If you compress gently ( isentropically ), the heating is weaker than when you compress violently ( by a shock wave ).
2.
In compressible flow the stagnation pressure is equal to total pressure only if the fluid entering the stagnation point is brought to rest isentropically.
3.
The possible use of an expansion machine for isentropically creating low temperatures was suggested by Carl Wilhelm Siemens ( Siemens cycle ), a German engineer in 1857.
4.
Because the total flow conditions are defined by isentropically bringing the fluid to rest, there is no need to distinguish between total entropy and static entropy as they are always equal by definition.
5.
If you allow the liquid to isentropically expand after the shock and to return to the original pressure, its temperature will end up higher than the initial one, and it may well boil.
6.
The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure plus static pressure . " Total pressure " is also equal to dynamic pressure plus static pressure so, in incompressible flows, stagnation pressure is equal to total pressure . ( In compressible flows, stagnation pressure is also equal to total pressure providing the fluid entering the stagnation point is brought to rest isentropically .)
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