Comparing these equations (16.5) to (16.8), with the earlier derived equations (15.8) to (15.12), it can be seen that these equations are identical if we ignore the variables involved in making them. However the equations (15.8) to (15.12) are for three dimensional steady flow and equations (16.5) to (16.8) are for two-dimensional unsteady flow. This information is helpful in depicting the hypersonic equivalence principle which states that, “The steady hypersonic flow over a slender object is equivalent to an unsteady flow in one less space dimension”. This analogy can be visualized using the Fig. 11.1. Consider a slender body translating x-direction direction as shown in Fig. 11.1. The frozen moment at initial time is shown in two views, one in x-z plane and other in y-z plane, are placed side by side in the same figure. The view in x-z plane is the configuration of the slender body while view in the y-z plane is just a point at origin in the initial time. If V_∞is the velocity of the object (in the negative x direction) then at any time later (say t₁), tip of the object moves in negative x direction by distance V_∞ x t₁. In this process the view of the object in x-z plane just gets translated as shown in Fig.11.1. However, the view of the same object in y-z plane is the section of the same object taken by y-z plane at origin or section at distance V_∞ x t₁ from the tip. Similarly after time t2 the view the view in x-z plane gets further translated while view in y-z plane portrays the section of the object at the distance V_∞ x t₂ from the tip.

Fig 11.1: Illustration of the Hypersonic Equivalence Principle

This illustration makes it very much clear that study of three dimensional steady hypersonic flow over a slender object is equivalent to study two dimensional unsteady flow over the same. However we will have to view it differently. This equivalence principle forms the basis of the Blast Wave Theory.