An open water conduit is to be cut in the shape of an isosceles trapezium and lined

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An open water conduit is to be cut in the shape of an isosceles trapezium and lined with material which is available in a standard width of 1 metre, as shown in Figure 8.21.

To achieve maximum potential capacity, the designer has to maximize the area of cross-section A(b). Show that

A(b) = [(1 + b)(1 - b)]/

and that this is maximized when b = 0.5.

Figure 8.21 Water conduit b 1 b 1

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