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7. The pressure and Mach number of Helium flowing through a channel at a certain location are found to be p = 30 psia, Ma = 1.5. At a point further downstream the pressure is 15 psia. Assuming isentropic flow through the channel, determine the Mach number at the second point. Assume y=1.67 (see below for tables). Ans. Ma₂ = 1.98 One-Dimensional Isentropic Compressible-Flow Functions For an ideal gas with constant specific heat and molecular weight, Y 1.67 P A P M M Po Po 0 1.0000 1.75 1.312 0.1721 0.05 11.265 0.9979 1.80 1.351 0.1601 0.10 5.661 0.9917 1.85 1.392 0.1490 0.15 3.805 0.9815 1.90 1.436 0.1386 0.20 2.887 0.9674 1.95 1.482 0.1290 0.25 2.344 0.9497 2.00 1.530 0.1201 0.30 1.989 0.9286 2.05 1.580 0.1119 0.35 1.741 0.9046 2.10 1.632 0.1042 0.40 1.560 0.8780 2.15 1.687 0.09712 0.45 1.424 0.8491 2,20 1.744 0.09053 0.50 1.320 0.8184 2.25 1.803 0.08442 0.55 1.239 0.7862 2.30 1.865 0.07875 0.60 1.176 0.7529 2.35 1.929 0.07349 0.65 1.126 0.7190 2.40 1.995 0.06862 0.70 1.0874 0.6847 2.45 2.064 0.06410 0.75 1.0576 0.6503 2.50 2.135 0.05990 0.80 1.0351 0.6162 2.55 2,209 0.05601 0.85 1.0189 0.5826 2.60 2.285 0.05239 0.90 1.0080 0.5497 2.65 2.364 0.04903 0.95 1.0019 0.5177 2.70 2.445 0.04591 1.00 1.0000 0.4867 2.75 2.529 0.04301 1.05 1.0018 0.4568 2.80 2.616 0.04032 1.10 1.0071 0.4282 2.85 2.705 0.03781 1.15 1.0154 0.4009 2.90 2.797 0.03547 1.20 1.0266 0.3749 2.95 2.892 0.03330 1.25 1.0406 0.3502 3.0 2.990 0.03128 1.30 1.0573 0.3269 3.5 4.134 0.01720 1.35 1.0765 0.3049 4.0 5.608 0.009939 1.40 1.0981 0.2842 4.5 7.456 0.006007 1.45 1.122 0.2647 5.0 9.721 0.003778 1.50 0.2465 6.0 165(10)-$ 1.55 1.176 0.2295 7.0 807(10) 1.60 1.207 0.2136 8.0 429(10) 1.65 1.240 0.1988 9.0 244(10) 1.70 1.275 0.1850 10.0 147(10) 0 15.68 23.85 34.58 48.24 65.18