Improved calculations of waterfalls and weir flows

Many works have considered two-dimensional free-surface flow over the edge of a plate, forming waterfall, and with uniform horizontal far upstream. The is assumed to be steady irrotational, whilst fluid inviscid incompressible. Gravity also taken into account. In particular, amongst these works, numerical solutions for supercritical flows been computed, utilising conformal mappings as well series truncation collocation method. We present an extension this work where more appropriate expression form complex velocity. justification lies in behaviour waterfall downstream wish better encapsulate parabolic nature such free-falling jet. New results will presented, demonstrating improved shape new profiles. These validated through comparisons asymptotic solutions, particular larger Froude numbers. For numbers closer 1, we demonstrate that revised velocity ansatz should employed place solution. further adjustments method lead enhanced coefficient decay. aforementioned are applied weir similar improvements jet can observed.