Submerged Flow Conditions Research Articles

Flow regime discrimination and methodology for calculating discharge in trapezoidal sluice gates

This study introduces a novel trapezoidal sluice gate designed for water division and flow control within irrigation networks featuring canals with trapezoidal cross-sections. Experiments were conducted on trapezoidal channels with side slopes of m = 1.5, 1.75, and 2.0, using trapezoidal sluice gates at various gate openings, upstream water depths, and downstream depths. A total of 411 experimental sets were conducted to study methodologies for discerning between free flow and submerged flow conditions and for determining discharge rates. A method was proposed to distinguish flow patterns of trapezoidal sluice gates: submerged flow occurs when the downstream channel depth (ht) exceeds the submergence threshold (Ht'), while free flow is indicated when ht is less than Ht'. The formula for calculating Ht' was derived, along with formulas for computing discharge rates under free flow and submerged flow conditions for trapezoidal sluice gates. The results revealed that the average relative errors of the formulas obtained through the partition method and the submergence coefficient correction method were 2.24 % and 5.37 %, respectively, demonstrating high accuracy and reliability. The scale effects on the flow regimes and formulas of discharge rates are also discussed. Findings from this study enhance the understanding of the hydraulic characteristics of trapezoidal sluice gates, which hold significant implications for the adoption and intelligent management of such gates in irrigation areas, offering a viable solution for selecting appropriate water gate configurations in irrigation systems.

Characteristics of discharge of skew side sluice gate

The present study is aimed to assess discharge characteristics of skew side sluice gate. It is determined to develop equations for elementary discharge coefficient, Ce when a side sluice gate is placed at an angle with the main channel. Also, the present study is undertaken to develop generalized equations for elementary discharge coefficient of skew side sluice gate both for free and submerged flow conditions. Solving governing flow equations and further numerical integration by using fourth order Runge–Kutta method are used to find computed discharge. Error between observed and computed discharge is found and it is minimized to obtain optimum set of constants to develop Ce. Equations for Ce when the side sluice gate is placed at various angles are developed both for free and submerged flow conditions. Also, generalized equations for elementary discharge coefficient are developed. Further, Kling-Gupta Efficiency, KGE and validation of generalized equations for elementary discharge coefficient both for free and submerged flow conditions have indicated that there is an agreement between observed and computed discharges and thus shown accuracy. The findings of the present study are useful to study further on flow characteristics of skew side sluice gate which has vital practical significance.

Experimental investigation of flow splitters' impact on the hydraulics of Piano Key Weirs

Piano Key Weirs (PKWs) have gained significant attention due to due to challenges associated with nappe oscillation in their flow dynamics. This experimental study explores the effectiveness of flow splitters—specifically circular, square, and rectangular designs—in enhancing the hydraulic performance of various PKW shapes: triangular, rectangular, and trapezoidal, under a range of hydraulic conditions, including both free and submerged flow. Experiments were conducted in a dedicated channel, 10 m long, 0.75 m wide, and 0.80 m high. The results indicate that under submerged flow conditions, discharge coefficients decreased by 61 % for rectangular, 59 % for triangular, and 55 % for trapezoidal PKWs compared to free flow, reflecting a reduction in efficiency. Notably, the trapezoidal PKWs maintained the highest discharge coefficient, improving efficiency by 2 % over triangular PKWs and by 12 % over rectangular PKWs. Flow splitters facilitate flow separation by linking entrapped air beneath the flow to the free surface, thereby mitigating nappe oscillation. In free flow conditions, rectangular and square splitters are more effective than circular ones for flow separation and energy dissipation, although geometric variations did not significantly influence the upstream water head in submerged flow scenarios. While flow splitters did not affect the discharge coefficient or efficiency of the various weir shapes under submerged conditions, they were found to decrease discharge by 10 % for triangular PKWs in free flow conditions. Overall, flow splitters demonstrated greater efficiency in submerged flow scenarios. In free flow, triangular PKWs were observed to dissipate approximately 4.4 % more energy than rectangular PKWs and 6 % more than trapezoidal shapes, with minimal differences in energy dissipation during submerged flow. This research also introduces a new equation for estimating the discharge coefficient in free flow, incorporating a correction factor yielding R2 = 0.967, RMSE = 0.217, and MRPE = 5.94 %, expanding upon the work of Zarei et al. [19] for submerged flows. The study enhances understanding of hydraulic behaviors and discharge coefficients of PKWs equipped with flow splitters, contributing to improved aeration performance.

