Question

2. Adam the shape of a trapezoid is shown below. The height is 40m, the bottom. Find the force on the dam due to hydrostatic pressure if the water n below. The height is 40m, the width is 60m at the top and 40m at dam. Assume that the density of water is p = 1000kg/m', and th c pressure if the water level is 4m from the top of the of water is p=1000 kg/m' and the acceleration of gravity is g 9.8 ms (Note that hydrostatic force is described by the equation F=PA, where P is the pressure y the equation F = PA where P is the pressure and A is the area of the dam. This could also be written as F=PgAd, where A so be written as F=pg&d, where is the area of the dam and dis the depth below the surface of the water.) (50 points) (Hint: This problem is similar to Example 1 on pages 598-599 in Section 8.3.)

Answer 1

water Surface K Solution consider only the part of dan - som That is actually submerged in water. At any depth y measured Hotom from water surface, let 'w' be the dam widoh. From the diagram, Triangles, AABC and AADE are similar. Therefore a = 20 ( Be - DE) az 20 * & a= 2 (y + 4) [since H= 4om] W = 60-a » We 60-1/2 Ly+4) W = 58-ly Hydrostatic force exerted on the down, re-density of water F = Sexgxyew.dy Je-de = 1000kg/? Ig-acceleration due F: 1000 x2.81* fʻy (58 - xy) dy de grandes neinte - 1000x4.41 x 589 -y* Solving, F = 292 416480 N... (Ans.)