![]() Of course, we can apply the Prandtl–Meyer (P–M) expansion relations at any point along the body at which the Newtonian method begins to become inaccurate. The Newtonian method works reasonably well and lends itself to application to bodies of quite arbitrary shape. Discussion of such details, which are not directly related to the problems considered here appears in Appendix A. In the case of axisymmetric bodies at angle of attack, C p,N of the conical tips would vary with azimuthal angle ϕ as would the body slope, that is, δ = δ ( ϕ ). In the case of two-dimensional bodies, the C p,Nw for the wedge would be used, while for axisymmetric bodies, C p,Nc for the cone would be used. This approach gives useful results until the body contour becomes nearly parallel to V ∞. Note that in the hypersonic limit, θ → δ so that cos 2 ( θ − δ ) → 1. Here, the correct C p,max values are greater than two. These laws will be, perhaps, useful in correlating the experimental data to be obtained in the near future by hypersonic wind tunnels now under construction. In this paper, the same method is used to derive the similarity laws for hypersonic flows. He deduced these laws by using an affine transformation of the fluid field so that the differential equations of the flows are reduced to a single non-dimensional equation. Recently, von Kármán has obtained the similarity laws for transonic flows where the fluid velocity is very near to the velocity of sound. Sänger has, in fact, used this concept to design the optimum wing and body shapes for hypersonic flight at extreme speeds. #In accordance with the pressure gradient quizlet freeThe pressure acting on an inclined surface is thus greater than the free stream pressure by a quantity which is approximately proportional to the square of the angle of inclination instead of the usual linear law for conventional supersonic flows. von Kármán has pointed out that in many ways the dynamics of hypersonic flows is similar to Newton's corpuscular theory of aerodynamics. Hypersonic flows are flow fields where the fluid velocity is much larger than the velocity of propagation of small disturbances, the velocity of sound. Hsue-shen Tsien, in Collected Works of H.S. ![]()
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