Irrotational flow over spillways of finite height

"Reprinted from Journal of the Engineering Mechanics Division Proceedings of the American Society of Civil Engineers, Volume 91, Number EM6, December, 1965.""December, 1965."Potential theory is used to analyze free-surface, irrotational flow over spillways of finite height. Numerical values were obtained for free-surface coordinates, pressures on the surface of the spillway, and discharge coefficients for three separate spillway shapes. The spillways considered included (a) one corresponding to the shape of the nappe produced by flow over a ventilated, sharp-crested weir, (b) one corresponding to the shape of the nappe produced by flow over a ventilated, sharp-crested weir with negative pressure head beneath the nappe equal to one-half the head on the weir, and (c) one having vertical upstream face, a cylindrical crest, and a downstream tangent inclined 30 degrees from the vertical. Because flows of several heads were analyzed for each spillway, certain conclusions were drawn relative to spillway operation under high heads