Answer to Question #190775 in Civil and Environmental Engineering for John Prats

Question

The face of the dam adjacent to the water is vertical and is 90 ft. wide at the top, 60 ft. wide at the bottom, and 20 ft. high in the form of an isosceles trapezoid. Find the total force on the face of the dam due to the water pressure.

Answer 1

The face of the dam adjacent to the water is vertical and is 90 ft. wide at the top, 60 ft. wide at the bottom, and 20 ft. high in the form of an isosceles trapezoid. Find the total force on the face of the dam due to the water pressure.

Change to SI unit:

Top width=90ft=27.43m

Bottom width=60ft=18.28m

Height of dam(h)=20ft=6.09m

Slope due to line of different sections constant width=(18.28-27.43)/6.09=-1.50

Width equation in form of depth

w=27.43-1.5h

Force due to submerged water= integrate over the range of 0 to 6.09 of PdA

P=1000*9.81*h

dA=wdh

dA=(27.43-1.5h)dh

PdA=1000*9.81*h*(27.43-1.5h)dh

PdA=9810(27.43h^2/2-1.5h^3/3)

F=9810{(27.43*6.09^2/2-1.5*(6.09^3/3)}

F=9810(508.66-112.93)

F=9810(508.66-112.93)

F=3882079.27N

F=3882.07927kN