DISCHARGE COEFFICIENT FOR A TRIANGULAR NOTCH WEIR THEORY AND EXPERIMENTAL ANALYSIS

Abstract

The study deals with the thin-plate triangular notch weir as a flow measurement device. Unlike previous studies on this subject, a theoretical development is proposed which takes into account the effect of the approach flow velocity. Between two well-chosen sections, the energy equation is applied with certain simplifying assumptions 1) the head loss and the effect of both viscosity and surface tension are neglected, 2) Assuming a hydrostatic distribution of the pressure. 3) The effect of the flow streamlines curvature over the weir is neglected. All the parameters influencing the discharge coefficient are well defined in the theoretical equation, as the experiment predicts so well. The theoretical equation of the discharge coefficient is adjusted to be in conformity with the experimental data. The adjusted relationship is a function exclusively of the relative weir height ratio P/h₁ and dimensionless number M₁=mh₁/B, where m is the side slope of the notch, i.e. m horizontal to 1 vertical, h₁ corresponds to the upstream water depth measured above the vertex of the notch, and B is the width of the rectangular channel of approach. The corrected theoretical relationship causes a maximum deviation of 6% on the calculation of the discharge coefficient, knowing that the average relative error is less than 1.88%. It is worth noting that among the 168 calculated values of the relative deviation on the computation of the discharge coefficient, 94% are less than 5% meaning that 6% only are greater than 5%, 87% are less than 4%, while 76.2% are less than 3%.