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Keywords = simple weirs

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19 pages, 3904 KiB  
Article
The Factors Affecting Stability and Durability of Flow Diversion Simple Weirs in Muchinga Province of Zambia
by Alex Lushikanda Kabwe, Masahiro Hyodo, Hidehiko Ogata, Yoshihiro Sagawa, Yoshinao Adachi and Masayuki Ishii
Water 2024, 16(13), 1852; https://doi.org/10.3390/w16131852 - 28 Jun 2024
Viewed by 1238
Abstract
The effectiveness of simple weirs and the ability of rural farmers to construct durable weirs are still areas of concern in rural areas in Zambia. The objective of this study is to investigate the factors contributing to the varying levels of durability of [...] Read more.
The effectiveness of simple weirs and the ability of rural farmers to construct durable weirs are still areas of concern in rural areas in Zambia. The objective of this study is to investigate the factors contributing to the varying levels of durability of the simple weir structures used for the diversion of river flows. This study was conducted in five districts where 33 simple weirs located in similar geographical zones were analyzed for their longevity. The research delved into catchment and climatic variables, as well as the social and psychological perception of simple weirs. This study conducted interviews with key informants who were familiar with the use of simple weirs in Muchinga Provinces between 26 December 2023 and 15 January 2024 using semi-structured questions. The findings of this study indicated that simple weirs constructed on relatively square-shaped catchments and narrow-shaped catchment areas were less vulnerable to damage and easy to operate and maintain. The study also found that climatic factors such as storm rainfall events had little impact on the operation and maintenance of these weirs in Muchinga province, as most sites are in the rainfall shadow while farmers’ views about the structures varied from site to site. Overall, planning is necessary for implementing small or large irrigation structures. Full article
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19 pages, 5362 KiB  
Article
Diagnostic Assessment in the Wet and Dry Seasons of Simple Weirs Constructed by Small-Scale Farmers in the Northern Region Provinces of Zambia
by Alex Lushikanda Kabwe, Masahiro Hyodo, Hidehiko Ogata, Yoshihiro Sagawa, Yoshinao Adachi and Masayuki Ishii
Water 2023, 15(22), 3935; https://doi.org/10.3390/w15223935 - 11 Nov 2023
Cited by 1 | Viewed by 1889
Abstract
An intervention recently made in Zambia is the promotion of small-scale irrigation using simple weirs, which aims to encourage small-scale farmers in the country’s rural areas to engage in irrigated food production throughout the dry season. This irrigation method relies on conventional weirs [...] Read more.
An intervention recently made in Zambia is the promotion of small-scale irrigation using simple weirs, which aims to encourage small-scale farmers in the country’s rural areas to engage in irrigated food production throughout the dry season. This irrigation method relies on conventional weirs to divert the river’s flow. This study was carried out in three northern region provinces of Zambia between November 2022 and January 2023 to conduct a functional diagnostic assessment of simple weirs during the dry and rainy seasons. In this study, 15 simple weirs were chosen for investigation. The goal of this study was to determine their physical status, identify their problems and scope, and evaluate simple weirs’ potential for river water diversion. According to this study, 26% of the weirs had broken sections and 67% were in excellent condition (being recently maintained and restored). Despite the challenges mentioned earlier, farmers have continued to construct them because they cannot afford to purchase stone or concrete irrigation structures due to the location and/or small-scale area available for irrigation development. Simple weirs may act as a beneficial supplement to irrigation technologies. The use of local building materials and the use of traditional skills is encouraged by this technology. Full article
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15 pages, 5531 KiB  
Article
Application of Simple Crested Weirs to Control Outflows from Tiles Drainage
by Michał Napierała
Water 2023, 15(18), 3248; https://doi.org/10.3390/w15183248 - 12 Sep 2023
Cited by 3 | Viewed by 3624
Abstract
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 [...] Read more.
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. Full article
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15 pages, 1479 KiB  
Article
Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces
by Giovanni Angiulli and Mario Versaci
Appl. Sci. 2022, 12(21), 11121; https://doi.org/10.3390/app122111121 - 2 Nov 2022
Cited by 10 | Viewed by 2158
Abstract
The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this [...] Read more.
