Water flows steadly in an open topped channel of rectangular cross section. The channel width is B and the depth of the water is D. The flow is designed using a rectangular coordinate system whose orgin is at the free surface midway between the walls. The x axis is normal to the walls, and the y axis points vertically downward. The velocity W is normal to the xy plane and is given by
W(xy) = Wmax[1-(4x^2/B^2)][1-(y^2/D^2)]
Find an expression for the flowrate and average velocity as functions of B,D and Wmax