Weir Type Research Articles

Hydraulic assessment of different types of piano key weirs

ABSTRACT Piano Key Weir (PKW) is a non-linear weir with a small foundation footprint that allows large discharges through a narrow channel. The presence of overhangs classifies it into A, B, C, and D. For different PKW types, this study aims to assess the discharge, hydraulic characteristics (flow regimes, water surface profile, and nappes interference), and energy dispersion. This study employs the FLOW-3D software and validated by comparing experimental types A and D PKW with numerical simulations. Experimental and simulation results agreed well, with lower MAPE values for both types. After that, eight simulations for each PKW type were run, with headwater ratios (H t /P) from 0.13 to 0.85 (H t : total upstream head above crest, P: PKW height). Regarding discharge performance, type-B was superior to all other PKW types at lower heads (H t /P ≤0.40) due to longer upstream overhangs. While at higher heads (H t /P > 0.40), type-A became the highest PKW type. Since PKWs disperse energy more effectively than linear weirs, they acquire new performance as energy dissipators. Type-C had the highest energy dispersion rate, followed by type-A, type-D, and type-B. Finally, an empirical equation was provided to predict energy dispersion rates over PKW types as a function of discharge coefficient.

Second Order Duality Involving Second Order Cone Arcwise Connected Functions and Their Generalizations in Vector Optimization Problem over Cones

In this paper, we introduce second order cone arcwise connected function and its generalizations. Further we study the interrelations among these functions also. Mond Weir type second order dual is formulated and duality results are proved using these functions.

Prediction of aeration performance of different types of piano key weirs using different machine learning models

ABSTRACT Aeration is a cost-effective and efficient method for increasing the available oxygen or dissolved oxygen content in water bodies, which is crucial for the existence of aquatic life. However, conventional techniques for estimating aeration in different hydraulic structures are time-consuming and incorrect ways to approximate aeration. Therefore, new, computationally more efficient, and more accurate methods are required. In this article, three machine learning models are presented: (1) ELM (extreme learning machine) model, (2) online sequential extreme learning machine model, and (3) I-ELM (incremental extreme learning machine) model. These models assess the air conditioning capacity of the three variants of Piano Key Weirs (PKWs), denoted as A, B, and C, about Cd, Cs, and Cu, which are the three most important parameters for aeration efficiency at different temperatures. The model performance is evaluated and compared based on mean squared error, root-mean-square error, correlation coefficient, mean absolute error, and Nash–Sutcliffe efficiency. This research concludes that I-ELM is the best-performing model for complete available data that are time invariant.

Kernel-based framework for improved prediction of discharge coefficient in vertically supported cylindrical weirs

ABSTRACT The present study represents the first use of kernel-based models to predict discharge coefficient (Cd) for two distinct types of cylindrical weirs, featuring vertical support and a 30-degree upstream ramp. For this purpose, kernel-based methods, including support vector machine, Gaussian process regression (GPR), Kernel extreme learning machine, and Kernel ridge regression, were used, as they offer notable advantages compared to other machine learning models, such as flexibility in handling various data patterns, robustness against overfitting, and effectiveness in high-dimensional data scenarios. The results indicated that the GPR model, with statistical metrics of R = 0.967, Nash–Sutcliffe efficiency (NSE) = 0.935, and root-mean-square error (RMSE) = 0.027, demonstrates superior accuracy in modeling the overall dataset collected from two distinct types of weirs. Through a conducted sensitivity analysis, it was identified that the upstream Froude number is pivotal in accurately predicting the Cd of a cylindrical weir. The modeling conducted for two distinct weir types revealed that a cylindrical weir with vertical support exhibits enhanced predictive capabilities (R = 0.997, NSE = 0.994, and RMSE = 0.007) for Cd. The findings indicate that the introduction of the upstream ramp alters hydraulic conditions, resulting in reduced modeling accuracy (R = 0.760, NSE = 0.529, and RMSE = 0.060).