The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this paper, we face this issue in the context of global analytic functions and Riemann surfaces. This point of view allows us to rigorously demonstrate the mathematical foundations of an algorithmic approach for avoiding the branch ambiguity problem, in which the phase unwrapping method is merged with K-K relations for recovering the effective parameters of an MM. In addition, exploiting the intimate relationship between the K-K relations and the Hilbert transform, a simple variant of the above algorithm is presented. Full article
(This article belongs to the Special Issue Progress and Application of Electromagnetic Materials)
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13 pages, 2582 KiB  
Article
New Stage–Discharge Relationship for Triangular Broad-Crested Weirs
by Alessio Nicosia, Francesco Giuseppe Carollo, Costanza Di Stefano and Vito Ferro
Water 2022, 14(19), 2993; https://doi.org/10.3390/w14192993 - 23 Sep 2022
Cited by 4 | Viewed by 2986
Abstract
Simple hydraulic structures, such as weirs, allow measuring flow discharge by using the upstream flow depth and a stage–discharge relationship. In this relationship, a discharge coefficient is introduced to correct all the effects neglected in the derivation (viscosity, surface tension, velocity head in [...] Read more.
Simple hydraulic structures, such as weirs, allow measuring flow discharge by using the upstream flow depth and a stage–discharge relationship. In this relationship, a discharge coefficient is introduced to correct all the effects neglected in the derivation (viscosity, surface tension, velocity head in the approach channel, flow turbulence, non-uniform velocity profile, and streamline curvature due to weir contraction). In this paper, the dimensional analysis and the incomplete self-similarity theory are used to investigate the outflow process of triangular broad-crested weirs, characterized by different values of the ratio between crest height p and channel width B, and to theoretically deduce a new stage–discharge relationship. A new theoretical stage–discharge relationship is suggested for the free-flow condition, and it is tested using experimental data available in the literature for the hydraulic condition p/B > 0. The obtained stage–discharge equation, characterized by low errors in discharge estimate, is useful for laboratory and field investigations. Finally, specific analysis for the triangular broad-crested weirs with p/B > 0 was developed to modify the stage–discharge relationship obtained for the case p/B = 0. This specific stage–discharge relationship allows to reduce the errors, which are generally less than ±5%, in the estimate of discharge for triangular broad-crested weirs with p/B > 0 and is also applicable for the case p/B = 0. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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19 pages, 5996 KiB  
Article
Modified Coptic Cross Shaped Split-Ring Resonator Based Negative Permittivity Metamaterial for Quad Band Satellite Applications with High Effective Medium Ratio
by Md Bellal Hossain, Mohammad Rashed Iqbal Faruque, Mohammad Tariqul Islam, Mayeen Uddin Khandaker, Nissren Tamam and Abdelmoneim Sulieman
Materials 2022, 15(9), 3389; https://doi.org/10.3390/ma15093389 - 9 May 2022
Cited by 16 | Viewed by 2347
Abstract
This research article describes a modified Coptic cross shaped split ring resonator (SRR) based metamaterial that exhibits a negative permittivity and refractive index with a permeability of nearly zero. The metamaterial unit cell consists of an SRR and modified Coptic cross shaped resonator [...] Read more.
