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Abstract

This paper presents the theoretical equations for the impact characteristics of free over-fall (ICFOF) in the pool zone with sloping upstream bed. The various impact characteristics considered are the brink depth, the impact position and impact angle, the tail water depth and the depth of water pool. In order to overcome the complexity in determining the ICFOF, they were expressed in dimensionless forms as functions of upstream bed slope (UBS), upstream Froude number and Drop number. The multiple regression analysis was used to obtain the empirical expressions for the ICFOF using the laboratory experimental results. It was found that the dimensionless brink depth decreases with an increase in upstream Froude number and UBS. With the increase in both the Drop number and UBS, the dimensionless impact position increases, while the impact angle decreases. On the other hand, the dimensional tail water depth and the dimensional depth of water pool vary directly with the Drop number and inversely with the UBS. In addition, the empirical equations proposed for horizontal upstream slope were compared with those of previous investigators. Further, a parameter called slope effect ratio is defined to state the effect of UBS on the ICFOF. Moreover, the empirical equation derived in this study can be used to design the structure of downstream apron practically. An example illustrates the calculation of the impact position/ tail water depth for downstream apron.

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