Hydrostatic force

Question

The Deligne Dam on the Carley River is built so that the wall facing the water is shaped like the region above the curve y = 0.1 x^2 and below the line y = 160. (Here the distances are measured in meters.) The water level is 26 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

x = ±√(10y)

F = ∫₀¹⁶⁰ρg(160 - y)·2√10ydy = 2√10ρg(320/3y^3/2 - 2/5y^5/2)₀¹⁶⁰ = 2√10·1000·9.8·160^5/2N = 5.352·10⁹ N