This research article describes a modified Coptic cross shaped split ring resonator (SRR) based metamaterial that exhibits a negative permittivity and refractive index with a permeability of nearly zero. The metamaterial unit cell consists of an SRR and modified Coptic cross shaped resonator providing quadruple resonance frequency at 2.02, 6.985, 9.985 and 14.425 GHz with the magnitude of −29.45, −25.44, −19.05, and −24.45 dB, respectively. The unit cell that was fabricated on a FR-4 substrate with a thickness of 1.6 mm has an electrical dimension of 0.074λ × 0.074λ; the wavelength (λ) is computed at the frequency of 2.02 GHz. The computer simulation technology (CST) microwave studio was employed to determine the scattering parameters and their effective medium properties, i.e., permittivity, permeability and refractive index, also calculated based on NRW (Nicolson–Ross–Weir) method through the implementation of MATLAB code. The frequency range of 2.02–2.995 GHz, 6.985–7.945 GHz, 9.985–10.6 GHz, and 14.425–15.445 GHz has been found for negative permittivity. An effective medium ratio (EMR) of 13.50 at 2.02 GHz shows that the proposed unit cell is compact and effective. The lumped component based equivalent circuit model is used to validate with simulation results. The proposed unit cell and its array were fabricated for experimental verification. The results show that the simulation result using CST and high-frequency structure simulator (HFSS) simulator, equivalent circuit model result using advanced design system (ADS) simulator and measurement results match each other better. Its near zero permeability, negative permittivity, negative refractive index, high EMR and simple unit cell design allow the proposed metamaterial to be used for S-, C-, X- and Ku-band satellite applications. Full article
(This article belongs to the Special Issue Metamaterial and Metasurface Design for Microwave Applications)
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24 pages, 9403 KiB  
Article
Comparison of Three-Parameter Distributions in Controlled Catchments for a Stationary and Non-Stationary Data Series
by Łukasz Gruss, Mirosław Wiatkowski, Paweł Tomczyk, Jaroslav Pollert and Jaroslav Pollert
Water 2022, 14(3), 293; https://doi.org/10.3390/w14030293 - 19 Jan 2022
Cited by 5 | Viewed by 2253
Abstract
Flood Frequency Analysis (FFA) and the non-stationary FFA approaches are used in flood study, water resource planning, and the design of hydraulic structures. However, there is still a need to develop these methods and to find new procedures that can be used in [...] Read more.
Flood Frequency Analysis (FFA) and the non-stationary FFA approaches are used in flood study, water resource planning, and the design of hydraulic structures. However, there is still a need to develop these methods and to find new procedures that can be used in estimating simple distributions in controlled catchments. The aim of the study is a comparison of three-parameter distributions in controlled catchments for stationary and non-stationary data series and further to develop the procedure of the estimation the simple distributions. Ten rivers from the Czech Republic and Poland were selected because of their existing or planned reservoirs as well as for flood protection reasons. The annual maximum method and the three-parameter Weibull, Log-Normal, Generalized extreme value, and Pearson Type III distributions were used in this study. The analyzed time series are stationary and non-stationary. The methodology used in this study, which makes use of the Maximum Likelihood Estimation, allows one to simplify the analysis whenever there is a series of data that is both stationary and non-stationary. The novelty in our research is the standardization and development of a new procedure for a stationary and non-stationary data series, taking into account to read a specific value of the maximum flow with a given exceedance probability from the lower or upper tail. It determines the optimal choice of the theoretical distribution that can be used, for example in the design of weirs in rural areas (lower quantiles) or in the design of hydrotechnical structures in areas at risk of flooding (upper quantiles). Full article
(This article belongs to the Special Issue Modelling Hydrologic Response of Non-homogeneous Catchments II)
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9 pages, 662 KiB  
Proceeding Paper
Surrogate-Enhanced Parameter Inference for Function-Valued Models
by Christopher G. Albert, Ulrich Callies and Udo von Toussaint
Phys. Sci. Forum 2021, 3(1), 11; https://doi.org/10.3390/psf2021003011 - 21 Dec 2021
Viewed by 1396
Abstract
We present an approach to enhance the performance and flexibility of the Bayesian inference of model parameters based on observations of the measured data. Going beyond the usual surrogate-enhanced Monte-Carlo or optimization methods that focus on a scalar loss, we place emphasis on [...] Read more.
