Water stands at a depth h behind the vertical face of a dam as shown. It exerts a resultant horizontal force (F) on the dam, which tends to slide it along its foundation to overturn the dam about O .

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The pressure exerted by water varies linearly with depth. The average pressure is P a vg ​ = 2 1 ​ ρ g h . The total force is F = P a vg ​ × A = 2 1 ​ ρ g h × ( h ℓ ) = 2 1 ​ ρ g ℓ h 2 .

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