Question

The control gate ACB is pinned at A and rests on the smooth surface at B. The gate has a width of 5 ft. Neglect the weight of the gate. ye 62.4 lb/ft3 Figure 1) ▼ Part A If the counterweight C is 1500 lb, determine the maximum depth of water h in the reservoir before the gate begins to open Express your answer using three significant figures View Available Hint(s ft Figure < 1of1 > Submit 3 ft Provide Feedback 1.5 ft

Answer 1

Given that gamma_0 = 62.4 l b/f t^3 width of Gate = 5 ft Now, Hydrasiatic Force on AC&BC Part of the Gate is Given As below F_AC = gamma_omega(h-y)(3 times 5) = 15 gamma_omega(h-y) F_BC = gamma_omega(h-y + 1.5/2)(1.5 times 5) = 7.5 gamma_omega(h-3.25) At the Point The gate begins to open, we have F_AC times 3/2 + F_BC times 1.5/2 = 2000 times 3 [Taking sigma M_A = 0] \r\n implies 2 F_AC + F_BC = 2500 times 3 times 2/1.5 implies 2 times [15 gamma_omega(h-y)] + 7.5 gamma_omega(h-3.15) = 10000 implies 30h-120 + 7.5h-24.375 = 10000/gamma_omega = 10000/62.4 implies 37.5 h = 304.63 implies h = 304.63 implies h = 304.63/37.5 = 8.12 ft implies h = 8.12 ft Hence the required height of water = 8.12 ft