Analytical Solution for the Free Over-Fall Weir Flow Using Conformal Mapping and Potential Flow Theory

In this study an analytical approach is presented based on the potential flow theory and conformal mapping technique to solve the problem of an ideal and steady flow over a free over-fall weir. The results are arranged for rectangular sharp-crested over-fall weirs with different vertical aspect ratios (h/P, h is the water head above the weir and P is the weir height). To validate the results of this approach, the free over-fall weir discharge equation and the water free-surface profiles obtained with the potential flow theory have been calibrated with the experimental data. In conclusion, the information made available and the close correlation among the results of present analytical approach and the experimental data are adequate to warrant the recommendation of this method as a valuable supplement to existing methods employed in engineering design.