Question

A dam has been designed with a parabolic contour - 2 x 12 40 on the retaining side, Figure 2. The reservoir is saltwater (SG = 1.03), and the dam has dimensions Xo = 20 ft, and zo = 48 ft. Compute a) The horizontal and vertical forces per unit width of dam Fh and F, b) The point of action (Xcp, ycp) on the dam wall c) The angle of action zo F CP To Figure 2. Dam System for Question 3

Answer 1

do= 2o3+, Z = 48ft. Salt water = 1.03 assume unit width 13T7 K N . ..to/ tan - F INK FH = sgarh CHrizontal force on projecteay

S4=1.03 (BD Dan g=32º2 ft/en : 8=.62.4168 1673. 31.03 (89)w (SI)eunt = (1-03)(89) (59)euk = (1-03) (32.2)(62-4) = 2069.55 Area = Zox1 = 48 ftv ha zo = 245€ Fu = gg añ. . r = 2 = (2069.55) (48)(24) FW = 2:3841312X100 lbs Fv is nothing total weight of the Huid above the Surface , volune = Areax width re varies from 230; } -(0) Z is som 0, +48 7.x=x". . . me = Areax cuidth so, Area ( 40 18-01-07 at they had O 130 4. g YA

= 2 80020 Area = ? x 20x48 1 = 640 ft. vdure = 640 ft3. weight of fluid =ng= pug 1. = (pg) v F0 = (2069155) 640) Fe = 1.324512 x10ʻlbe. ģ= 24 2X X . Yoq= gt 7 g 24+ (x2) Yep = T12X84) Jp = 28 # form free surface, fom the base 48=28=20ft Kepa fomegn Ž - (a)" x = 12.90ft

FR c) angle of action o - Tano = F Ostant (1932451! ) Fr= ✓ FTFEN (213841312) 8 = 29.05°