The study is devoted to the parabolic-shaped thin-plate weir. It is the flow coefficient which is of particular interest to the study. This is planned to be determined from a theoretical point of view using the energy equation. This is applied between two well-chosen sections, the first of which is located in the approach channel upstream of the weir and the second is considered at the location of the weir. The state of the flow over the weir is subject to the realistic assumption that it is critical. Other simplifying assumptions are adopted such as the head loss which is neglected between the chosen sections, or that the pressure is considered to be hydrostatic. The effect of the curvature of the flow streamlines above the weir is also neglected. The strength of the theory lies in the fact that the approach flow velocity is taken into consideration.

Taking into account all the simplifying assumptions made during the study, it is obvious that the theoretical discharge coefficient must be different from the experimental discharge coefficient. In order to correct the deviation observed between these two discharge coefficients, experimental data available in the literature are used. The corrected theoretical discharge coefficient relationship was established on the basis of 157 significant measuring points, giving rise to an average error of less than 1.3% on the discharge coefficient calculation, while the maximum deviation is of the order of 6%. It is worth noting that 92.85% of the calculated values of the deviation are below 3%, meaning that 7.15% only are greater than 3%, while 82.5% are less than 2%.


Parabolic weir, discharge coefficient, approach channel, approach velocity.

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