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When I read through text in fluid mechanics, I see various ways of non-dimensionlising the pressure. (Please see the figure)

To me, non-dimensionlize a quantity is to make it of order unity to facilitate the mathematical processes needed afterwards.

So, I can understand why density*gravity*H is used as a characteristic scale to non-dimensionlize the pressure since it is the maximum hydrostatic pressure.

But I don't understand why density*U^2 is used to non-dimensionalize the pressure as well? In what situation is this nondimensionlization valid?

What about the P(infinity), what is it?

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# Nondimensionlization of Pressure

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