Question

Answer should be 13450 lbf

5. (25 pts) The angled gate shown below should be designed to just begin opening when the total water depth is 6 ft. If the gate is constructed of a homogeneous material and hinged at the bottom as shown, what is the minimum weight of the gate needed to satisfy this condition? The width of the gate into the page) is 10 ft. resh water at 2 ft Gate standard conditions 60° Hinge 0

Answer 1

* WIDTH of GATE = 10 ft DENSITY OF WATER p = 60.4 16/ft? at FROM WATER C.G. HEIGHT SURFACE 5 = 4+2 = 5 ft aft * PRESSURE AREA . Az LENGTH & WIDTH = 2 * 10 23.094 ft sin 60 ☆ PRESSURE Force Ее рећа = (62.4) (23.094) (5) (3814) F = 231795.5098 lbf

AREA OF MOMENT OF INERTIA OF Fee = (años ) x10 X/o 10.264 ++ ► HEIGHT OF PRESSURE FORCE POINT 5*= 6 + dCG Singo) Deck timbang - 5.133 66 - = 5.133 to АГ → Apply EQUILIBRIUM CONDITIONS Em( HINGE) =O +2 wetenci) + f (6-=0 sinto W = 401778.884 168