We present an approach to enhance the performance and flexibility of the Bayesian inference of model parameters based on observations of the measured data. Going beyond the usual surrogate-enhanced Monte-Carlo or optimization methods that focus on a scalar loss, we place emphasis on a function-valued output of a formally infinite dimension. For this purpose, the surrogate models are built on a combination of linear dimensionality reduction in an adaptive basis of principal components and Gaussian process regression for the map between reduced feature spaces. Since the decoded surrogate provides the full model output rather than only the loss, it is re-usable for multiple calibration measurements as well as different loss metrics and, consequently, allows for flexible marginalization over such quantities and applications to Bayesian hierarchical models. We evaluate the method’s performance based on a case study of a toy model and a simple riverine diatom model for the Elbe river. As input data, this model uses six tunable scalar parameters as well as silica concentrations in the upper reach of the river together with the continuous time-series of temperature, radiation, and river discharge over a specific year. The output consists of continuous time-series data that are calibrated against corresponding measurements from the Geesthacht Weir station at the Elbe river. For this study, only two scalar inputs were considered together with a function-valued output and compared to an existing model calibration using direct simulation runs without a surrogate. Full article
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12 pages, 3626 KiB  
Article
Application of Stage-Fall-Discharge Rating Curves to a Reservoir Based on Acoustic Doppler Velocity Meter Measurement Data
by Yeonsu Kim, Sungryul Oh, Seungsoo Lee, Jisun Byun and Hyunuk An
Water 2021, 13(17), 2443; https://doi.org/10.3390/w13172443 - 5 Sep 2021
Cited by 7 | Viewed by 3242
Abstract
The applicability of the stage-fall-discharge (SFD) method in combination with acoustic Doppler velocity meter (ADVM) data, upstream of a hydraulic structure, specifically, the Sejong-weir located in the Geum River, Korea, was examined. We developed three rating curves: a conventional simple rating curve with [...] Read more.
The applicability of the stage-fall-discharge (SFD) method in combination with acoustic Doppler velocity meter (ADVM) data, upstream of a hydraulic structure, specifically, the Sejong-weir located in the Geum River, Korea, was examined. We developed three rating curves: a conventional simple rating curve with the data measured using an acoustic Doppler current profiler (ADCP) and floating objects, an SFD rating curve with the data measured using the ADCP and floating objects, and an SFD rating curve with the data measured using an ADVM. Because of the gate operation effect, every rating curve involved many uncertainties under 1000 m3/s (3.13 m2/s, specific discharge). In terms of the hydrograph reconstruction, compared with the conventional simple rating curve, the SFD developed using ADVM data exhibited a higher agreement with the measured data in terms of the pattern. Furthermore, the measured discharge over 1000 m3/s primarily ranged between 97.5% and 2.5% in the graph comparing the ratio of the median and observed discharge. Based on this experiment, it is confirmed that the SFD rating curve with data to represent the backwater effect, such as ADVM data, can reduce the uncertainties induced by the typical rating curve Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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23 pages, 6265 KiB  
Article
Application of Multivariate Statistical Techniques and Water Quality Index for the Assessment of Water Quality and Apportionment of Pollution Sources in the Yeongsan River, South Korea
by Md Mamun and Kwang-Guk An
Int. J. Environ. Res. Public Health 2021, 18(16), 8268; https://doi.org/10.3390/ijerph18168268 - 4 Aug 2021
Cited by 32 | Viewed by 4911
Abstract
This study assessed spatial and temporal variations of water quality to identify and quantify possible pollution sources affecting the Yeongsan River using multivariate statistical techniques (MSTs) and water quality index (WQI) values. A 15 year dataset of 11 water quality variables was used, [...] Read more.
