hence, Rated power of compreanor = 30 Mal. Pan-250k. comprend Work done in adiabatic procean for compreanor klen a PV₂-Piu m²R (Pout - Pen) x-1 une x = 1.4 Let . 30 X10 39.198 x 28+ (Tout-250) 30 x 6 OU: Tout = 1316.683K:]

. d) The working huid entean the combontor after the compreano procear. - fuel consumed by Engine = IL sec * Rate of heat releare per Engine L Rate of heat release per engine - 35 MIL. e) The combintl an which the heat from to the working huid Source: a heat exchanger en combustion gets transferred an an outside heat Qin = 35Mbl. Mouto moin

> If there in no heat lon from the combenter, then the specific enthalpy change in, Chout -hau). 35* LOT Isec. 39.198.bglsec. = 398.902 kilog f) The specific entralpy & temperature after - Combortion. preanure at Onlet to compressor = 2520opa. 7qu = 250k Tout = 1316.683K Puh= conntant PT countant . praeci plota = content Pin a countant.

80. ** cfare) P = pix(*)(*) =>B, 3 ssboy ( Tergy (la compress) B: 35800m (Slect B = 8. Que mpa P = 8-Burmpa 19 At Pa = 1316.683k , and. P₂ = 8.848 MPa. ha = 1016 kJ/kg. Enthalpy of air at the enit of compresor herit = 116 +892.902 Thenit = $38.902 kilka I

for temperature after combention cp (Pout - Ppm ) = 893.902. los ( Four - 1316.683) = 898.902: At exit of 1 Fout = 2167.065k. 1 (comporemor ) g) The forbine au the jet engine only need to supply enough power to compress the air in the compreanor If the turbine an to produce Junt enough power srom the comprensor then - kit = mep (Pout - Tin) power to WT = => 30% 40°x 39.198*105 ( - Tout +2167.065) Sec. Tout = 1938-16uk/ (Temperature of airl lat exit of turbine,