Question

Question 2 (15 points) As shown in Fig. 2, if Ywater 9810 N/m2 and the gate is 2 m wide (into the paper), what is the moment M (N-m, clockwise is positive) at O to hold the gate closed? (Neglect friction and the weight of the gate.). Assume that Pam is constant in the air surrounding the system. м 45 Gate 2 m wide 1.2 m Water P atm Patm 0.6 m 0.3 m SG 6.0 Fig. 2

Answer 1

Water pressure Diagram 13 450 1. 2m Palm water uso om 2003) S6=6 t At section Pressure on will be equal [ Because klater Level in tank say h both side limb on gate Patm is Acting) from Bottom of tank Pertm + 0.3x6x 9810 = (0.6 +003 th) 9810 + Paim Th=o.gm . Gate is in clined So Horizontal as well as vertical force will Act

from walter surface = 9810x0.9% 0.9x2 TFn = 7946. 1 M Ev = weight of water Fu = volume xro azko.Gx0.9*9810 Impounded Above gate Oa9 - 7946.1 M FR = Jenna = 7946.177 1946.12 = 11237,48 N

Moment - Force x Distance [prependicular to force] hep = 2h from water surface = {xous = 0.6 m tama = FM 489 7946.) 21. - 0.6 m 19461 @2450 re Hence 0.3+0.6 20.9 N 0.9 Sinus = 1.272m Emring 20 M + FRU=0 ME - (1237,48 x 1.272 1 M = - 14.303 knom -ve Show poisition moment is in Required to just in close Anticlock wise Direction