Experimental study of simple flumes with converging triangular walls

For water management, the accurate measurement of discharge in irrigation channels is essential. Static flow measuring devices such as weirs and flumes play a significant role in discharge measurement in open channels. Flumes are one of the most commonly used devices for flow measurement. Many researchers have focused on application of simple flumes in irrigation networks. This investigation aims to study the flow discharge through a simple flume with converging triangular walls under free-flow conditions. The flume is constructed by placing two right-angled triangular plates on either side of a rectangular open channel. The channel cross section is rectangular while height of the converging walls reaches to zero at the end of the flume opening. The proposed flume is inexpensive, its operation is simple, its installation is easy and does not require high maintenance (maintenance free). The present study is designed to determine the effect of different variables on flow discharge of this kind of flumes. For this, an experimental program was conducted under upstream subcritical flow regime and under free outflow conditions to formulate the flow discharge of the flume. Flume discharge relationship was deduced using dimensional analysis method and then calibrated using the experimental data collected in this study (318 runs). The proposed discharge equation has an average absolute relative error of 1.66 %, and for 96.5 % of the measured discharge values, the relative errors are within ±5 %. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equation with an average absolute relative error less than 3.44 % was presented to estimate the submergence threshold. This flume is suitable for the rectangular channel for accurate measurement of free flow at any location on field. This particular device has considerable advantages over the other devices, as it can be quickly installed and removed for use in irrigation channels. The findings and results of this study will be of interest for practical applications.

Experimental investigation of scour downstream of a type A trapezoidal piano key weir under free and submerged flow conditions

Abstract In this paper, the scour downstream of a trapezoidal Piano key weir (PKW) is investigated under free and submerged flow conditions. For this purpose, an experimental model was used in a laboratory channel with a length of 10 m, width of 0.75 m, and height of 0.8 m at various discharges and tailwater depths. The results showed an increase and decrease in the maximum scour depth with an increase in the discharge and submergence ratio, respectively. In addition, increasing the particle Froude number enhanced the geometric features of the scour hole downstream of the PKW. The rate of bed changes slowed down over time. The average values of maximum scour depth, the distance of the maximum scour depth from the weir toe, maximum scour hole length and weir toe scour depth increased in the free flow compared to the submerged flow. The scour hole volume and scour hole area in the submerged flow were less compared to the free flow. The average maximum level of the sedimentary ridge in the free flow is less than the submerged flow. New equations for calculating the geometric characteristics of the scour hole downstream of the trapezoidal PKW are presented with acceptable accuracy.

Investigation of Hydraulic Performance and Arrangement Optimization of Non-Prismatic Water Conveyance Tunnel—A Case Study of Project X

The water conveyance tunnel is an important hydraulic structure in water conservancy projects. Typically, it manifests as a non-prismatic tunnel due to variations in the cross-sectional geometry, which give rise to an unpredictable flow pattern that significantly impacts the secure and stable operation of the tunnel. This study takes water conservancy project X as a case and investigates the hydraulic performances of a non-prismatic water conveyance tunnel using a scale model test and numerical simulation; the hydraulic performance, such as flow pattern, discharge, flow velocity, and water depth profile are analyzed for both free flow and submerged flow conditions. The results show that the simulation data fit well with the experimental value observed in the scale model test for free flow; however, a substantial discrepancy emerges under submerged flow conditions. This discrepancy is attributable to the presence of a vacuum in the distortional plan section. Notably, the effect of water entrainment phenomena on flow rate and velocity is diminished in the scale model test, emphasizing the advantage of numerical simulation in predicting hydraulic parameters for the prototype. On this basis, the optimization of the gate shaft arrangement is executed through numerical simulation; the results indicate that the vacuum issues in the contraction section were partially resolved through structure optimization. The simulation values are close to the experimental results, and the modified design of the tunnel can be used in a water conveyance project.

Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.

Hydraulic Behavior of Weir-Gate Structure with Rectangular Side Obstacle under Free and Submerged Flow Conditions

Hydraulic Behavior of Weir-Gate Structure with Rectangular Side Obstacle under Free and Submerged Flow Conditions

Metaheuristic learning algorithms for accurate prediction of hydraulic performance of porous embankment weirs

A porous weir is an environmentally friendly structure with minimal negative environmental impact. Due to the complex flow mechanism around porous weirs, it is difficult to provide a general empirical relationship to estimate the free and submerged discharge coefficients and threshold submergence or modular limit. Hence, the current study attempts to introduce an efficient alternative approach leveraging on multilayer perceptron (MLP) coupled with generalized normal distribution optimization (GNDO), Runge-Kutta optimization algorithm (RUN), slime mould algorithm (SMA), whale optimization algorithm (WOA), and grey wolf optimizer (GWO). These models' robustness and accuracy are investigated to solve the free discharge coefficient (FDC), modular limit index (MLI), and submerge discharge reduction factor (SDRF) of the porous embankment weirs (PEWs) modeling problem where 6514 datasets are studied experimentally for free, modular limit, and submerged flow conditions. The performance of developed metaheuristic-MLP models is compared with a gradient algorithm-based MLP, namely Levenberg-Marquardt (LM) model. The obtained results from analysis of different performance indicators demonstrate that the GNDO-MLP outperforms other developed MLP models. The results demonstrate that the metaheuristic-based MLP models are more reliable in forecasting FDC, MLI, and SDRF of PEWs than the ML-MLP model. To measure how much the MLP model improved when combined with meta-heuristic algorithms, an aggregated statistical index called objective function was applied. The results of this index showed that the MLP model with GNDO performed better than the MLP models with WOA, SMA, GWO, RUN, and LM by 82%, 66%, 69%, 69%, and 96% for FDC, by 41%, 13%, 9%, 8%, and 48% for MLI, and by 64%, 20%, 8%, 4%, and 69% for SDRF condition, respectively. Furthermore, the results of the uncertainty analysis, using the P-factor and R-factor, demonstrated that GNDO-MLP had lower uncertainty compared to other models. The robustness of the GNDO-MLP model indicates that it can be used for further research on the probabilistic analysis of the PEWs.

The discharge coefficient of SMBF flumes under free and submerged conditions

In this study, the discharge coefficients (Cd) of SMBF flumes under free and submerged flow conditions were analytically investigated. The dimensionless parameters involved in the discharge coefficient, derived from the dimensional analysis, are the contraction ratio [rcrn = ratio of flume width (w) to channel width (B)], relative head (hw: the ratio of the upstream head (h) to the w\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w$$\\end{document}) and, in the case of submerged flow, also the submergence ratio [Sr=ht/hu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{{\ ext{r}}} = h_{{\ ext{t}}} /h_{{\ ext{u}}}$$\\end{document}: downstream flow depth (ht\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{{\ ext{t}}}$$\\end{document}) to upstream flow depth (hu)]. Cd decreases logarithmically from 1.2 to 0.75 in the range of hw\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{w}$$\\end{document} between 0.4 and 1.8. The submerged condition does not reduce the Cd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{{\ ext{d}}}$$\\end{document}, but it reduces the discharge capacity (up to 50%), so that in some cases, to pass a given flow discharge, hu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{{\ ext{u}}}$$\\end{document} should increase by about 100% compared to the free condition.

