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Analytical and Numerical Boundary Layer Solutions at Weir Crest Control Section

Author(s): Oscar Castro-Orgaz; Willi H. Hager

Linked Author(s): Oscar Castro-Orgaz, Willi H. Hager

Keywords: Experimentation; Scale effects; Surface tension; Viscosity; Weir flow

Abstract: Fluid viscosity is one of the major sources of scale effects at control sections of round-crested weir flow. It produces a notable reduction of the ideal fluid flow discharge coefficient originating from the boundary layer displacement thickness at the weir crest. Typically, the boundary layer is laminar in models and assumed for simplified computations that it behaves like a zero-pressure gradient flat plate. This is against the basic flow features of curvilinear weir flow, for which the pressure distribution is definitely non-hydrostatic. However, a systematic study of the laminar boundary layer development along round-crested weir flows is lacking. In this work a detailed two-dimensional finite-difference solution of the boundary layer development along the roundcrested weir is presented. The numerical solution of the boundary layer equations was obtained using the outer potential velocity distribution in the curvilinear flow zone as obtained from a two-dimensional irrotational flow solution for round-crested weir flow by semi-inverse mapping. Further, a one-dimensional solution using the integral laminar boundary layer equations was obtained numerically and compared with the twodimensional results, indicating a good agreement. To facilitate engineering computations of water discharge measurement, neither the two-nor the one-dimensional numerical solutions are suitable. Therefore, the integral method was applied to seek a simplified analytical solution of the boundary layer displacement thickness at the weir crest, based on an exponential near-bottom velocity distribution of the curvilinear flow. A comparison of the new analytical solution against the full two-dimensional results indicates good results for engineering purposes. The analytical solution was also compared with the classical flat plate computation, resulting in a superior performance.


Year: 2015

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