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So I have just learned that the formula for a fluid's hydrostatic pressure (let's say water for the purpose of simplification) in terms of depth is:

P = ρ * g * h

Now I have been reading a bit on my textbook and I found out that the derivation of this formula is based on the assumption that for a given water column with volume V and height h resting on an area A on a given surface, the pressure is:

P = F/A = mg/A = (ρV)g/A = ρ(Ah)g/A = ρgh

Now I've also noticed that the same formula is used even when dealing with vertical contact surfaces, which I don't understand because when in that case (let's say in the case of a dam with a horizontal interface), there is no water directly "resting" on the surface and thus we cannot use the given formula.

So could you please tell me what I have missed in my reasoning and the misunderstandings (if any) that I have about the concept ? Thanks in advance.

(Please note that I am not denying the existence of hydrostatic pressure, I am just saying that its expression shouldn't be that of the conventional ρgh)