Question

Problem 2 (20 points) Consider a subsonic compressible flow in cartesian coordinates (x and y in meters), with velocity potential: $(x, y) = Vox + VI - M For an altitude of 10 km and velocity of 240 m/s, Calculate M, P, and T for the location (0.10 m, 0.15 m). 70 -24V1-My sin 27X

Answer 1

Tables

Concu 513 Springer Science+Business Media Dordrecht 2015 R. Vos and S. Farokhi, Introduction to Transonic Aerodynamics, Fluid Mechanics and Its Applications 110, DOI 10.1007978-94-017-9747-4 514 Appendix A: Isentropic Flow Table A/A T/T* p/p* 1.38E+00 1.34E+00 1.30E+00 1.27E+00 1.24E+00 1.21E+00 1.19E+00 1.17E+00 1.15E+00 1.13E+00 1.11E+00 1.09E+00 1.08E+00 1.07E+00 1.06E+00 1.15E+00 1.14E+00 1.14E+00 1.13E+00 1.13E+00 1.12E+00 1.12E+00 1.11E+00 1.11E+00 1.10E+00 1.10E+00 1.09E+00 1.09E+00 1.08E+00 1.08E+00 1.07E+00 1.06E+00 1.05E+00 Table A.1 (continued) M T/T | Pilp 0.48 1.05E+00 1.17E+00 0.5 1.05E+00 1.19E+00 0.52 1.05E+00 1.20E+00 0.54 1.06E+00 1.22E+00 0.56 1.06E+00 1.24E+00 0.58 1.07E+00 1.26E+00 0.6 1.07E+00 1.28E+00 0.62 1.08E+00 1.30E+00 0.64 1.08E+00 1.32E+00 0.66 1.09E+00 1.34E+00 0.68 1.09E+00 1.36E+00 0.7 1.10E+00 1.39E+00 0.72 1.10E+00 1.41E+00 0.74 1.11E+00 1.44E+00 0.76 1.12E+00 1.47E+00 0.78 1.12E+00 1.49E+00 0.8 1.13E+00 1.52E+00 0.82 1.13E+00 1.56E+00 0.84 1.14E+00 1.59E+00 0.86 1.15E+00 1.62E+00 0.88 1.15E+00 1.66E+00 0.9 1.16E+00 1.69E+00 0.92 1.17E+00 1.73E+00 0.94 1.18E+00 1.77E+00 0.96 1.18E+00 1.81E+00 0.98 1.19E+00 1.85E+00 1.20E+00 1.89E+00 1.02 1.21E+00 1.94E+00 1.04 1.22E+00 1.98E+00 1.06 1.22E+00 2.03E+00 1.08 1.23E+00 2.08E+00 1.1 1.24E+00 2.14E+00 1.12 1.25E+00 2.19E+00 1.14 1.26E+00 2.24E+00 1.16 1.27E+00 2.30E+00 1.18 1.28E+00 2.36E+00 1.2 1.29E+00 2.43E+00 1.22 1.30E+00 2.49E+00 1.24 1.31E+00 2.56E+00 1.04E+00 Pile 1.12E+00 1.13E+00 1.14E+00 1.15E+00 1.16E+00 1.18E+00 1.19E+00 1.20E+00 1.22E+00 1.23E+00 1.25E+00 1.26E+00 1.28E+00 1.30E+00 1.31E+00 1.33E+00 1.35E+00 1.37E+00 1.39E+00 1.41E+00 1.43E+00 1.46E+00 1.48E+00 1.50E+00 1.53E+00 1.55E+00 1.58E+00 1.60E+00 1.63E+00 1.66E+00 1.69E+00 1.72E+00 1.75E+00 1.78E+00 1.81E+00 1.85E+00 1.88E+00 1.92E+00 1.41E+00 1.40E+00 1.38E+00 1.37E+00 1.35E+00 1.34E+00 1.33E+00 1.31E+00 1.30E+00 1.28E+00 1.26E+00 1.25E+00 1.23E+00 1.22E+00 1.20E+00 1.18E+00 1.17E+00 1.15E+00 1.13E+00 1.12E+00 1.10E+00 1.08E+00 1.07E+00 1.05E+00 1.03E+00 1.02E+00 1.00E+00 9.83E-01 9.67E-01 1.03E+00 1.02E+00 p/p* 1.62E+00 1.60E+00 1.57E+00 1.55E+00 1.53E+00 1.51E+00 1.48E+00 1.46E+00 1.44E+00 1.41E+00 1.39E+00 1.36E+00 1.34E+00 1.32E+00 1.29E+00 1.27E+00 1.24E+00 1.22E+00 1.19E+00 1.17E+00 1.14E+00 1.12E+00 1.10E+00 1.07E+00 1.05E+00 1.02E+00 1.00E+00 9.77E-01 9.54E-01 9.31E-01 9.09E-01 8.87E-01 8.65E-01 8.43E-01 8.22E-01 8.01E-01 7.81E-01 7.60E-01 7.41E-01 1.02E+00 1.01E+00 1.01E+00 1 1.06E+00 1.05E+00 1.05E+00 1.04E+00 1.03E+00 1.03E+00 1.02E+00 1.01E+00 1.01E+00 1.00E+00 9.93E-01 9.87E-01 9.80E-01 9.73E-01 9.66E-01 9.59E-01 9.52E-01 9.46E-01 9.39E-01 9.32E-01 9.25E-01 9.18E-01 1.01E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00 1.01E+00 1.01E+00 1.01E+00 1.02E+00 1.02E+00 1.02E+00 1.03E+00 1.04E+00 1.04E+00 9.50E-01 9.34E-01 9.18E-01 9.01E-01 8.85E-01 8.69E-01 8.54E-01 8.38E-01 8.22E-01 8.07E-01 1.95E+00 (continued)

