Fixed inclination examination

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Reference no: EM13134700

An irrigation canal has the shape of a trapezoid. Let x = the bottom width, y = the water depth, and theta = the angle of inclination of the sides from the horizontal.

a) Show that the area A = y(x|ytan(theta)) and the wetted perimeter P = x|cos(theta).

b) It is known that the best design for a fixed inclination is found by minimizing P subject to the constraint that the area A = A_0 is constant. Show that this implies that y^2 = (A_0)(cos(theta))/(2-sin(theta)).

Reference no: EM13134700

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