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Prove that the magnitude of the hydrosta...

Prove that the magnitude of the hydrostatic pressure is proportional to the height of the column of liquid (or gas) and is independent of the vessel's shape. 

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No matter what the shape of the vessel is, one can always imagine it to be made up of small vertical columns of liquid for which the formula `p = rho gh` was derived (see Fig.). But since the pressure at all points at a given depth is the same (a corollary of Pascal.s law), to compute the pressure at the depth h one should add up the pressures of all the upper layers:
`p = p_1 + p_2 + p_3 + … =  rho g(h_1 + h_2 + h_3 + ….) = rho gh`
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