Prediction of the key parameters of free over-fall flows within the generalized circular cross-section with varying flat bases

Free over-fall occurring due to the sudden bed drop at the channel end that referred as the brink, facilitates the determination of the flow amount (discharge) by only trailing the value of the water depth at that section. This paper mainly focuses on a new theoretical approach that analysis the free over-fall within a channel of circular cross-section with flat base at different elevation levels by applying the continuity and the energy equations based on one velocity point method. The hydraulic behaviors of the circular cross-section especially having different elevation of the flat base have been investigated in sub-critical flow regime to obtain the end depth ratio (EDR) from which the end depth discharge (EDD) values are computed. The non-horizontal free surface profile at the upstream of the end section due to the accelerated flow velocity is also computed based on the extended energy equation. Subsequently, due to its practical importance direct equations for the free surface profile are provided for each channel cross-section for different values of the non-dimensional critical depth. Furthermore, in order to ease the use of the solution for practitioner in this field, the generalized unique relationships for the EDR, the non-dimensional discharge, and the free surface profile are presented, since there is no direct general equation for all the derivatives of the circular channel as a single solution in the previous studies due to its complexity. Even, relevant experimental and theoretical studies are used to obtain more robust assessment of the applied approach.