This study assessed spatial and temporal variations of water quality to identify and quantify possible pollution sources affecting the Yeongsan River using multivariate statistical techniques (MSTs) and water quality index (WQI) values. A 15 year dataset of 11 water quality variables was used, covering 16 monitoring sites. The nutrient regime, organic matter, suspended solids, ionic contents, algal growth, and total coliform bacteria (TCB) were affected by the summer monsoon and the construction of weirs. Regression analysis showed that the algal growth was more highly regulated by total phosphorus (TP; R2 = 0.37) than total nitrogen (TN, R2 = 0.25) and TN/TP (R2 = 0.01) ratios in the river after weir construction and indicated that the river is a P-limited system. After constructing the weirs, the mean TN/TP ratio in the river was about 40, meaning it is a P-limited system. Cluster analysis was used to classify the sampling sites into highly, moderately, and less polluted sites based on water quality features. Stepwise discriminant analysis showed that pH, dissolved oxygen (DO), TN, biological oxygen demand (BOD), chemical oxygen demand (COD), chlorophyll-a (CHL-a), and TCB are the spatially discriminating parameters, while pH, water temperature, DO, electrical conductivity, total suspended solids, and COD are the most significant for discriminating among the three seasons. The Pearson network analysis showed that nutrients flow with organic matter in the river, while CHL-a showed the highest correlation with COD (r = 0.85), followed by TP (r = 0.49) and TN (r = 0.49). Average WQI values ranged from 55 to 141, indicating poor to unsuitable water quality in the river. The Mann–Kendall test showed increasing trends in COD and CHL-a but decreasing trends for TP, TN, and BOD due to impoundment effects. The principal component analysis combined with factor analysis and positive matrix factorization (PMF) showed that two sewage treatment plants, agricultural activities, and livestock farming adversely impacted river water quality. The PMF model returned greater R2 values for BOD (0.92), COD (0.87), TP (0.93), TN (0.91), CHL-a (0.93), and TCB (0.83), indicating reliable apportionment results. Our results suggest that MSTs and WQI can be effectively used for the simple interpretation of large-scale datasets to determine pollution sources and their spatiotemporal variations. The outcomes of our study may aid policymakers in managing the Yeongsan River. Full article
(This article belongs to the Special Issue Environmental Hygiene, Water Quality and Human Health)
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13 pages, 7019 KiB  
Article
A Method for Estimating the Risk of Dam Reservoir Silting in Fire-Prone Watersheds: A Study in Douro River, Portugal
by Daniela Patrícia Salgado Terêncio, Rui Manuel Vitor Cortes, Fernando António Leal Pacheco, João Paulo Moura and Luís Filipe Sanches Fernandes
Water 2020, 12(11), 2959; https://doi.org/10.3390/w12112959 - 22 Oct 2020
Cited by 19 | Viewed by 4208
Abstract
Forest fires are an increasing problem over recent decades. The fires, among other consequences, lead to an increase in the soil vulnerability to water erosion and a consequent increase in sedimentation rates. When barriers are present, such as dams or weirs, there is [...] Read more.
Forest fires are an increasing problem over recent decades. The fires, among other consequences, lead to an increase in the soil vulnerability to water erosion and a consequent increase in sedimentation rates. When barriers are present, such as dams or weirs, there is an amplified risk of sediment and ash deposition in their reservoirs, causing siltation. Thus, there is an interest in studying in more detail the risk of siltation of barriers and reservoirs in the Douro River watershed following wildfires. A detailed barrier inventory was lacking for the Douro River, hampering the identification of siltation-prone areas. In order to fill in this gap, an extensive inventory of barriers in the Douro river basin was carried out for the present study. The result was an abundant and reliable dataset on the Douro River barriers, which allowed a prognosis on the watershed siltation risk. The method for calculating the siltation risk relied on the relationship between the frequency of forest fires, the erosion risk and the frequency of reservoirs. The sub-basins with the greater siltation risk are the Tâmega, Corgo, Sousa and Paiva river basins. Most reservoirs with the highest siltation risk were from small dams. The modelling results were compared with stream connectivity and concentrations of stream water phosphorus (associated with the sediments that flow into the rivers due to the fires). With regard to connectivity, only two reservoirs were at high risk of sedimentation due to fires, so the categories of connectivity risk and fire-based sedimentation risk are probably not related. With regard to risk of high phosphorus loadings, in 8 basins the upper classes for fire-based erosion risk coincided with the upper class for phosphorus loadings suggesting that high phosphorus loading could be associated with fire-based erosion. This study works as a simple but reliable example on the assessment and mapping of siltation risk in stream networks intersected by abundant barriers. It allowed for identifying barriers that can accumulate a large quantity of fine sediments and ashes, interfering with water quality and soil erosion as well as with the storage capacity of the respective barriers. Full article
(This article belongs to the Special Issue Flowing Waters and Threatened Aquatic Life)
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18 pages, 6588 KiB  
Article
New Empirical Model Using Landscape Hydric Potential Method to Estimate Median Peak Discharges in Mountain Ungauged Catchments
by Andrzej Wałęga, Dariusz Młyński, Jakub Wojkowski, Artur Radecki-Pawlik and Tomáš Lepeška
Water 2020, 12(4), 983; https://doi.org/10.3390/w12040983 - 30 Mar 2020
Cited by 11 | Viewed by 3536
Abstract
Designing hydraulic structures, such as culverts, bridges, weirs, and check dams, while planning new flood inundation areas, needs correct assessment of design discharges. In gauged catchments with long time series of discharges, statistical methods are commonly used based on fixed theoretical distributions and [...] Read more.
