Comment on stilmant et al. flow at an ogee crest axis for a wide range of head ratios: Theoretical Model. Water 2022, 14, 2337

Abstract

Critical flow in irrotational motion is important in theoretical hydrodynamics and dam hydraulics. Therefore, the commented paper is relevant in theory and practice. It deals with an approximation for critical flow based on a set of simplified irrotational flow equations in the gravity field. The underlaying model equations were found by the discussers to strongly rely on Jaeger’s work. Therefore, some important aspects need a detailed clarification. Jaeger’s velocity profile was determined here by a possibly novel procedure starting from the irrotational flow relations in the complex potential plane. It was shown that, though not perfect, a theory assuming critical crest conditions gives consistent estimates of the discharge coefficient, crest flow depth, bottom pressure head, and velocity profile. A new method for computing the flow profile over an ogee crest is presented by simultaneous determination of the discharge coefficient and the real critical point position using the Bélanger–Böss theorem, resulting a physically based determination of the critical point in spillway flow. It is demonstrated that Jaeger’s curvature parameter K is not a universal value, such that neither the current comment nor the discussed paper are therefore “free” from empirical parameters.