Consider the vertically submerged rectangular plate. We are going to determine the total force due to liquid pressure on the plate. The dimensions of the plate are W = 15 ft, L = 4 ft. The top of the plate is at a depth of D = 10 ft below the surface. The weight density of water is 6 = 62.4 lbs/ fts. X=0 SURFACE D Xi TAX Ax X=h W This problem depends on the vertical coordinate system to the left. The force, Fi, on the i" strip of the plate = weight of the i" " column of water" (diagram on right) = 6 . wi, where u; = volume of the " column of water". For this problem, F; = 6 . vi = 6 15r Ar lbs Adding up the force on all the subintervals and allowing n + 00, where n represents the number of subintervals, gives the integral for total force due to liquid pressure, F. (Don't forget 6) 11 X F 93order x dax syntax error. Check your variables - you might be using an incorrect one. 10 Finally, F lbsA dam on a river is built so that the wall facing the water is shaped like the region above the curve y = 0.71' and below the line y = 160. (Here, distances are measured in meters.) The water level is 30 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. kg (Water has a density of 1000 -, and the acceleration of gravity is 9.8 Ser2 1203744080 XA dam is in the shape of a trapezoid as seen. We are going to determine the total force due to liquid pressure on the dam. The dimensions of the dam are W = 40 ft, L = 400 ft, and a depth of D = 300 ft. The weight density of water is 6 = 62.4 lbs/ ft3. X = 0 W SURFACE W Xi Ax Ax X = D L This problem depends on the vertical coordinate system to the left. The force, Fi, on the i" strip of the dam = weight of the " " column of water" (diagram on right) = 6 . vi, where u; = volume of the " " column of water". Note: Use similar triangles to determine the cross-sectional width of your strip. For this problem, F = 6. vi =6. lbs Adding up the force on all the subintervals and allowing n -> 00, where n represents the number of subintervals, gives the integral for total force due to liquid pressure, F. (Don't forget 6) F dx Finally, F = lbs