This paper presents two separate solutions for potential flow through circular spillway buckets. The first solution, which considers gravity effects, employs finite difference equations in combination with a successive approximation procedure in order to satisfy the Laplace equation and the boundary conditions. The second solution, which neglects gravity effects, employs a perturbation expansion in combination with conformal mapping and analytical continuation. The two solutions are compared, and recommendations are made for their application.
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Lenau et al. (1969) studied this question.