Effect of specific energy variation on lateral overflows

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. Keywords: Control structure, Conventional weir, Discharge coefficient, Spatially varied flow, Trapezoidal side weir, Water surface profile

Study of flow at side weir in narrow flume using visualization techniques

Bottom-hinged flap gates on side weirs are often used for the regulation of flow diversion in case of water abstraction for a variety of needs. In this study, a new equation for the discharge coefficient of a bottom-hinged flap gate on a side weir was proposed on the basis of discharge measurements. The equation was divided into two parts. The first part covers the impact of the sharp-crested side weir and the second the influence of the position and the width of the flap gate. In this manner, the discharge coefficient can be calculated with other authors’ equations for a sharp-crested side weir, which then must be multiplied by the new proposed coefficient. Very good agreement was found between the obtained discharge coefficients and the one calculated with the proposed equation. Furthermore, the results were compared with the equations of other authors for the discharge coefficients of sharp- and broad crested side weirs. The agreement was found to be very good. Additionally, measurements of water levels along the edge of the flap gate and measurements of the velocity field were carried out with a computer-aided visualization method. From these measurements, it was possible to show that the contraction of the water jet varies with the gate-opening angle. It was also found that the side weir with a flap gate has the most favorable hydrodynamic shape around the gate-opening angle of 33°, where the discharge coefficient reaches its maximum.

The 3D flow over side weirs is investigated using Computational Fluid Dynamic (CFD). The study aims to assess the capability of ANSYS CFX code for modeling flow characteristics in a circular channel with side weir for subcritical flow condition. Twelve models were studied for some ranges of variables such as discharge, length and height of side weir. The numerical simulation was based on the solution of continuity and momentum equations for three dimensional, incompressible, steady and turbulent flow. The volume of fluid (VOF) method was used to predict the free surface changes and the RNG k-e model was employed for simulating the flow field. The experimental data of Uyumaz and Muslu (1985) were used for verification. For all models, the specific energy is obtained and the average energy difference at the upstream and downstream side of the weir was very small and the assumption of constant energy in the circular channel was acceptable. The numerical results predicted the changes in the water surface profile at the main channel central axis and indicated that the water level rises from upstream to downstream end of the weir. The discharge coefficient (Cd) variation with the upstream Froude number (Fr1) for different weir height and length were studied and it was found that the value of (Cd) decreased with the increase of (Fr1) value. For each side weir length, the variation of (Cd) with the ratio of the weir height to channel diameter (P/D) were studied and it was observed that with the increase of (P/D) ratio the value of the (Cd) increased. The relation between the (Cd) and the ratio of the side weir length to channel diameter (L/D) for different weir height were also investigated. It was noticed that the (Cd) value increased gradually as the (L/D) ratio increased. The combined effects of (Fr1), (P/D) and (L/D) on the (Cd) were studied for all models and an empirical expressions for describing this relation was obtained and it was found that (Cd) was a function of all the above parameter.

Discharge coefficient of a semi-elliptical side weir in subcritical flow

Side weirs are flow diversion devices that are widely used in irrigation, drainage and urban sewage systems. The present study focuses on the investigation of the effect of oblique side weirs on the discharge coefficient of a side weir under subcritical flow condition in rectangular channels. In this study 106 laboratory tests were conducted and the results were analyzed to find out the influence of non-dimensional parameters on the discharge coefficient of the weirs. The angles of side weirs varied from 0 to 17.5 degrees in six steps, three heights (5, 10 and 15 centimeters) and three lengths (100, 80 and 40 centimeters). Two descriptions of the discharge coefficient (traditional side weir coefficients, Cd, and De-Marchi, CM), along with different discharges and related parameters were used. According to the results, Cd is more sensitive to b1/b2 (ratio of channel bottom widths), whereby CM is sensitive to L/b1 (ratio of side weir length to bottom width). The correction formula for estimating the oblique side weir discharge coefficient with a traditional shape shows that a 17.5 degree angle with side wall causes 40 percent change in the discharge coefficient.

A piano key side weir (PKSW) is a non-linear weir that discharge exceeds linear weirs by increasing the length in width. PKSW can be used in side weirs with space limitation. As side weirs are extensively used in flood control, water level control in rivers, and water supply channels, it is necessary to use PKSW as side weirs. This research discusses the discharge coefficient of a PKSW by assessing a C-type PKSW at 30° and 120° sections of a channel with a longitudinal curve. Dimensional analysis was used for identifying the parameters effective in the discharge coefficient. The effects of these parameters are examined by analysing the effective parameters. Finally, an empirical relationship has been proposed for determining the discharge coefficient based on the dimensionless parameters for calculating the discharge coefficient with the correlation coefficient of 0.88 and the mean error of 0.091. The influence of the parameter on the PKSW is more than that of the remaining parameters: With an increase in the value of this parameter, considering decreases in the length of the deviation and a lack of submerged inlet keys, the coefficient of discharge increases.