Appendix A: Isentropic Flow Table 517 T/T* Table A.1 (continued) M T/T PI/P 2.82 2.59E+00 2.80E+01 2.84 2.61E+00 2.88E+01 2.86 2.64E+00 2.97E+01 2.88 2.66E+00 3.07E+01 2.9 2.68E+00 3.16E+01 2.92 2.71E+00 3.26E+01 2.94 2.73E+00 3.36E+01 2.96 2.75E+00 3.46E+01 2.98 2.78E+00 3.56E+01 3 2.80E+00 3.67E+01 3.05 2.86E+00 3.96E+01 3.1 2.92E+00 4.26E+01 3.15 2.98E+00 4.59E+01 3.2 3.05E+00 4.94E+01 3.25 3.11E+00 5.32E+01 3.3 3.18E+00 5.72E+01 3.35 3.24E+00 6.15E+01 3.4 3.31E+00 6.61E+01 3.45 3.38E+00 7.10E+01 3.5 3.45E+00 7.63E+01 3.55 3.52E+00 8.19E+01 3.6 3.59E+00 8.78E+01 3.65 3.66E+00 9.42E+01 3.7 3.74E+00 1.01E+02 3.75 3.81E+00 1.08E+02 3.8 3.89E+00 1.16E+02 3.85 3.96E+00 1.24E+02 3.9 4.04E+00 1.33E+02 3.95 4.12E+00 1.42E+02 4 4.20E+00 1.52E+02 4.05 4.28E+00 1.62E+02 4.1 4.36E+00 1.73E+02 4.15 4.44E+00 1.85E+02 4.2 4.53E+00 1.98E+02 4.25 4.61E+00 2.11E+02 4.3 4.70E+00 2.25E+02 4.35 4.78E+00 2.40E+02 4.4 4.87E+00 2.55E+02 4.45 4.96E+00 2.72E+02 Pile 1.08E+01 1.10E+01 1.13E+01 1.15E+01 1.18E+01 1.20E+01 1.23E+01 1.26E+01 1.28E+01 1.31E+01 1.38E+01 1.46E+01 1.54E+01 1.62E+01 1.71E+01 1.80E+01 1.90E+01 2.00E+01 2.10E+01 2.21E+01 2.33E+01 2.45E+01 2.57E+01 2.70E+01 2.84E+01 2.98E+01 3.13E+01 3.28E+01 3.45E+01 3.62E+01 3.79E+01 3.97E+01 4.16E+01 4.36E+01 4.57E+01 4.78E+01 5.01E+01 5.24E+01 5.48E+01 A/A 3.57E+00 3.64E+00 3.71E+00 3.78E+00 3.85E+00 3.92E+00 4.00E+00 4.08E+00 4.15E+00 4.23E+00 4.44E+00 4.66E+00 4.88E+00 5.12E+00 5.37E+00 5.63E+00 5.90E+00 6.18E+00 6.48E+00 6.79E+00 7.11E+00 7.45E+00 7.80E+00 8.17E+00 8.55E+00 8.95E+00 9.37E+00 9.80E+00 1.03E+01 1.07E+01 1.12E+01 