discharge computation of trapezoidal side weir in subcritical flow regime using conventional weir theory

introduction: side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. side weirs are also used as an emergency structure. this structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. lateral outflow takes place when the water surface in the main channel rises above the weir sill. flow over a side weir is a typical case of spatially varied flow with decreasing discharge. there have been extensive studies on side weir overflows. most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. in the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. materials and methods: the experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. the main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. it was set up parallel to the main channel; walls and its bed were made up of plexiglas plates. the side weir was positioned at a distance of 6 m from the channel’s entrance. a total of 121 experiments on trapezoidal side weirs were carried out. results and discussion: for trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and buckingham's pi-theorem. finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow. in which fr1= upstream froude number, p= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and t=top flow width of the trapezoidal side weir. water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. different elevations in water surface profile depend on the upstream froude number in the main channel; depth differences in low froude numbers are at minimum values, and in high froude numbers are at maximum amounts. the water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. afterwards, the water level rises towards the downstream of the weir. according to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. according to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. finally, the general equation was proposed. the general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. the mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5% , respectively. conclusion: in this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. for this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. the results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. it was found that for trapezoidal side weir, the discharge coefficient depends on the froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. in this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. for this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. the average value of error for discharge coefficient estimation by the proposed equation is 2.6%. thus this equation is proposed for use in practice by water engineers.