If you imagine an aircraft cruising, at incidence, with a pressure tapping underneath its fuselage, the forward trace of a streamline taken from just outside of the fuselage's boundary layer may indeed avoid all shocks and just be pure freestream flow, with a static pressure of - p1. both subsonic and supersonic, can be measured by means of a Pitot tube, but the equations are different from Equation (3.34). The pressure read at a pressure tapping is the pressure of the inviscid part of the flow, just outside of the boundary layer. This could be the answer, but if you trace a streamline from the location of the static tapping forwards along its path, it would have to avoid going through a strong shock at any point. Therefore, it is essential that compressible flow relations be used when evaluating flow velocity from Pitot probe measurements. Even if it goes through the edge of the bow shock, oblique shocks are much weaker than normal shocks, like the one right at the centre of the bow shock.
I thought that maybe, because the fluid flow that goes past the static pressure tapping may not go through the bow shock directly, that means it doesnt go through a normal shock, and hence it is indeed p1 not p2. I could be wrong about this though, I didn't look very hard for confirmation of the Rayleigh formula! I quickly dismissed this however as it names the equation the Reighleigh formula and so I assume P02/p1 is used universally to calculate supersonic aircraft speed. Initially I considered the that perhaps the only reason the relation is described as P02/p1 is for the plot on the final page - so that they can directly compare P01/p1 and P02/p2 in the graph, to clearly show the energy loss over the shock, and the incorrect aircraft speed that would be calculated if the right equation is not used. I'm surely too late in replying, since you posted the question over 2 months ago, but I thought I would have a good stab at it anyhow as I enjoy the subject and these sorts of questions are good fun! Static Pressure Measurement in Supersonic Flow - CFD Online Discussion Forums
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