Hydrostatic Forces & Buoyancy

Worked: a vertical gate

A vertical gate 4 ft wide and 6 ft tall has its top at the water surface. h_c = 3 ft and A = 24 ft², so F = 62.4 × 3 × 24 = 4,490 lb. I_c = 4 × 6³/12 = 72 ft⁴, so y_cp = 3 + 72/(3 × 24) = 4 ft below the surface — two thirds of the way down, as for any rectangle reaching the surface.