Discharging capacity of rectangular side weirs in straight open channels

A side weir is a hydraulic control structure used in irrigation and drainage systems and combined sewer systems. A comprehensive laboratory study, including 843 tests for the discharge coefficient of a sharp-crested rectangular side weir in a straight channel, was conducted in a large physical model under subcritical flow conditions. The discharge coefficient is a function of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth. An equation was developed considering all dimensional parameters for discharge coefficient of the sharp-crested rectangular side weir. The average error of the proposed equation is 4.54%. The present study data were compared with ten different discharge coefficient equations developed by several researchers. The study also presents water surface profile and surface velocity streamlines.     

Experimental analysis of combined side weir-gate located on a straight channel

Flow measurement and control in open channel system for lateral flow is important to support the system management. The flow characteristics of combined side weir-gate are complicated due to changes in flow conditions along the side weir-gate section. Experimental investigation of the flow characteristics of both weir and sluice gates is crucial for predicting the flow through a combined side weir-gate structure. Although weir-gate structures are widely used for frontal flow in hydraulic structures, the same is not true for lateral flows. In this study, 650 laboratory tests were conducted to determine the flow characteristics of combined side weir-gate for subcritical flow, and the experimental results were analyzed to determine the effect of these characteristics and weir-gate geometry on discharge capacity. Interaction factor of combined side weir-gate is a function of the upstream Froude number, the ratio of gate opening to upstream flow depth, the ratio of distance between the top of the sluice gate and the weir crest to gate opening, the ratio of weir and gate length to upstream flow depth, and the ratio of weir and gate length to main channel width. Consequently, more discharge is passed through combined side weir-gate compared to side weir and sluice gates. The empirically derived equations for the discharge of combined side weir-gate show good compatibility with the experimental data.     

A review of studies on estimating the discharge coefficient of flow control structures based on the soft computing models

The discharge coefficient (Cd) plays a vital role in the accurate design and safety of weirs, spillways, and dams. In the last decade, Soft Computing(SC) models, which showed excellent capabilities for non-linear mapping between parameters, were widely used to estimate the discharge coefficient of flow control structures. This study provides a comprehensive review of the application of SC models for estimating Cd of different flow control structures such as ogee spillways, orifices, side weirs, etc. In addition, the most common empirical relations which are obtained from laboratory experiments are discussed briefly. The findings revealed that weir length/flow depth ratio, weir length/channel width ratio, weir height/flow depth, and Froude number are widely used to estimate Cd in the side weirs. Besides, the ratio of orifice crest height to height of side orifice, the ratio of main channel width to length of side orifice, ratio of main channel width to height of side orifice, and ratio of the height of side orifice to upstream flow depth were extensively employed to calculate Cd of orifice structures. The common parameters for measuring Cd of labyrinth weirs are, discharge over a labyrinth cycle, weir height, channel width, apex constant, upstream head, discharge over the weir, effective length, convergence constant, sidewall angle, and Froude number. In the weir-gate structure, some factors such as contraction coefficient of the gate, head loss, and weir height are key parameters for the accurate evaluation of Cd. The trends of SC models, features of popular models, and the background of models are discussed briefly in this paper. Also, research gaps and possible directions for new studies are suggested.     

Experimental study for measuring discharge through compound broad crested weir

This paper deals with a new compound broad crested weir for measurement of discharge. Calibration of broad crested weir is mainly dependent upon the length of the weir crest (L), weir height and upstream water head over weir crest (h). Hence measurement of discharge varies as per change in the flow characteristics due to change in the geometry of weir for a given flume. Based on experimental analysis, past researchers have shown that discharge coefficient (C_d) changes proportionally with h/L ratio, maintaining an average range of C_d for various h/L values. In the present study a novel approach towards design of compound broad crested weir is proposed which can effectively measure wide range of discharges thereby maintaining a constant discharge coefficient irrespective of the head over weir. Experimentation has been carried out in a laboratory horizontal tilting flume 2.5 m long, 20 cm wide and 30 cm deep. The investigation is carried out for discharge ranging from 10 lps to 2 lps. In the earlier experimentation conducted C_d was varying in the range from 0.518 to 0.648, after which the broad crested weir model is modified for suiting best results thereby resulting in the reformed discharge coefficient values of 0.546–0.599 which is in close proximity to the design input value of 0.6.     

