THEORETICAL DISCHARGE COEFFICIENT RELATIONSHIP FOR A CONTRACTED TRIANGULAR NOTCH WEIR. EXPERIMENTAL ANALYSIS FOR THE SPECIAL CASE OF THE 90-DEGREE V-NOTCH

Abstract

The study proposes a theoretical development in order to determine the relationship which governs the discharge coefficient of a contracted triangular weir. The theoretical approach takes into account the effect of the approach flow velocity which can be considered as a novelty in comparison with previous studies. The theoretical development consists in applying the energy equation between two well chosen sections with certain simplifying assumptions, namely: i) the head loss and the effect of both viscosity and surface tension are neglected, ii) the hydrostatic distribution of the pressure is considered hydrostatic, iii) the effect of flow streamlines curvature over the weir is neglected. The first section chosen is located in the supply channel at a certain distance upstream of the weir, while the second section corresponds to the location of the weir supposed to be crossed in a critical flow regime. Based on the data available in the literature on the 90° opening angle triangular weir, the experimental and theoretical discharge coefficients are compared and relative errors varying between 4% and 10% are observed. The theoretical discharge coefficient relationship is thus adjusted to be in conformity with the experimental data relative to this apex angle. The corrected theoretical relationship causes a maximum deviation of 1.5% on the calculation of the discharge coefficient, but this error is observed only for the ratio P/ B = 1. For the other values of P/B, the maximum error varies between 0.35% and 1.3%, where P is the weir crest height and B is the width of the rectangular channel of approach.