Manufacturing process transfer to a 30 kg/h continuous direct compression line with real-time composition monitoring

Transferring an existing marketed pharmaceutical product from batch to continuous manufacturing (CM) without changes in regulatory registration is a challenging task in the pharmaceutical industry. Continuous manufacturing can provide an increased production rate and better equipment utilisation while retaining key quality attributes of the final product. Continuous manufacturing necessitates the monitoring of critical quality attributes in real time by appropriate process analytical tools such as near infra-red (NIR) probes. The present work reports a successful transfer of an existing drug product from batch to continuous manufacturing process without changing the formulation. A key step was continuous powder blending, whose design and operating parameters including weir type, agitation rate, dynamic hold-up and residence time were systematically investigated with respect to process repeatability. A NIR-based multivariate data model for in-line composition monitoring has been developed and validated against an existing quality control method for measuring tablet content uniformity. A continuous manufacturing long-run with a throughput of 30 kg/h (approx. 128,000 tablets per hour), uninterrupted for 320 min, has been performed to test and validate the multivariate data model as well as the batch to continuous process transfer. The final disintegration and dissolution properties of tablets manufactured by the continuous process were found to be equivalent to those manufactured by the original batch process.

Numerical modeling of ice control on the Albany River, Ontario, Canada

The Kashechewan First Nation (KFN) community is located on a floodplain of the north branch of the Albany River, on the west coast of James Bay. Each spring, the community faces the uncertain prospect of evacuation due to ice-jam flooding, the most severe of which occurred in 2006. A study was conducted to develop long-term options for reducing the flood risk to the community, which included dams, dykes, pier and weir type ice-control structures, and conveyance channels. This paper presents a numerical model study on the Albany River in Ontario, Canada to develop ice control as a potential means for mitigating ice-jam flooding at the KFN community using the two-dimensional ice dynamics model DynaRICE. A method was developed to simulate pier type ice-control structures within the model such that the physical channel conditions, flow conditions, and combinations of ice control could be evaluated. The model allowed detailed simulation of ice retention, resulting inundation, and the forces on the individual piers. To optimize the design of the piers, including pier spacing, height, and size, various combinations of ice, flow, and pier conditions were simulated. Numerical modeling facilitated a comparative examination of flood risk reduction to the community from the various ice control options.

Flow behavior over well-escape weirs

ABSTRACT Weirs play an important role in controlling and managing water in irrigation canal networks through several functions, such as discharge measurements, water distribution, and lowering the water level. Weirs also play a crucial role in protecting canals from flooding, which might cause the earthen banks to collapse, by eliminating surplus water at the ends of the canals. Over the previous decades, the flow over the traditional sharp-crested weirs was extensively investigated by many researchers; however, the well-escape weirs have not received sufficient attention. These types of weirs were mostly constructed in the form of vertical wells that may be circular or rectangular in shape, and water may flow through the entire perimeter of the weir or part of the perimeter. In the present research, the effect of the well-escape-weir shape on the characteristics of flow over the weir was studied. A set of models were constructed in different shapes, circular and square, and the entire perimeter of the weir or part of the perimeter is working as the weir crest length. The discharge passing over the unit length of the weir crest (q) is investigated and compared for the circular and square weirs of various crest lengths and positions. The results indicated that the discharge capacity of the circular weirs increases by a rate ranging between 7.5% and 15% more than that of the square weirs at the same head. Also, results indicated that the discharge coefficient of the circular weirs increases by a rate ranging between 9.3% and 10.3% more than that of the square weirs. This behavior can be attributed to the interference between the orthogonal water nappes at the corners of the square models. In addition, the flow direction has little effect on the discharge coefficient at small discharges, and this effect becomes more obvious at higher discharges. Additionally, the well-escape weirs of the upstream crest have a slightly higher discharge capacity than those of the downstream crest due to the effect of the approach velocity, which increases the water entrance velocity at the upstream crest. The results of flow patterns around the weir showed that the locations of maximum flow velocities (u, v, w) are mostly near the weir crest and depend entirely on the crest length and position.

