Question

a vertical dock gate is 5m wide and is hinged at 1m from the base of the dock.
the dock has sea water with density of 1025 kg /m^3 to a depth of 7.5 on one side and
fresh water to depth of 3m on the other side
a) find the resultant horizontal force
b) Determine the overtunning moment that the gate hinge has to withstand

Answer 1

I assume you want force on gate, not on the wall to the bottom

force salt = 8*1025 g integral z dz from 0 to 6.5 (z is down from surface)
= 8*1025*9.81 (6.5)^2/2 =1.7 *10^6 Newtons on gate from salt water

force fresh on gate =8*1000g int zdz from 0 to 2
=8000*9.81* 2^2/2 = 157*10^3 =.157*10^6
net force = (1.7-.157)10^6 = 1.54*10^3

moment from salt = 1.7*10^6 (1/3)(6.5)
(centroid of triangle 1/3 of distance from base)
= 3.68*10^6 Nm
for fresh .157*10 ^6 *(1/3)(2)
= .105*10^6 Nm
net moment = (3.68-.105)10^6 =3.57*10^6Nm