Consider a simple model of a dam. A reservoir of water behind the dam is filled to a height h. Assume that the width of the dam is L. As the reservoir behind a dam is filled with water, the pressure that the water exerts on the dam increases. Eventually, the force on the dam becomes substantial, and it could cause the dam to collapse.
There are two significant issues to be considered: First, the base of the dam should be able to withstand the pressure. This means that the material of which the dam is made needs to be strong enough so that it doesn't crack (compressive strength).
(a) What is the total force that the water in the reservoir exerts on the dam?
The second issue has to do with the strength of the foundation of the dam. The force of
the water produces a torque on the dam. In a simple model, if the torque due to the water
were enough to cause the dam to break free from its foundation, the dam would pivot
about its base (point P). The foundation of the dam should be strong enough so that the
dam does not topple, which means that the material has to be strong enough that the dam
does not snap (shear strength).
(b) What is the magnitude of the torque about the point P due to the water in the reservoir?
F= P X A
The Attempt at a Solution
For part a)
break dam into little strips, each strip has a dif force...
dF = PdA = density(g)(L)(h)dh <-- integrate this?
= 1/2 (density *g * L)(h^2)???
for part b)
to find torque, sum up the little pieces?
Integration of d(Torque) = integration of dFrmoment arms = integration of dFy
from here I'm not sure where to go??? any help is appreciated :)