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Mach 2 in air: the Report 1135 Table II row, the 10° oblique shock and the Fanno and Rayleigh states

Tool	Compressible Flow Tables
Source	Ames Research Staff (1953). Equations, Tables, and Charts for Compressible Flow. NACA Report 1135, National Advisory Committee for Aeronautics, Washington, DC. Table II (p. 634, row M = 2.00), eqs. 43–51, 80, 93–102, 128–145, 171c; Shapiro, A. H. (1953). The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1. Ronald Press, New York. Chapters 6 and 7 (Fanno and Rayleigh lines).
Level	Undergraduate

Problem

Air (γ = 1.4) flows at Mach 2 with a static pressure of 14.696 psi and a static temperature of 59 °F. Give the isentropic ratios of the stream, the normal-shock ratios, the weak oblique shock on a 10° wedge, the Prandtl-Meyer angle, the Fanno and Rayleigh ratios to the sonic state, and the dimensional state ahead of and behind the normal shock.

Inputs to Enter

Gas air, γ 1.4 (R 53.35 ft⋅lbf/(lbm⋅°R)); mode Every mode at one Mach number, M_1 2.0, deflection 10°
Dimensional state on: static pressure 14.696 psi, static temperature 59 °F

Open the Compressible Flow Tables tool (loaded with this example)

Answers

Isentropic (Table II, M = 2.00): p/p_t 0.1278, ρ/ρ_t 0.2300, T/T_t 0.5556, β 1.732, q/p_t 0.3579, A/A* 1.688, V/a* 1.63299, ν 26.380°, μ 30.00°
Normal shock: M_2 0.5774, p_2/p_1 4.500, ρ_2/ρ_1 2.667, T_2/T_1 1.688, p_t2/p_t1 0.7209, p_1/p_t2 0.1773 (pitot ratio p_t2/p_1 5.640), Δs/R 0.3273
Oblique shock, δ = 10° weak: θ = 39.31° (strong 83.70°), M_1 sin θ 1.267, p_2/p_1 1.707, M_2 1.641, p_t2/p_t1 0.9846; δ_max 22.97° at θ 64.67°, sonic limit θ 61.49°
Fanno: T/T* 0.6667, p/p* 0.4082, p_t/p_t* 1.688, fL*/D 0.3050 (Darcy f; subsonic twin M 0.6573); Rayleigh: T_t/T_t* 0.7934, T/T* 0.5289, p/p* 0.3636, p_t/p_t* 1.503
State: ρ 0.07648 lb/ft³, a 1,116 ft/s, V 2,233 ft/s, q 41.15 psi, p_t 115.0 psi, T_t 933.6 °R; behind the normal shock p_2 66.13 psi, T_2 875.3 °R, V_2 837.3 ft/s, p_t2 82.89 psi

Notes

The tool's default inputs are this case; press Submit. The isentropic and normal-shock values are the printed row of Report 1135 Table II (read from the page render filed in References/Compressible-Flow/); the oblique-shock, Prandtl-Meyer, Fanno and Rayleigh numbers are reproduced by an independent numpy / scipy implementation (compflow_check.py) and the whole library by test_compressible_flow.php (741 checks, 441 of them table cells).