The effect of water surface slope in the lateral direction on flow over side weirs was studied. Water surface elevation on the weir plane was expressed by a parameter ψ based upon the hydraulic profile on the channel axis. Two different relationships of ψ as a function of the Froude number were used to calculate side weir discharges. Results were compared with the experimental data. It was shown that better results are obtained when transition conditions of ψ=1 at the ends of the side weirs with no lateral surface slope are taken into account. However the effect of water surface slope in lateral direction is of secondary importance as compared to the angle of the deflected water jet along the side weir.

The effect of increasing the number of cycles on the performance of labyrinth side weir

Side weirs or lateral weirs are widely used for water level control in water treatment plants and irrigation and drainage systems. The side weir is a fixed structure installed at one side of a channel to divert flow laterally. Computation of the water surface profile along the side weir is essential in determination of the discharge over the side weir. An analytical solution of the dynamic equation for spatially varied flow with decreasing discharge, in prismatic channels with a side weir, is available in the technical literature only for the special case of a rectangular channel based on the constant specific energy assumption. However, in irrigation networks, the most common irrigation channels are of trapezoidal cross-section. This paper presents an elegant analytical solution for establishing the water surface profile along a side weir in a trapezoidal channel. Since triangular and rectangular cross-sections are special cases of the trapezoidal cross-section, the proposed analytical solution is also applicable to these cross-sections. The solution, which yields a direct computation of the flow profile in subcritical and supercritical flow regimes, should be a useful engineering tool for the evaluation and design of side weirs in open channels.

Discharge coefficient for an inclined side weir crest using a constant energy approach

The adaptive neuro-fuzzy inference system (Anfis) is considered for flow over rectangular side weirs located on a straight channel as a substantial part of distribution channels in irrigation systems and treatment units. To estimate the outflow over a rectangular sharp-crested side weir, the discharge coefficient in the side weir equation needs to be determined in accordance with the effective dimensionless parameters F1 (Froude number), L/b (weir length/channel width), L/h1 (weir length/flow depth), and p/h1 (weir height/flow depth). The discharge coefficient of rectangular side weirs was determined using 843 laboratory test results. The performance of the Anfis model is compared with multilinear and nonlinear regression models. The criteria used for the evaluation of the performance of models are root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics. Comparison results indicated that the Anfis technique could be successfully employed in modelling discharge coefficients. It is found that the Anfis model with RMSE of 0·043 in the test period is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0·054 and 0·106, respectively.

This study comprehensively investigated the hydraulic behavior of labyrinthine side weirs in open channels using newly developed statistical approaches based on experimental data compiled from the literature. The model used in this study is a multiple linear regression model. The main objective was to reveal the complex relationships between the discharge coefficient (Cd) and the dimensionless flow parameters and the discharge. Experimental data showed that Cd values exhibit a nonlinear relationship with the flow regimes, which is characterized by the dimensionless h/w ratio with the optimal hydraulic performance region being h/w=2.0−2.6. Furthermore, a general decreasing trend in Cd was observed as the discharge (Q) increased, with a particularly dramatic decrease at high flow rates above 10 L/s, indicating potential choking effects at high discharges. A model was developed to estimate the flow coefficients using SPSS statistical software. While this model successfully captured the general trends, it showed significant deviations from the experimental data in certain flow regimes. Regression analyses revealed that the model can predict with high accuracy in low and medium-high flow rate ranges (e.g., R2=0.91 for 6-8 L/s, R2=0.95 for 11-12.5 L/s), but that there is a significant decrease in predictive power at very high flow rates (R2=0.70 for 17-23 L/s). These findings point to limitations in the generalizability of the model and the need for more sophisticated modeling approaches, especially for the complex flow dynamics in high flow regimes. Regression analyses showed that the model performed with high accuracy in medium flow ranges (R2=0.91 and R2=0.95), but its predictive power decreased at high flow rates (R2=0.70). These findings contribute to the hydraulic design of labyrinth weirs and underscore the need for advanced predictive tools in high-flow scenarios. The obtained data provide significant contributions to the hydraulic design principles of labyrinth weirs and provide a scientific basis for the development of more effective and reliable tools for water resources engineering applications.

Support vector regression for modified oblique side weirs discharge coefficient prediction

Prediction and modeling of hydraulic phenomenon is an important part of hydraulic engineering activities. One of the applications of prediction and modeling is estimating the discharge coefficient for hydraulic structures. Side weirs are widely used for allocating and removing excess flow in water engineering projects. The governing equation on side weir hydraulic characteristics is spatially varied flow (SVF). Computer modeling of hydraulic characteristics this structure includes the calculation of water surface profiles and estimating the discharge coefficient (Cdsw). The numerical method was used to calculate the water surface profile and there are several ways to estimate the Cdsw, such as experimental formulas and computational intelligence techniques. In this paper, the Fourth Runge Kutta method is used for numerical solution of SVF and firstly to estimate Cdsw, some famous empirical equations are assessed. Among the empirical formulas, the Borghei is the most accurate one. To increase the accuracy of computer modeling, the Multilayer Neural network (MLP) is developed to estimate Cdsw. The result shows that using neural network to estimate Cdswincreases the accuracy of the final model about 16 %.