Designing hydraulic structures, such as culverts, bridges, weirs, and check dams, while planning new flood inundation areas, needs correct assessment of design discharges. In gauged catchments with long time series of discharges, statistical methods are commonly used based on fixed theoretical distributions and on empirical distributions. However, in ungauged catchments, this approach is not possible. In addition to more advanced methods, which are used today, e.g., rainfall–runoff models, much more simple approaches are still needed based on regionalization and empirical models. Thus, the objective of this work is to develop a new empirical model for calculating peak discharge expressed as the median of annual peak discharge (QMED). The innovative aspect of this paper is the use of a new parameter, named landscape hydric potential (LHP), as a descriptor of water storage in catchments. LHP has a crucial role as the descriptor of water storage in catchment and, thus, it has an influence on forming discharges. The work was done in the Upper Vistula basin in the Polish Carpathians. This study was carried out in mountain catchments located in the Upper Vistula basin, in the south part of Poland in in the Polish Carpathians. Results show that the proposed model could provide appropriate calculations in changing climate conditions, as well as when land use is changed. The proposed model is simple and effective; for calculating QMED, it needs only two parameters: catchment area and LHP. Since the model has a significant and high correlation coefficient, it could be used for assessing of QMED in ungauged mountain catchments. The determined form of the empirical equation finds application in the entire Upper Vistula basin, for catchments with a surface area from 24 km2 up to 660 km2. Full article
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18 pages, 7277 KiB  
Article
Discharge Coefficient of Rectangular Short-Crested Weir with Varying Slope Coefficients
by Yuejun Chen, Zongfu Fu, Qingsheng Chen and Zhen Cui
Water 2018, 10(2), 204; https://doi.org/10.3390/w10020204 - 14 Feb 2018
Cited by 12 | Viewed by 14788
Abstract
Rectangular short-crested weirs are widely used for simple structure and high discharge capacity. As one of the most important and influential factors of discharge capacity, side slope can improve the hydraulic characteristics of weirs at special conditions. In order to systemically study the [...] Read more.
Rectangular short-crested weirs are widely used for simple structure and high discharge capacity. As one of the most important and influential factors of discharge capacity, side slope can improve the hydraulic characteristics of weirs at special conditions. In order to systemically study the effects of upstream and downstream slope coefficients S1 and S2 on overflow discharge coefficient in a rectangular short-crested weir the Volume of Fluid (VOF) method and the Renormalization Group (RNG) κ-ε turbulence model are used. In this study, the slope coefficient ranges from V to 3H:1V and each model corresponds to five total energy heads of H0 ranging from 8.0 to 24.0 cm. Comparisons of discharge coefficients and free surface profiles between simulated and laboratory results display a good agreement. The simulated results show that the difference of discharge coefficients will decrease with upstream slopes and increase with downstream slopes as H0 increases. For a given H0, the discharge coefficient has a convex parabolic relation with S1 and a piecewise linearity relation with S2. The maximum discharge coefficient is always obtained at S2 = 0.8. There exists a difference between upstream and downstream slope coefficients in the influence range of free surface curvatures. Furthermore, a proposed discharge coefficient equation by nonlinear regression is a function of upstream and downstream slope coefficients. Full article
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