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→Compressible effects
What will happen is that the density and temperature will increase simultaneously. The precise amount we cannot solve for based on the equations presented in this article: other thermodynamic formulae relating temperature to pressure must be introduced. The exact solutions will be presented as a function of '''Mach number''' (the ratio between velocity and the local speed of sound).
Compressible effects get more obvious as the speed becomes higher. Back to the date when this was not well understood, quite a few aviation pioneers were killed by pushing the frontier of how fast we can fly. We should commemorate these sacrifices with great respect when we appreciate the great achievement the aviation industry has made to date. If you are still interested, you may contact the author. You are encouraged to become an aeronautical engineer. For the purposes of this article, forget about the Equation of State and assume that the density and temperature will remain constant when the flow is stagnated. If you cannot get your head around this, imagine we fly gliders in water. It can be shown that, for typical gliding speeds, the error introduced by ignoring the compressible effects are on the order of 0.1%.
=== Pressure coefficient ===
