The relationship between the discharge and the depth at the brink of a freely discharging circular section is investigated. Through application of the momentum equation between a section upstream from the brink and a section downstream from the brink, the limits for the brink depth are established from theory. Experimental test points are found to lie between the limits so delineated. A dimensionless plot is provided, from which the discharge versus brink depth can be calculated for design purposes for any size of pipe.
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C. D. Smith (1962) studied this question.