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Abstract
Extended Bernoulli-type energy equations are deduced for highly curved potential flows. The errors from various approximations for potential flow with curved and sloped streamlines are discussed. The impact of the linear streamline curvature distribution is addressed by using the complete, numerical solution of the potential flow equations considering a generalized curvature distribution law. Further, the limitations of the mathematical developments after integration of the governing equations are analysed. If the mathematical limitations and the curvature variation are properly accounted for, the error becomes acceptable for an approximate treatment of highly curved flows. Two approximations for these flows are proposed, and the approach is verified for highly curvilinear flow over a spillway as a test case.