mathematics behind the construction of dams
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There are many engineering considerations and
calculations needed when building a dam, the most important being the
water pressure behind the structure. Engineers know that as the
elevation of water behind a dam increases, the height and density of the
water causes higher pressures at the bottom of the dam. Thinking in
mathematical terms, the horizontal force acting on the dam is the
integral of the water pressure over the area of the dam that is in
contact with the water. The force exerted by the water pushes
horizontally on the dam face, and this is resisted by the force of
static friction between the dam and the bedrock foundation on which it
rests. The water also tries to rotate the dam about a line running along
the base of the dam; the torque resulting from the weight of the dam
acts in the opposite sense.However
Dam, an impressive structure on the Colorado River, could only have
been made possible by engineers designing it in such a way that the
walls were thick enough to withstand massive water pressure.For
example, take the water pressure on a dam, such as the Hoover Dam on
the Colorado River between Arizona and Nevada. Before building that dam,
engineers needed to know the pressure not only along the entire
structure, but also—and especially—at its base. In general, the pressure
exerted by water equals the density times the depth, in which the
density of water is 62.4 pounds per cubic foot. For Hoover Dam, this
gives a pressure of 37,440 pounds per square foot, or 18.72 tons per
square foot; the pressure calculated at half the height of the dam is
9.36 tons per square foot. This is why the base width of the dam is
1,660 feet (201.2 meters)—it is thicker to compensate for the increase
in pressure at the bottom of the dam—while the width of the crest of the
dam is only 45 feet (13.7 meters).
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Answer:
Thinking in mathematical terms, the horizontal force acting on the dam is the integral of the water pressure over the area of the dam that is in contact with the water. ... In general, the pressure exerted by water equals the density times the depth, in which the density of water is 62.4 pounds per cubic foot
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