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I started to learn basics of physics in a university. I know that it is wrong to compare for example pressure and length, like $2\mbox{ Pa}\ne 2\mbox{ m}$. But from algebra I know that $0=0\cdot 2\mbox{ Pa}=0\cdot 2\mbox{ m}$. So if I have the situation that I can choose the zero levels of pressure and height at certain area $A$, am I allowed to write $p_A=h_A=0$?

For example: The equation for the pressure in a fluid of uniform density is of the form $p_2-p_1=-\rho g(y_2-y_1)$. If we choose $p_1=y_1=0$, we get the equation $p_2=-\rho gy_2$.

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marked as duplicate by user36790, garyp, Community Oct 27 '16 at 19:58

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In terms of this equation it wouldn't really make sense to set those quantities to 0. You have to think in terms of what those 0s actually mean.

To have a pressure of 0 we'd be talking about a vacuum which is void anything, including fluid.

By saying a height of 0 you're essentially asking what the pressure is without gravity, so in an enclosed space it would be directly proportional to the volume/density ratio. In an unenclosed space the pressure would be the same every whatever's around the fluid since there's no gradient.

That simplified equation you get is nothing more than pressure modified by the force of gravity.

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