Hydrostatic Force

Question

The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y = 0.4x^2 below the line y = 180. . (Here, distances are measured in meters.) The water level is 20 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000 kg/m^3 , and the acceleration of gravity is 9.8 m/s^2)

Answer 1

Elementary force on y level: dF = ρg(160 - y)·2√2.5ydy; F = 2√2.5ρg∫₀¹⁶⁰(160y^1/2 - y^3/2)dy =

2√2.5·1000·9.8(2/3·160^5/2 - 2/5·160^5/2) N = 2676053333 N