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I came across this question in "Fundamentals of Aerodynamics" by John Anderson, although I knew how to solve the question, I didn't understand why we had the surface pressure on the wedge 1.31×10^5 N/m^2 higher than the freestream pressure 1.01×10^5 N/m^2, I thought it is intuitive to consider the freestream pressure always higher than surface pressure.

Here is the image from the exercise illustrating the situation

Here is the question if you needed more information

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  • $\begingroup$ There is a difference between total pressure and static pressure. The total pressure is always higher in the free stream, while the static pressure can be higher at the surface. A simple idea is to think about it like total energy (total pressure), which consists of the the kinetic part (dynamic pressure) and the potential part (static pressure). While you are losing energy because of friction you can still convert kinetic Energy (dynamic pressure) into potential Energy (static pressure). $\endgroup$
    – Artur
    Commented Feb 10, 2022 at 16:56

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At supersonic speed, air makes way for a body by increasing density and pressure, so the same air takes up less volume when flowing around this body. It does so by forming compression shocks when the inclination of the body surface to its direction of movement increases, and by forming expansion fans when that inclination is reduced or the body contracts again. A second shock is produced when the flow around both sides meets again at the end of the body.

That free stream pressure is higher than surface pressure is mostly true only at subsonic speed, where air speeds up (and reduces static for an increase in dynamic pressure) to make way for a passing body, except at and near the stagnation points (rsp. stagnation lines on wing-like structures).

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Pressure at the surface facing the free stream is higher than free stream pressure, for supersonic as well as subsonic flow. The body surface is displacing a certain volume of air - at subsonic speeds the body can warn the air that it is arriving, slowing it down in exchange for a rise in pressure. With the highest pressure at the stagnation point.

enter image description hereImage source

At supersonic speeds there is no fore-warning, air can only be compressed after the stream hits the body front. Nevertheless, compression still takes place because of the body taking up air space.

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