Experimental study of flow over piano key weirs with different plan shapes

ABSTRACT The piano key weir (PKW) is an evolution with more hydraulic efficiency, compared to labyrinth weir. The studies on this type of weir have shown a significant increase in its discharge efficiency, especially at low heads. In this study, discharge coefficient of various shapes of piano key weir (i.e. rectangular, trapezoidal, and triangular) is investigated experimentally. Also, the aeration process of the studied weirs is described. According to the results, it was found that the discharge coefficient of the triangular PKW is about 28.2% more than the discharge coefficient of the rectangular PKW, and the discharge coefficient of the trapezoidal PKW is about 12.9% more than the discharge coefficient of the rectangular PKW. Also, the discharge capacity of the rectangular, triangular, and trapezoidal PKWs are 3.8, 3.96, and 3.96 times the sharp crest weir, respectively. The equations introduced for the discharge coefficient show good agreement (with R2 from 0.968 to 0.988 and average percentage error from 0.82 to 2.6%) between the actual and calculated values.

Prediction of the Discharge Coefficient of a Labyrinth Weir Type D by an Artificial Neural Network Method

Abstract This study presents the use, and its advantages, of artificial intelligence methods to predict the discharge coefficient (Cw ), considering the approach conditions of the labyrinth weir type D. The study suggests modifying the training and validation rates in AI tools, which are often fixed without proper justification in previous studies. Unlike most studies that use geometric dimensions as inputs, this work focuses on the approach conditions (the emplacement of the labyrinth weir and filling the alveoli upstream and downstream) of the labyrinth weir type D. The results, based on laboratory experiments, show that these modified inputs significantly impact the e ciency and cost of constructing the weir. Moreover, the C w predictions based on these inputs are highly satisfactory compared to laboratory test results. In terms of training and validation ratios, the study confirms that the optimal ratio is 70/30 for accurate and highly satisfactory predictions.

Simulation of the Hydraulic Performance of Parallel Pivot Weirs with Different Angles

Pivot weirs are one of the most important structures for regulating the water level in rivers and canals. These weirs are constructed with one or more gates in a row in the waterways. Changing the angle of each gate is done individually with an independent system. Based on available information, the hydraulic performance of this type of weirs (especially in several gates and different angles) in different operational conditions has not been investigated. In present study, pivot weirs with two gates are simulated using Ansys CFX software with the angles of 27.8 to 90 degree and the discharges between 40 to 130 L/s. Further, the importance of the open space between the two adjacent weirs with different angles (lack of retail wall) and its hydraulic behavior have been studied. The model was calibrated based on valid laboratory data and using the K-ϵ turbulence model. Therefore, the weirs with equal angles were studied in the first step. In this case, the effective discharge angle coefficient was studied and its maximum value compared to the vertical angle was obtained 1.076 for the angle of 52°. Furthermore, relationships for discharge coefficient versus upstream water depth were developed. In the next step, the effective length of the crest was found to be increases by 30% under unequal angles operation and the discharge coefficient raised by 1.3 to 2.4 times. Also, it was recognized that, in case of two weirs with unequal angles, about 26% to 69% of the flow passes through the distance between the two weirs. Therefore, the performance of unequal angles operation seems to be more effective in controlling the water level and discharge in different conditions and especially in flood events.

Investigation of labyrinth weirs discharge coefficient with the same length

One of the approaches to reduce flood depth in dams and rivers is the application labyrinth weirs instead of simple linear weirs. Labyrinth weirs have a longer length than linear weirs; therefore, the flood will pass through it with a lower depth. In this study, two types of triangular and semicircular labyrinth weirs were experimentally investigated. Experiments were performed in a flume with a width of 0.8 m and a flow discharge of up to 70 L/s. Eight weir models with a thickness of 4 mm were made, of which four models are triangular weirs and four models are semicircular weirs. Weirs were used in two types, one-cycle and two-cycle. The height of the weirs is 15 cm and the ratio of the weir length to the flume width (L/W) is equal to 1.57. The results showed that the increase in the total water head ratio (HT/P) decreases the discharge coefficient in all models, which is due to the increase in the Nappe interference and the local submergence. Also, increasing the number of cycles in labyrinth weirs has reduced its efficiency. The reason for this decrease is the impact of the issuing jets at the junction of the cycles and the flow disturbance over the weir. The comparison between triangular and circular weirs showed the better efficiency of triangular weirs. In addition, the results showed that the placement of the top of the cycle towards the upstream will cause a better performance in the weir. It seems that the low angle of the weir wall in the downstream with the channel wall causes the Nappe flow to collide with the channel wall and consequent local submergence will ultimately reduce the discharge coefficient.