Flow Visualization on Submerged Flow Conditions in Open Channel Weir Downstream

Submerged flow regimes are common phenomena observed in open channel flow, such as rivers and spillways, with or without weirs. These flow regimes involve a sudden rise in the liquid surface downstream when high-velocity liquid discharges into a region of lower velocity. The rapid deceleration of the flowing liquid results in an increase in height and a conversion of kinetic energy into potential energy, with some energy dissipated as turbulence and heat. In this study, flow visualization techniques were employed to investigate the two-dimensional hydrodynamic characteristics of submerged hydraulic jumps within the Froude number range of 1.0 to 5.4 over a fixed bed. The obtained results were compared with existing literature data, showing a good agreement. This research contributes to the understanding of submerged flow phenomena and provides valuable insights into the hydrodynamics of submerged hydraulic jumps.

Flow pattern formed over steps at a low-head dam: Salmon River Dam

ABSTRACT Building Stepping way over the low-head dams has been proposed to reduce the risk of drowning in submerged flow conditions. In the Salmon Barrier, adding two steps downstream of weir was previously suggested as an effective method for reducing the risk of drowning downstream of this dam. Given the effect of steps on the flow pattern downstream of the weir, the occurrence of dangerous submerged flows at different tailwaters was predicted, and the flow pattern expected at variable tailwaters was studied in comparison with the flow pattern passing over the sharp crested weir. According to the results, the submerged flow pattern downstream of the dam is a combination of the submerged flow pattern over the abrupt drop at low tailwaters and that over the sharp crested weir at high water levels. Consequently, similar correlations for predicting the flow regime downstream of these structures can be presented to predict the flow pattern at different tailwaters. The flow pattern over the step was compared with that over the abrupt drop, and a few diagrams were presented for predicting the occurrence of different flow patterns based on the submergence ratio of steps. Given the similarity of the flow pattern with those in the literature for sharp crested weirs, the flow pattern was also investigated at higher tailwaters. The comparison of correlations developed in this study indicated that the flow pattern approaches that reported in the literature for sharp crested weirs with increasing discharge.

Hydraulic characteristics of a sluice gate over a broad-crested weir

Vertical sluice gates are commonly used to control and measure flow in irrigation and drainage networks. To reduce their size and associated maintenance and operation costs, they are sometimes installed above broad-crested weirs. To explore the effects of the installation location of the sluice gate and the sill height on the hydrodynamic characteristics of the flow passing through the sluice-gated weir, six laboratory models were tested. The 427 and 449 data points included both free- and submerged-flow conditions, respectively. Analytical relationships were developed for the contraction, head-loss, and Henry's (1950) discharge coefficients. Based on the maximization of the discharge and contraction coefficients and the minimization of the head-loss coefficient, results suggest that a gate should be installed at a distance of L/2 (where L is the sill length) from the upstream end of the weir crest, and the height of 1.25Hd (where Hd is the water depth as referenced from the weir sill elevation) is the optimal height for the weir. By conducting experiments and constructing correlations for determining the contraction and head-loss coefficients under free flow conditions, the average values of these coefficients for the laboratory models were obtained as 0.664 and 0.133, respectively. Applying the average contraction and head-loss coefficients to the developed relationship for estimating the free and submerged discharge coefficients resulted in an error of 4% and 6%, respectively. WinGate alpha 0.2 software was used to estimate the experimental free and submerged discharge coefficient of the gated weir with an average error of 5.4% and 12.7%, respectively. It was done without any consideration of the cross-section shape of the weir or the location of the gate on the weir sill. In addition, an inspection of the submergence threshold of the gated weir showed an increase in the submergence threshold when the gate was moved further downstream from the upstream end of the sill.

