Question

3) The 8 meter diameter flat circular plate (full circle) is positioned vertically with the bottom of the circle sitting on the bottom of a tank. The water in the tank is only 6 meters deep. COMPUTE the hydrostatic force on one side of the plate: The integral you need to compute is: The computed force is:

Hello, if possible, please submit answers in neat as possible writing, my vision in not too great thanks

Answer 1

First we 21 have set up a coordinate System whorse origin is at the Centre of plale. Ay 1 2m 1 ui 8M Gm Let us divide the plate in width which is at distance gi from from n strips of 27 N-axis. Depth below water surface of a each strip is 2- yil di = So, Pressure strip Pi's Pgdi 9810(2-4 Area of Each Strip Aizaki Ay [ni = (16-(y,« As Equation of is [n+ g = 16 Circle Ai = 2 j 16-lyit sy Flydoostatic force then - Fiz Pi Ai 9810 (2-4) (2) / 16. (gilt by Total force than

F 2 2 Gཀ 2 ·༢ 62༠ (7 -d) ( ( 16-qj-） ༧ nao - ཧ F = ( 1 626 y)/16-42 dy Integral =༦ we need to compute solving the Intezaal: 2/16 - yz dy - 19620 /j 116-yz dy F – ལ༠༠ ལ ༌ རུ F）

F2 Fit F2 2 Fiz 19620 2 116-yz dy y = 4 sino dy 46so do Flo e 19620 196203 2x4x4 G12o do Th to Ž Ge2o do = 627840 지 NO 313920 (It Grzo) do -kla To 313920 + 1 Sinzo) 11 2 -T/2 Fi = 793403.8579 N. Fz - 19620 y llo-y² v=16-42 du a - 2g dy 162. Jadi MELOM du = ydy fr 271862.6948 N

Total Hydroelatic force F = 793403.8579 + 271862.6948 L = 1065266.553 N