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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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Answer» <P> Solution :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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