Answer Happy

5. A perfect gas with y=1.4 flows steadily through the nozzle as shown below. The entropy of the gas remains constant and R = 53.3 ft-lbf/lbm-R. The inlet temperature and pressure are 200 °F, 100 psi, respectively. The exit pressure is 20 psi. The inlet is relatively large w.r.t. the exit area which is 12 in^2. Determine the following: exit Mach number, exit T, exit p, mass flow rate through the nozzle, and the velocity at the smallest cross-sectional area. (see tables next page). Po= 100 lb,/in? A₂ <= 12 in² To 200°F P2 == Minimum cross-sectional area = 20 lbr/in?

ISENTROPIC FLOW (y=1.4) A/A P/Po P/Po T/T₂ 1.20 1.03 0.4124 0.5311 0.7764 1.22 1.04 0.4017 0.5213 0.7706 1.24 1.04 0.3912 0.5115 0.7648 1.26 1.05 0.3809 0.5019 0.7590 1.28 1.06 0.3708 0.4923 0.7532 1.30 1.07 0.3609 0.4829 0.7474 1.32 1.08 0.3512 0.4736 0.7416 1.34 1.08 0.3417 0.4644 0.7358 1.36 1.09 0.3323 0.4553 0.7300 1.38 1.10 0.3232 0.4463 0.7242 1.40 1.11 0.3142 0.4374 0.7184 1.42 1.13 0.3055 0.4287 0.7126 1.44 1.14 0.2969 0.4201 0.7069 1.46 1.15 0.2886 0.4116 0.7011 1.48 1.16 0.2804 0.4032 0.6954 1.50 1.18 0.2724 0.3950 0.6897 1.52 1.19 0.2646 0.3869 0.6840 1.54 1.20 0.2570 0.3789 0.6783 1.56 1.22 0.2496 0.3710 0.6726 1.58 1.23 0.2423 0.3633 0.6670 1.60 1.25 0.2353 0.3557 0.6614 1.62 1.27 0.2284 0.3483 0.6558 1.64 1.28 0.2217 0.3409 0.6502 1.66 1.30 0.2151 0.3337 0.6447 1.68 1.32 0.2088 0.3266 0.6392 1.70 1.34 0.2026 0.3197 0.6337 1.72 1.36 0.1966 0.3129 0.6283 1.74 1.38 0.1907 0.3062 0.6229 1.76 1.40 0.1850 0.2996 0.6175 1.78 1.42 0.1794 0.2931 0.6121 1.80 1.44 0.1740 0.2868 0.6068 1.82 1.46 0.1688 0.2806 0.6015 1.84 1.48 0.1637 0.2745 0.5963 1.86 1.51 0.1587 0.2686 0.5910 1.88 1.53 0.1539 0.2627 0.5859 1.90 1.56 0.1492 0.2570 0.5807 1.92 1.58 0.1447 0.2514 0.5756 1.94 1.61 0.1403 0.2459 0.5705 1.96 1.63 0.1360 0.2405 0.5655 1.98 1.66 0.1318 0.2352 0.5605 2.00 1.69 0.1278 0.2300 0.5556 2.02 1.72 0.1239 0.2250 0.5506 2.04 1.75 0.1201 0.2200 0.5458 2.06 1.78 0.1164 0.2152 0.5409 2.08 1.81 0.1128 0.2104 0.5361 2.10 1.84 0.1094 0.2058 0.5313 Ans. po = 100 psi, To =200 °F = 660 R, T₂ = 416 R, V₂ = 1718 fps, po-0.410 pcf, p₂-0.130 pcf, mass flow rate = 18.6 lbm/sec, at min. cross-sectional area T₁ = 550 R, V₁ = 1151 fps. Ny