Study of the hydraulic properties of the cylindrical crested weirs

Since the cylindrical and circular crested weirs are economical and easily made compared to some other weirs, they can be used to measure the flow velocity, the water discharge and flow surface control structures in the canals and reservoirs. In this paper, the hydraulic properties of the cylindrical and circular crested weirs, such as the discharge coefficient, the depth on the crest of the weir and the energy loss in 18 laboratory models categorized in 5 categories have been investigated. The results of the experiments indicated that in both the cylindrical and circular crested weirs by increasing the total partial head, the discharge coefficient increases and any changes in the upstream wall slope has no effect on the discharge coefficient. Also, the partial energy loss more occurs in the cylindrical weirs than the half shaped cylindrical weirs and by increasing the downstream inclination angle, the partial energy loss increases subsequently. The partial flow depth on the crest of both the cylindrical and half shaped cylindrical weirs is equal to 0.7 and by increasing of the upstream inclination angle, the partial flow depth on the crest in the values greater than 0.6, increases slightly and the downstream inclination angle changes of the partial flow depth has no effect on the crest.     

Hydraulic characteristics of a new weir entitled of quarter-circular crested weir

Weirs are used for flow measurement, flood control in reservoirs and water level control in irrigation systems. In this study, a new weir entitled of quarter-circular crested weir is investigated. This weir is geometrically consisted of a quarter-circular crest of radius R, upstream slope α and vertical downstream face. The downstream face of the weir must be ventilated. Discharge coefficient, crest section velocity and pressure profiles, pressure distribution on the crest surface and upper and lower nappe profiles of flow over the quarter-circular crested weir were experimentally investigated. Results indicated that discharge coefficient of the weir is a constant value and equals to 1.261. In the range of H/R<1.5, it is more than the discharge coefficient of circular crested weir. The lower nappe profile of free jet over the weir can also be considered as the ogee shape of the proposed weir.     

Sensitivity analysis of the factors affecting the discharge capacity of side weirs in trapezoidal channels using extreme learning machines

Side weirs are installed on the side walls of main channels to control and regulate flow. In this study, sensitivity analysis is planned using Extreme Learning Machines (ELM) to recognize the factors affecting the discharge coefficient in trapezoidal channels. A total of 31 models with 1 to 5 parameters are developed. The input parameters are ratio of side weir length to trapezoidal channel bottom width (L/b), Froude number (Fr), ratio of side weir length to flow depth upstream of the side weir (L/y₁), ratio of flow depth upstream of the side weir to the main channel bottom width (y₁/b) and trapezoid channel side wall slope (m). Among the models with one input parameter, the model including Froude number modeled the discharge coefficient more accurately (MAPE=4.118, R²=0.835). Between models with two input parameters, the model using Fr and L/b produced MAPE and R² values of 2.607 and 0.913 respectively. Moreover, among the models with four input parameters, the model containing Fr, L/b, L/y₁ and y₁/b was the most accurate (MAPE=2.916, R²=0.925).     

Minimizing the hydraulic side effects of weirs construction by using labyrinth weirs

It is no doubt that weirs are one of the most important hydraulic structures that play a vital role in irrigation project. So, it is necessary to minimize the hydraulic side effects of weirs. Throughout this paper, experiments were conducted to investigate the suitable dimensions and shape of weir's crest to increase head loss, decrease upstream bank level upstream weir and get the most economic structure. Various crest angles of labyrinth weir were tested under different flow conditions. Also back water curve upstream weir was studied according to different weir crest angles. A case of linear weir crest was also included in the test program. The experimental results indicated that labyrinth weirs have lower operating heads and longer crest length compared with a linear weir having the same lateral space and the same discharge. Results showed that the crest weir angle of 60° is the best angle of weir crest. It reduces water level above crested level and the relative jump depth by 18% and 20%, respectively. In addition, it increase the average values of the dissipated energy and the discharge coefficient by 15% and 14%, respectively. It also gave maximum reduction in backwater curve profile by about 17%. Furthermore, the model was verified using CFD numerical model. The numerical results agreed with the experimental results.     

