Force on a trapezoidal dam – A vertical dam has
the shape of an isosceles trapezoid that is 3m high, 5m wide at the base
and 2m wide at the top, which is just level with the surface of the
water upstream of the dam. Use two different methods to determine the
total force (N) exerted by the water on the dam:(a) Derive an expression
for the width of the trapezoid as a function of the depth, w(z). (b)
Integrate the pressure acting on differential areas of the dam (dA =
w(z)dz) over the entire surface to determine the total force (N) exerted
by the water on the dam. (c) Calculate the total force exerted on the
dam by multiplying the pressure at the centroid pc by the total
area.Note: For a vertical trapezoid with the top edge coincident with
the surface of the liquid, the depth of the centroid equals:hc =h 3(2w1 +
w2) (w1 + w2)in which h is the height of trapezoid, w1 is the width of
the base and w2 is the width of the top
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