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Application of Pascal's Law

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Question

Find the exerted by a liquid of density $ρ$ , on the dam of width $b$ , as shown in the figure. Atmospheric pressure is $P_{0}$ .

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Solution

Consider a differential area of width by ans length $b$ at a depth $y$ from the free surface of liquid.
$d F = (P_{0} + ρ g y) (b d y)$
$F = h \int 0 (P_{0} + ρ g y) (b d y) = P_{0} b h + ρ g b \frac{h^{2}}{2}$

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