Discharge characteristics of a modified oblique side weir in subcritical flow

Side weirs are frequently used in many water projects. Due to their position with respect to the flow direction, side weirs are categorized as plain, oblique and labyrinth. One of the advantages of an oblique side weir is the increase in the effective length of the weir for overflowing and, therefore, diverting more discharge with the same channel opening, weir height and flow properties (i.e., upstream discharge, upstream Froude number and so on). In this paper, an experimental set-up of a new design of an oblique side weir with asymmetric geometry has been studied. The hydraulic behavior of this kind of oblique side weir, with a constant opening length, different weir heights and asymmetric oblique angle, has been investigated in a subcritical situation. The results from over 200 test measurements show that this kind of weir is up to 2.33 times more efficient with respect to the conventional side weir in a rectangular channel among the tested conditions. Finally, the discharge coefficient as a function of geometrical and flow variables are presented for design engineers. In addition, a more precise relation has been obtained for flow with Froude numbers less than 0.4.     

Experimental investigation of flow characteristics over asymmetric Joukowsky hydrofoil weirs for free and submerged flow

Weirs are one of the most common hydraulic structures used to regulate the upstream approach flow depth and measure the flow discharge. The hydrofoil weirs are a type of short-crested weirs that are designed based on the airfoil theory. These weirs have some merits compared to other types, such as a higher discharge coefficient, more stability, better submergence limiting condition, and lower fluctuations of the pressure and the free-surface profile. In the present study, experimental models of hydrofoil weirs with different relative eccentricities, cambers, angles of attack, and upstream slope angles are applied to investigate their hydraulic characteristics under free and submerged flow conditions. The longitudinal profiles of static pressure over different hydrofoil weirs are compared to circular-crested and ogee weirs. The results indicate that the maximum bed negative pressure belongs to the circular-crested weir, and the lowest bed pressure over the hydrofoil and ogee weirs are approximately the same. Applying a hydrofoil weir with an appropriate curvature and angle of attack instead of a circular-crested weir not only increases the structural weir height as well as the upstream water depth but also results in the lowest values of bed negative pressure, thereby reduces the potential of cavitation over the weir body, being safer hydraulic structures. The results also show that the discharge coefficient of hydrofoil weirs is greater than that of the broad- and short-crested weirs for the upstream approach flow depth relative to the weir crest to weir length h₁/L > 0.12 and is greater than that of the ogee weirs for 0.35 < h₁/L < 0.45. Furthermore, the derived relationships for the discharge coefficient, threshold submergence, and the discharge reduction factor due to submergence accurately predict the hydraulic characteristics of hydrofoil weirs compared to the available developed empirical relationships for these weirs and can be used efficiently for design purposes.     

The effects of various upstream arches of crest of the circular crested weir on hydraulic parameters

Weirs are one of the oldest hydraulic structures ever built by mankind. Weirs are used to measure and regulate the flow. In this paper by using obtained experimental data from physical model, the effects of the various upstream crests on some hydraulic parameters were investigated. The experiments were carried out in the arch angles of 0°, 30°, 45°, 60°, and 90° from the upstream crest in the hydraulics laboratory of Kermanshah Islamic Azad University. The results indicated that effects of the upstream crested arch on the discharge coefficient and energy loss had been negligible, and except for the arch angle of 0°, such effects upon the velocity distribution and the depth of the flow upon the crest of weir are not effective.     