1.17E+01 1.22E+01 1.28E+01 1.34E+01 1.40E+01 1.46E+01 1.52E+01 1.59E+01 4.63E-01 4.59E-01 4.55E-01 4.51E-01 4.47E-01 4.44E-01 4.40E-01 4.36E-01 4.32E-01 4.29E-01 4.20E-01 4.11E-01 4.02E-01 3.94E-01 3.86E-01 3.78E-01 3.70E-01 3.62E-01 3.55E-01 3.48E-01 3.41E-01 3.34E-01 3.27E-01 3.21E-01 3.15E-01 3.09E-01 3.03E-01 2.97E-01 2.91E-01 2.86E-01 2.80E-01 2.75E-01 2.70E-01 2.65E-01 2.60E-01 2.55E-01 2.51E-01 2.46E-01 2.42E-01 p/p 6.77E-02 6.56E-02 6.37E-02 6.18E-02 5.99E-02 5.81E-02 5.64E-02 5.47E-02 5.31E-02 5.15E-02 4.78E-02 4.44E-02 4.12E-02 3.83E-02 3.56E-02 3.31E-02 3.08E-02 2.86E-02 2.67E-02 2.48E-02 2.31E-02 2.16E-02 2.01E-02 1.87E-02 1.75E-02 1.63E-02 1.53E-02 1.43E-02 1.33E-02 1.25E-02 1.17E-02 1.09E-02 1.02E-02 9.58E-03 8.98E-03 8.42E-03 7.90E-03 7.42E-03 6.96E-03 p/p* 1.46E-01 1.43E-01 1.40E-01 1.37E-01 1.34E-01 1.31E-01 1.28E-01 1.26E-01 1.23E-01 1.20E-01 1.14E-01 1.08E-01 1.03E-01 9.73E-02 9.23E-02 8.76E-02 8.32E-02 7.90E-02 7.51E-02 7.14E-02 6.78E-02 6.45E-02 6.14E-02 5.84E-02 5.56E-02 5.29E-02 5.04E-02 4.80E-02 4.58E-02 4.36E-02 4.16E-02 3.97E-02 3.79E-02 3.62E-02 3.45E-02 3.30E-02 3.15E-02 3.01E-02 2.88E-02 (continued) 518 Appendix A: Isentropic Flow Table A/A T/T Table A.1 (continued) M T/T Pi/p 4.5 5.05E+00 2.89E+02 4.55 5.14E+00 3.08E+02 4.6 5.23E+00 3.28E+02 4.65 5.32E+00 3.48E+02 In zor Pulp 5.73E+01 5.99E+01 1.66E+01 1.73E+01 1.80E+01 1.88E+01 1 p/p* 6.54E-03 6.15E-03 5.78E-03 5.43E-03 1 on 2.38E-01 2.33E-01 2.29E-01 2.25E-01 r 01 6.26E+01 p/p 2.75E-02 2.63E-02 2.52E-02 2.41E-02 6.54E+01 cornu la o

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