By the Pythagorean theorem,the height of the dam is . (See Figure 5.9.2(a).)
As per Figure 5.9.2(a), measure y positive upwards from the bottom of the dam. To find dA, the area of a horizontal strip at depth , observe (from similar triangles) that
so
Adding 15 to twice this length gives
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Figure 5.9.2(a) Hydrostatic force on a trapezoidal dam
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so that . The force is the product of the pressure and the area, or
≐ lbs
Alternatively, obtain the hydrostatic force as the product of the area and the pressure at the centroid of the dam.
From Example 5.7.5, = , and .
Consequently, the hydrostatic force is =