Direct solution for discharge in generalized trapezoidal free overfall

In open channels, free overfall can be used as a discharge measuring structure by a single measurement of depth at the end of the channel. If the slope of channel is negative, zero or mild, the flow at upstream of end section will be critical and end depth value depends only on the shape of the approach channel and its critical depth. This research presents a theoretical end depth–discharge (EDD) relationship for free overfall (end section) in a horizontal open channel with generalized trapezoidal section. The generalized trapezoidal shape reduces to the commonly used trapezoidal section as well as to the Δ-shaped section. Two direct discharge equations in terms of end depth for subcritical flows are proposed by simulating free overfall as a weir without crest. Experimental data are then used to verify the proposed EDD relationships. The calculated discharges, using the proposed EDD relationships, show excellent agreement with the experimental data.     

Estimating the uncertainty of discharge coefficient predicted for oblique side weir using Monte Carlo method

Side weir is a hydraulic structure, which is used in irrigation systems to divert some water from main to side channel. It is installed at the entrance of the side channel to control and measure passing water into the side channel. Many studies provided side weir water surface profile and coefficient of discharge to measure water discharge diverted into the side channel. These studies dealt with different side weir shapes (rectangular, trapezoidal, triangular and circular), which were installed perpendicular to the flow direction. Recently, some studies dealt with skew side weir, but these studies still need to more investigation. Here we report to investigate oblique side weir theoretically using statistical method to supported other studies in this case. Measurement uncertainty discharge coefficient C_d was obtained by two methods: analytical according to the ‘Guide to the expression of uncertainty in measurement’ and the Monte Carlo method. The results indicate that all experimental results are consistent with the analytical results. The relative expanded uncertainty of the discharge coefficient C_d does not exceed 2%.     

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

In this paper, the inclined side weir discharge coefficient was studied using a side weir with three different crest angles (θ=4°,8°,12°) fixed either against and in the flow direction, and the results are compared with those from a horizontal side weir crest (θ=0°). In total there were seven models.The results show that the De Marchi assumption of constant energy for all side weir crested angles is acceptable, and thus that the calculated weir discharge value can therefore be undertaken.An equation for the discharge coefficient was obtained for an inclined side weir, so the value of C_d for crest angle θ=12° increased by 13.6% with respect to the value for θ=8°, by 29% with respect to that for θ=4°, and by 39% with respect to that for the horizontal case (θ=0°), for a crest inclined against the flow direction, while when the crest was inclined in the flow direction all those values exceed, to 14.5%, 31.0%, and 40.7%, respectively. This means that the discharge increases with increasing side weir crest angle, so when we want uniformity in the flow direction and exceed discharge we need to make the side weir crest incline against the flow direction while when we want furthermore discharge we need to make the side weir crest incline in the flow direction.     

Discharge equation for the gabion weir under through flow condition

A gabion weir is considered to be more environmentally friendly as compared to an impermeable weir, as its permeability allows substances and aquatic life to pass through it. Also, gabion weirs offer an alternative design with low afflux that could be adopted for flash flood mitigation. In the present study, a series of laboratory experiments were performed on flow through gabion weir of various sizes and for varying boulder sizes and discharges. Collected data were used to check the accuracy of the existing relationships between hydraulic gradient and flow velocity for highly porous material like gabion filled with boulders. It is found that Ergun's equation predicts the hydraulic gradient more accurately than the other available equation. Ergun's equation is extended to calculate the flow through the gabion weir. The derived discharge equation for flow through gabion weir was validated with the collected data. A qualitative performance of the present model indicates that it has the highest coefficient of correlation (R = 0.956) and the lowest MAPE (16.902), RMSE (0.002), AAD (15.52). It was found that the derived equation computes discharge within a maximum of ±10% error for almost all data sets, which can be considered satisfactory from practical consideration. Sensitivity analysis reveals that the discharge through the gabion weir is more sensitive to the boulders diameter and upstream depth as compared to the downstream depth of the gabion weir.     

