Transition Effects in Flow Over Side Weirs

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

Interaction of side weir overflow with bed-load transport and bed morphology in a channel

Effect of specific energy variation on lateral overflows

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

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.

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.

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

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.

Water surface slope (WSS) of rivers is a key parameter in hydrological modelling, which allows for estimation of the transport and erosion capacity of a river, its flow velocity and discharge. On a local scale, WSS can be measured with a GNSS receiver installed on a boat, using remote sensing techniques (e.g. airborne lidar) or from a Digital Elevation Model (DEM). The most accurate method to measure WSS avoiding high-cost field campaigns is based on Water Surface Elevations (WSE) measured at in-situ stations. However, in poorly gauged rivers the neighboring gauges can be up to hundreds of kilometers apart, which inhibits a proper river profile observation. The gap in decreasing number of gauge readings is partially filled with satellite altimetry over rivers. Altimetry based WSE can be used to estimate WSS between neighboring measurements. Here, we present an innovative approach for estimating high-resolution WSS derived from multi-mission satellite altimetry for the largest Polish rivers.In this study, we used measurements from 9 altimetry missions: CryoSat-2, Envisat, ICESat-2, Jason-2/-3, SARAL, Sentinel-3A/-B, and Sentinel-6A. These observations cover the years from 2002 to 2022. We extracted the river centerlines from the global “SWOT Mission River Database” (SWORD). In order to validate the obtained results, we used WSE from 81 gauges, which are maintained by the Institute of Meteorology and Water Management – National Research Institute (Instytut Meteorologii i Gospodarki Wodnej – Państwowy Instytut Badawczy, IMGW-PIB). These measurements are referenced to the Kronsztadt’86 vertical datum and they range from 01.2016 to 05.2022. Additionally, we used the reach-scale “ICESat-2 River Surface Slope” (IRIS) and the DEM-derived WSS values from SWORD.To obtain WSS, we first determined WSE at each satellite pass crossing the studied river. Next, we split rivers into sections without dams and reservoirs. The Support Vector Regression (SVR) has been applied to reject outliers. Then, water levels were assigned to a given river kilometer (bin). For each of them a median WSE has been calculated. Finally, WSS were calculated at river sections between bins, excluding those disrupted by hydraulic structures. Finally, we weighted the section-wise WSS inversely proportional to the length of each section and applied a Least Square Adjustment with an additional Laplace condition to obtain bin-wise WSS for each river kilometer.To assess the accuracy of the proposed approach, we compared the obtained WSS with the slopes between IMGW-PIB gauges. For large rivers (Vistula, Odra, Warta), the multi-mission approach revealed high accuracy with preliminary Root Mean Squared Error (RMSE) below 30 mm/km. For smaller, mountain rivers (San, Dunajec) the preliminary errors were slightly larger (RMSE ~100 mm/km). We also compared our accuracies with those of the slopes based on DEM models, lidar data, ICESat-2 altimetry, and SWORD database. In general, the multi-mission approach revealed the highest accuracy. The research is supported by the National Science Centre, Poland, through the project no. 2020/38/E/ST10/00295.

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.

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

Theoretical and experimental investigations of the flow over sharpedged side weirs in circular channels are reported. A theoretical model can be obtained from energy principles, and it is solved by a finite difference method. The results are presented in diagrammatic form for practical use. The experiments cover sub‐ and supercritical flow regimes, and water surfaces are observed for both. The discharge coefficients are obtained for sub‐ and supercritical regimes. Derived expressions for the side weir discharge and water surface profiles for these regimes are compared with experimental results.

The side weir is one of the most important hydraulic structures that is used by hydraulic engineers for adjusting and controlling flow in urban waste collection systems, irrigation and drainage networks. In this study, an equation is proposed for computing side weir discharge located on circular channels. The equation computes the side weir discharge with sufficient accuracy. Then, the RNG k–ε turbulence model is used for simulating the turbulence of the flow field and the free surface flow variations are modeled using volume of fluid scheme. Comparing experimental results with numerical simulations indicates acceptable accuracy of the numerical model. Also, the side weir discharge coefficients, flow free surface variation, behavior of dividing stream surface and variations of stagnation point height for different discharges within a circular channel along a side weir were examined.

Side weirs are hydraulic structures widely used for flow control in rivers and canals. Whenever the water level rises above the side weir crest elevation, a fraction of the main flow is diverted so that the water discharge flowing downstream in the main channel is reduced. In movable bed channels, the lateral outflow may have significant interactions with the sediment transport processes affecting the side weir flow. The spilled discharge creates a reduction of the downstream sediment transport capacity with a consequent deposition in the side weir proximity. In addition, sediment in the main channel can be diverted into the lateral branch. To investigate these interactions, experimental data at the laboratory scale have been collected and analyzed. The increase of the spilled discharge induced by the local sediment deposition is described according to the classical De Marchi hypothesis. Furthermore, the sediment transport leaving the main channel through the lateral structure is modeled in terms ...

A method for analysing supercritical flow in a channel fitted with a side weir has been developed and tested against experimental data. Results of the experimental programme have established the conditions under which supercritical flow occurs along a side weir, and showed that in cases where the flow upstream of the weir is subcritical the draw-down to supercritical flow produces sufficient curvature of the streamlines to affect the vertical pressure distribution. Modification of the differential equation to allow for curvature effects has significantly improved the accuracy of computation of depths and discharges. The depth at the upstream end of the weir is shown to be a function of the upstream critical depth, the weir crest height and the slope of the channel, and the rate of change of surface curvature along the upstream portion of the weir is found to depend on the upstream critical depth. Apart from these relationships little use is made of empirical formulae in analysis, so that the method may be applied to any side weir where supercritical flow occurs.