Mechanics of Fluids

Table A3.2 Isentropic flow
M p/po ϱ/ϱo T/To A/At Prandtl–Meyer angle
θ degrees
0 1.000 1.000 1.000 ∞
0.05 0.998 0.999 0.9995 11.59
0.10 0.993 0.995 0.998 5.82
0.15 0.984 0.989 0.996 3.91
0.20 0.973 0.980 0.992 2.964
0.25 0.957 0.969 0.988 2.403
0.30 0.939 0.956 0.982 2.035
0.35 0.919 0.941 0.976 1.778
0.40 0.896 0.924 0.969 1.590
0.42 0.886 0.917 0.966 1.529
0.44 0.876 0.909 0.963 1.474
0.46 0.865 0.902 0.959 1.425
0.48 0.854 0.893 0.956 1.380
0.50 0.843 0.885 0.952 1.340
0.52 0.832 0.877 0.949 1.303
0.54 0.820 0.868 0.945 1.270
0.56 0.808 0.859 0.941 1.240
0.58 0.796 0.850 0.937 1.213
0.60 0.784 0.840 0.933 1.188
0.62 0.772 0.831 0.929 1.166
0.64 0.759 0.821 0.924 1.145
0.66 0.746 0.812 0.920 1.127
0.68 0.734 0.802 0.915 1.110
0.70 0.721 0.792 0.911 1.094
0.72 0.708 0.781 0.906 1.081
0.74 0.695 0.771 0.901 1.068
0.76 0.682 0.761 0.896 1.057
0.78 0.669 0.750 0.892 1.047
0.80 0.656 0.740 0.887 1.038
0.82 0.643 0.729 0.881 1.030
0.84 0.630 0.719 0.876 1.024
0.86 0.617 0.708 0.871 1.018
0.88 0.604 0.698 0.866 1.013
0.90 0.591 0.687 0.861 1.009
0.92 0.578 0.676 0.855 1.006
0.94 0.566 0.666 0.850 1.003
0.96 0.553 0.655 0.844 1.001
0.98 0.541 0.645 0.839 1.000
Appendix 3: Tables of gas flow functions 675
Not applicable for M < 1
continued overleaf
Where A/At varies rapidly, say up to M = 0.5, interpolation of reciprocals
is more satisfactory than linear interpolation. For example, for M = 0.23
� �
At 1 0.23 − 0.20 1 1
= + − = 0.3846
A 2.964 0.25 − 0.20 2.403 2.964
and hence A/At = 1/0.3846 = 2.600.