Free overfalls in flat-based circular and U-shaped channels

This paper presents a theoretical model based on the free vortex theorem that is capable of predicting the pressure head distribution at the brink of free overfalls in open channels. This approach is coupled with the momentum equations to obtain the end-depth-ratio (EDR) from which the discharge can be estimated. In order to illustrate its flexibility, the theory is successfully applied to flat-based circular and U-shaped channels. Using previous experimental data, the proposed method is validated.

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► In U-shaped channels, the value of the EDR is approximately 0.75 for a value of yˆc=0.5.
► In flat based circular channels, the EDR can be considered as a constant when hˆc≤0.8.
► In subcritical flow the theoretical results enable one to estimate the discharge within 4%.
► At low relative depths the overall end pressure coefficient has been shown to be 0.33.
► This method can also be applied when the approaching flow is super-critical.