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Why does stagnation pressure remain unchanged when velocity of air increases if the formula is:

stagnation pressure = static pressure + (1/2×density×velocity$^2$)

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    $\begingroup$ jfksgya. Does it? $\endgroup$ Feb 19 at 20:27

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The formula you cite is for incompressible flow, such as liquid or very low speed gas flows. If no work is done on the fluid the stagnation pressure remains constant so increasing velocity will decrease static pressure (and vice versa). Flow through a pipe that gradually changes diameter would be an example (though we do need to neglect friction losses).

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