Rotary gate discharge determination for inclusive data from free to submerged flow conditions using ENN, ENN–GA, and SVM–SA

Abstract This study aims at evaluating the performance of the Elman Neural Network (ENN), Elman Neural Network-Genetic Algorithm (ENN–GA), and Support Vector Machine-simulated annealing (SVM–SA) in determining the discharge of a newly proposed rotary gate for the inclusive data range from free flow to highly submerged conditions. For individual free and submerged flows, the models performed as well as that of the traditional relationships. However, the superiority of the intelligent models comes when dealing with the inclusive data set of both flow conditions, where no deterministic approach is available for discharge evaluation prior to specifying the threshold condition. In such complex flow conditions, the ENN–GA hybrid model with a proper structure determined the discharge with rather a high accuracy, i.e., SE of 6.12%. Also, in defining the threshold state, the ENN and ENN–GA models achieved superior results compared to the currently available relationship, i.e., it accurately recognized the threshold condition in almost 100% of the cases while the traditional relationship results were limited to 93% of the cases. Such accuracy of the employed model in assessing the discharge of the structure and its high ability in recognizing the flow state could be of great advantage for irrigation network structure automation.

Modeling of drag coefficient under emergent and submerged flexible vegetated flow

In an open-channel flow, vegetation study is crucial to be investigated with any type of plants including trees, shrubs, and grasses, which are growing within or near the channel banks and beds in natural or artificial waterways, such as rivers, streams, and canals. These plants are different in height, size, shape, and arrangements, which have a big impact on the turbulence and flow resistance structures. In this paper, a regression analysis has been used based on collected experimental data to improve a specific equation for the drag coefficient for rigid vegetation stems and expanded to flexible stem types under emergent and submerged flow conditions. The equation suggests a length scale metric that, by analogy with the log wake law, normalizes velocity profiles of the depth-limited open channel flow with submerged, rigid vegetation. It has been formulated by drawing regression analysis for each parameter including (Re) Reynolds number, (h*) submergence ratio, and (λ) vegetation density by considering the (Fr) Froude number ranges for the water flows and vegetated channel flows. Using the Reynolds number, which is determined by the height and diameter of the vegetation, the results demonstrate an increase and decrease in the drag coefficient. For assessing the impact of vegetation on flow resistance at the surface layer, the notion of the drag coefficient is introduced. It shows better performance than other length scales in collapsing resistance data gathered under a variety of vegetation circumstances. The proposed scaling is more accurate than those based on the logarithmic, velocity-defect, and power laws in collapsing regression analysis for the studied parameters.

Effect of the pipe bend of the morning glory spillway on the cavitation number

Cavitation phenomena always threats the hydraulic structures with high velocity flow and suddenly varying the flow direction. It is assumed that the process of the flow depleting with high ratio through the morning glory spillway accompanied by suddenly varying the flow direction caused by the bend pipe can deteriorate the condition of the cavitation. Introducing the ratio R/D (diameter size of the vertical and horizontal shaft divided with radius of the bend pipe) can be beneficial to propose the novel design plan to avoid the cavitation caused by the bend pipe. Present study carried out a series experimental tests to validate a numerical model of the morning glory spillway with different R/D ratio to show the impacts of the suddenly varying the flow direction on the variation of the cavitation number. The cavitation values of the free, semi-submerged and submerged flow conditions showed that cavitation was mainly occurred on the internal arch of the bend pipe for free flow and the level of the danger for semi-submerged flow was the major danger level for internal arch of the bend pipe and due to submerged flow, the crest level at the entrance of the morning glory spillway was additionally threated by cavitation. To prevent from the cavitation, the values of the cavitation number due to different R/D as 0.55, 0.45, 0.35, and 0.25 were calculated by employing the validated numerical model due to high danger of the cavitation in semi-submerged condition. Results showed that due to D/R > 0.35, the possible cavitation damage is obtained for the internal and external arch of the bend pipe of the morning glory spillway; however, for D/R < 0.25, the bend pipe position is located in safe zone and the danger of the cavitation is negligible.