Discharge equation of semi-circular side weirs: An experimental study

Side weirs are diverting structures and usually used for diverting and controlling the water flow into the side open channel. The present study deals with an experimental study regarding the hydraulic performance of side weirs with semi-circular vertical sections along the main channel. As flow depth of the main channel increases the top flow width of the semi-circular side weir (SCSW) increases which is an advantage when high discharge enters the main channel and should be immediately diverted for safety reasons. In this study, the flow discharge of semi-circular sharp-crested side weirs and their affecting parameters are investigated. To investigate the hydraulic behavior and geometric characteristics of the SCSWs, a comprehensive laboratory study including 155 tests (for three weir diameters 0.25, 0.30 and 0.40 m) was conducted in a physical model under subcritical flow conditions. Flow discharge of the SCSW was investigated in relation to height, diameter and flow head of side weir, also approach Froude number (Froude number at upstream end of the side weir) and main channel width. Three different discharge models were developed based on; purely dimensional analysis technique, classical weir equation with linear water surface and classical weir equation with horizontal water surface profile (conventional weir theory along with dimensional analysis technique). The presented mathematical discharge models enable estimation of discharge along the SCSW with acceptable accuracy (best model has an average error of 1.87% with a maximum error of 6.31%) compared with the measured data under subcritical flow conditions. Additionally, a relationship was proposed for computing the limiting flow depth at the downstream end of the SCSW. Experimental results confirm that the proposed relationship well explains the behavior of flow over the SCSW regarding the downstream flow conditions.     

Effect of specific energy variation on lateral overflows

A numerical model was used to study the effect of change in specific energy height along a side weir on flow. Discharge coefficient was considered as a local variable that includes flow depth and the angle of the deflected water jet along side weir. Hydraulic profile on the weir plane and the hydraulic head on the weir were obtained using two dimensionless parameters ψ and m as a function of Froude number. Flow depths and flow rates were then computed and minimum standard errors were determined based upon these parameters. The agreement between computed values and observations was demonstrated. It was concluded that rates of flow are considerably affected by the variation of specific energy along the side weir when weir head is based on flow depth at the weir plane. Considerable deviations from the constant specific energy assumption may be observed in this case specially when a great change in flow rates exists along side weirs with zero end discharges.     

Multi-objective reliability-based optimization for design of trapezoidal labyrinth weirs

In the present research, the reliability-based design optimization (RBDO) of labyrinth weirs has been investigated. The optimization problem is formulated such that the optimal shape of trapezoidal labyrinth weir described by a number of variables is found by minimizing the volume of the trapezoidal labyrinth weir and maximizing the reliability index. The constraint conditions are the weir geometric shape and its different ratios. In order to achieve this purpose, a framework is presented whereby non-dominated sorting genetic algorithm (NSGA-II) is integrated with monte carlo simulation (MCS) method to solve the RBDO approach of trapezoidal labyrinth weirs. The proposed method is applied to UTE Dam labyrinth weir, and the results are compared with the real one. The results show the need for design based on reliability in the labyrinth weirs that propose using RBDO for weir design. The results showed that RBDO approach can achieve a more reliable design in addition to reducing the volume of the trapezoidal labyrinth weir. Finally, the sensitivity analysis of the parameters effective on the reliability index revealed that three design variables of weir width, total upstream head and discharge coefficient are the main parameters affecting weir RBDO solution.     

Experimental analysis of flow characteristics over hydrofoil weirs

The rounded crested weirs are commonly used for discharge measurements and this overflow structures have advantages such as stable overflow pattern and good accuracy. Hydrofoil weirs with streamlined properties are similar to the ogee weirs and can be used as a spillway profile. The hydraulic features of flow over hydrofoil weirs created by the NACA0018, NACA0021 and NACA0024 hydrofoil geometry placed in an open channel are investigated experimentally under free-flow conditions. The velocity field of hydrofoil weir flows are measured by one-dimensional Laser Doppler Anemometer. Experimental velocity profiles are measured along the middle section of the channel, especially around the weir structure, to determine the boundary layer separation. According to the determination of optimum weir structure the free surface profiles, pressure distributions on weir surfaces, experimental discharge coefficients and head losses over weir structures are determined for different structure and flow conditions. Pressure distributions over the hydrofoil weir are presented. In addition, the relationships between discharge coefficient (C_d) and flow rate (Q), specific total head (H/R), relative weir height (P/H), relative total head (H/P) and dimensionless total energy head upstream of the weir (H/L) are investigated.