An equilateral triangular plate with sides 8 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral (let the positive direction be downwards) and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the maa density of water is 1000 kg/m3.)

A triangular plate with base 6 m and height 2 m is submerged vertically in water such that the highest vertex of the plate is 6 meters below the surface and the base is horizontal to the surface. 6 m 6 m 2 m Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.)

The end plates (isosceles triangles) of the trough shown to the right were designed to withstand a fluid force of 6400 lb. Assuming the density of water is 62.4 lb/ft³, how many cubic feet can the trough hold without exceeding this limitation? What is the value of h, the depth of water that exerts a fluid force of 6400 lb? What is the integral that gives the fluid force exerted on the end of the trough when filled with water to a depth of h? h Sody The maximum volume is ft³. (Round down to the nearest cubic foot.) The value of his (Round to two decimal places as needed.) (-3,14) (0,h) y (ft) (3,14) 14 y 3x x (ft) 0 End view of trough 14 ft 30 ft 6 ft → Dimensional view of trough

A tidal barrage is in the shape of a quarter cylinder of radius r=16m, as shown in the picture above. If the barrage is 13m wide and holds back water of density 1014kg/m³ to its full height, what is the magnitude of the vertical force on the barrage? Assume that the atmospheric pressure is constant. Give your answer in Kilo Newtons to the nearest whole number. Use an acceleration due to gravity of g=9.81m/s²