Investigation of the Different Models of Elliptical-Lopac Gate Performance under Submerged Flow Conditions

The effect of the elliptic ratio on the hydraulic performance of the LOPAC gate has been investigated using experimental and Computational Fluid Dynamics CFD simulations (Flow-3D Hydro). Experiments and simulations were carried out at three different flow discharges, three different submerged ratios, and five different elliptic ratios. In this context, the CFD model was first calibrated and verified using the measured data, and then CFD simulation was performed. The ratio of upstream/downstream flow depth, the flow discharge coefficient, and the energy dissipation through the gate have been calculated and analyzed, and the three-dimensional features of the flow have been described. Based on the results, the elliptical LOPAC gates with circular weirs determine extreme values of the controlled flow parameters. Asymmetric recirculation downstream of the gate is sometimes observed in the model predictions. The use of Coriolis coefficients relevant to the entire cross-section, here deployed just for the circular and the traditional rectangular Lopac gates, has allowed a concise way to report and compare complex flows for any experimental condition.

Discussion on paper “Flow through a sluice gate over a broad crested weir under free and submerged-flow conditions”

ABSTRACT Please insert a as per journal style:This discussion paper is regarding the values of coefficient of discharge (Cd) and submergence (S) of a vertical type of sluice gate mounted on a broad casted weir. Discusser has used open channel specific energy principles justifying the values of Cd found by the author theoretically. Discusser has furnished the experimental values of Cd for a vertical type and tainter type gates. Discusser has also added the experimental values of Cd under free and submerged flow conditions in a model study for Salal dam spillway. An innovative proportional type flow meter developed by the discusser has been furnished for flow measurement within a given flow range.

Novel application of robust GWO-KELM model in predicting discharge coefficient of radial gates: a field data-based analysis

Abstract Accurate determination of discharge capacity in radial gates as commonly designed check structures is of great importance in hydraulic engineering research. The discharge coefficient plays the most dominant role in calculating the flow discharge through the radial gates. The main goal of this study is to adopt Grey Wolf Optimization-based Kernel Extreme Learning Machine (KELM-GWO) to further improve the prediction accuracy of the discharge coefficient of radial gates. To compare the supreme performance of the proposed model, kernel-depend support vector machine (SVM) and Gaussian process regression (GPR) were employed. An extensive field database consisting of 546 data samples gathered from different types of radial gates was established for building prediction models. The modeling results indicated that the proposed KELM-GWO model (correlation coefficient [R] = 0.927, and root mean squared error [RMSE] = 0.018) and SVM model (correlation coefficient [R] = 0.940, and root mean squared error [RMSE] = 0.022) demonstrated better performance under free and submerged flow conditions, respectively. Moreover, it was found that the applied kernel-depend approaches can be suitable options to predict the discharge coefficient of radial gates under varied submergence conditions with a satisfactory level of accuracy.

Experimental study of simple flumes with trapezoidal contraction

There are different devices available for measuring the flow discharge. Static measuring devices such as weirs and flumes (without any moving parts) play a significant role in discharge measurement in open channels. Many researchers have focused on application of flumes in irrigation networks. This investigation set out to study the flow discharge through a trapezoidal cut-throated flume (TCTF). The flume is simply constructed by placing two triangular plates on either side of a rectangular open channel to form a trapezoidal throat. The channel cross section is rectangular while throat cross section of the flume is trapezoidal. The proposed flume is simple, low-cost, easy to install and does not require high maintenance. The present study was designed to determine the effect of different variables on the flume discharge. For this, an experimental study was carried out under free outflow conditions and under upstream subcritical flow regime to formulate the flume discharge. Three models are defined for flume discharge relation based on the Buckingham's theorem of dimensional analysis, and then calibrated using the experimental data collected during this study. The first discharge model has an average error of 1.81%, while the second and third improved models have average errors of 0.96% and 1.44% respectively. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equations with an average error less than 2.23% were presented to estimate the submergence threshold. The results of this study indicate that while the downstream wall slope influences the submergence threshold, the flume discharge is not influenced by this variable. The proposed models are simple and accurate and present appropriate estimation of discharge for flows through the TCTFs. The findings of this study will be of interest for practical hydraulic engineers.