Application of Simple Crested Weirs to Control Outflows from Tiles Drainage

Triangular sharp-crested weirs are commonly used to measure low-flow measurements in open channels. The flow over such a V-notch is proportional to the height of water above the weir on the upstream side. Therefore, it is relatively easy to calculate the flow from standard equations by using only recordings of water levels. Thus, these types of weirs can provide inexpensive measurements of flow volumes and resulting nutrient loads from subsurface drainage systems and associated conservation practices. The objective of this study was to develop appropriate weir equations for a 22.5° V-notch weir developed for a new tubular water level control structure in a controlled drainage system (CD). Analyses using this weir, with three typical slope angles of 30°, 45°, and 60°, were also conducted. There were no significant differences in the fitted parameters across the three analyzed slope angles. The coefficient of determination (R2) values were 0.9955, 0.9981, and 0.9980, respectively. However, the best-fitted equation for a 22.5° V-notch weir was for a slope angle of 45°. The flow equation was Q = 0.2235H2.4182, with Q in liters per minute and H in centimeters. This equation can be used for measuring flow through tubular-controlled drainage structures.

Pareto Efficiency Criteria and Duality for Multiobjective Fractional Programming Problems with Equilibrium Constraints on Hadamard Manifolds

This article deals with multiobjective fractional programming problems with equilibrium constraints in the setting of Hadamard manifolds (abbreviated as MFPPEC). The generalized Guignard constraint qualification (abbreviated as GGCQ) for MFPPEC is presented. Furthermore, the Karush–Kuhn–Tucker (abbreviated as KKT) type necessary criteria of Pareto efficiency for MFPPEC are derived using GGCQ. Sufficient criteria of Pareto efficiency for MFPPEC are deduced under some geodesic convexity hypotheses. Subsequently, Mond–Weir and Wolfe type dual models related to MFPPEC are formulated. The weak, strong, and strict converse duality results are derived relating MFPPEC and the respective dual models. Suitable nontrivial examples have been furnished to demonstrate the significance of the results established in this article. The results derived in the article extend and generalize several notable results previously existing in the literature. To the best of our knowledge, optimality conditions and duality for MFPPEC have not yet been studied in the framework of manifolds.

Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity

This paper focuses on a nonsmooth nonconvex interval-valued optimization problem. For this, we propose interval-valued symmetric invexity, interval-valued symmetric pseudo-invexity and interval-valued symmetric quasi-invexity in terms of the symmetric gH-differentiable interval-valued functions. Some important properties of these generalized convexities are also discussed. By utilizing these new concepts, we establish sufficient Karush–Kuhn–Tucker conditions for the considered problem. Further, the Wolfe and Mond–Weir type dual problems are associated and weak, strong and strict converse duality results have been derived. Finally, we apply the developed theory to a binary classification problem of interval data by support vector machine.

Determination of flow characteristics over sharp-crested triangular plan form weirs using numerical simulation

