fliud mechanics for chemical engineering

 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