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compressible
There is an extra requirement that the stagnation happens in an isentropic manner, but this is usually true when we consider air at low speeds. In fact, the stagnation of air is usually treated as isentropic unless we know it is not (for example, if we know a shock wave is present). Not being isentropic means mechanical energy is dissipated in the process, if you spill water on the ground and let itself come to a rest, you will not observe the level rise, for example.
==== Compressible effects ====
You may ask, if the static pressure is to increase, then by the ideal gas Equation of State, definitely the density and the temperature are to change? You are correct and this is the compressible effect which, up to now, the author has tried to avoid like the plague. Some people say that, because the flow is incompressible, the density remains constant and the temperature increases, but this is wrong because by invoking the Equation of State the assumption of incompressibility is voided automatically. In other words, the Equation of State has its foundation on the fact that gas molecules can get closer or further apart as governed by some rules.
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).
If you are still interested, you may contact the author. You are encouraged to become an aeronautical engineer.
=== Pressure coefficient ===