ABSTRACT Triangular plan form weirs are one type of long-crested weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. This study aims to investigate the effects of different number of teeth (3, 4, and 5 teeth), angle of the weir tip (90, 60, 120, and 150 degrees), and the amount of different discharges (0.009–0.0063 m3/s) of sharp-crested triangular plan form weirs on the hydraulic parameters by using the Finite Volume Method (FVM). It was found that, increasing the effective length of the crest, increases the discharge coefficient up to 95% in the case with 5 teeth (L/B = 4.14 and h/W = 0.128), 45% in the case with 4 teeth (L/B = 3.71 and h/W = 0.168) and 39% for 3 teeth (L/B = 3.28 and h/W = 0.188) compared to the simple triangular plan weir (without teeth). Also, Results indicated that the discharge coefficient has an inverse relationship with the h/w ratio. In contrast, the investigations showed that the velocity in the flow jet is affected by the effective length of the triangular plan crest, and the increase in the effective length results in a decrease in the average velocity of the flow jet. So that these disturbances caused the highest dissipation of energy to occur in the triangular plan crest with 5 teeth (27% compared to the upstream section (Section 1) and 37% compared to the downstream section (Section 2)).

A pair of Mond–Weir type third order symmetric duality

A pair of Mond–Weir type third order symmetric duality

Nonsmooth semi-infinite roughly B-invex multi-objective programming problems

In this paper, we will study a nonsmooth semi-infinite multi-objective programming problem involving roughly B-invex functions. Sufficient optimality conditions for the primal problem are derived. We shall formulate Mond–Weir type dual and establish weak and strong duality theorems under various roughly B-invexity assumptions.

On the Hydraulic Characteristics of Submerged Flow over Trapezoidal-Shaped Weirs

Abstract Subcritical flows over highway and railway embankments, commonly encountered during flood events, can be treated like submerged flows over trapezoidal-shaped weirs. In earlier studies, the equation of the submerged-flow discharge for such types of weirs was developed as a function of the degree of submergence and free-flow discharge. However, the application of this equation in practice requires a pre-determined discharge from experiments performed under free-flowconditions. In this study, a discharge equation was deduced from the streamwise momentum balance equation, which overcomes the drawback of the previous approaches. The results of the validation demonstrated that the proposed equation is capable of predicting the submerged-flow discharge of a trapezoidal-shaped weir within ±6.0% of the measured value. Furthermore, the most prominent features of the submerged overflows were examined by systematically analyzing the experimental data. For such flows, the free-surface and bed-pressure profiles are self-similar only over the upstream face of the weir. Results of this investigation confirmed that the degree of submergence and the slope of the downstream weir face significantly affect the characteristics of the submerged flow, but the effect of the latter on the non-modular discharge is marginal.

Hydrometric flow measurement in water management

The main problem in the operation of irrigation systems is to ensure the accuracy and reliability of measuring the main hydrometric parameters in managing water resources of irrigation facilities. When operating systems with pumping stations, it becomes necessary to measure a set of technological parameters, which can be divided into the following groups by type: hydraulic parameters (flow rate, fluid pressure, water flow in the channel), parameters of pumping units, linear-angular parameters (channel section length, channel width, gate movement, mixed parameters (clear area, flow depth, wetted perimeter length). Analysis of existing methods and instruments for measuring water flow for the rational use of water resources is used in all areas the volume of water taken from the water intake and supplied to the irrigation network. This task contributes to operational and control of pumping station parameters without hydrometric instruments at the stations themselves. The problem of organizing automated technological accounting of irrigation water at graduated hydraulic structures equipped with gates and operating in a flooded or backwater-variable mode is solved by new hydrometric methods with the integrated use of ultrasonic, acoustic, or float level gauges as part of modern microprocessor devices that convert water level readings at such structures into flow and runoff readings, according to the calibration characteristic each specific building. The article presents the recommended water metering devices for different hydraulic flow regimes and water quality. To speed up the process of measuring water flow in canals with flow rates of 1-10 m3 / s and large facilities of pumping stations with flow rates of 10-200 m3 / s, types of standard weirs, flumes of various profiles, and water measuring nozzles are recommended. According to the working formulas, changes in water flow are determined, taking into account the error of the gauging station and the indicated weirs.

Quasi Efficient Solutions and Duality Results in a Multiobjective Optimization Problem with Mixed Constraints via Tangential Subdifferentials

We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized convexity assumptions, we state strong, weak and converse duality relations of Wolfe and Mond–Weir types. We give a number of examples to illustrate the new concepts and main results of this paper.