Question

5.     The plane rectangular gate can pivot about the support at B. For the conditions shown, would the gate pivot or not? Neglect the weight of the gate.

Answer 1

8 m Water CP 3.5 m B 45° G be the centroid of the gate at a slant height y from the water surface P be the center of pressure at a slant height ycp from the water surface Consider the gate as our system: 8m 45° Here, x is the gate length From the geometry of the figure, sin 45°- x11.3137 m sin 45° x 11.3137 y 5.655 m We know that, 12 1x11.31373 12 (1x113137) (5.655) +5.655 УСР 7.541 m The point Bis at a distance of b from water surface b (11.3137-3.5) 7.8137 m As yCP Is above point B from the water surface, the gate is unstable and the gate doesn t pivot