Showing 43 results for سرریز
S. A. Banishoaib, A. Bordbar, A. A. Kamanbedast, A. Masjedi, M. Heidarnejad,
Volume 23, Issue 4 (12-2019)
Abstract
A ‘spillway’ is a structure used to provide the controlled release of flood water from upstream into downstream area of a dam. As an important component of every dam, a spillway should be constructed strongly, reliably and efficiently to be used at any moment. Labyrinth and stepped spillways are presented as appropriate modifications to those spillways hardly capable of managing the maximum potential discharge. Owing to their nonlinear crests for a given width, labyrinth and stepped spillways have a larger discharge rate than linear- crest spillways at an identical height. Compared to other energy dissipaters, the combination of stepped and labyrinth spillways is known as a very strong energy dissipater. In the following part, the combination of these two structures and their dimensional change for increasing the water- energy dissipation are addressed. To conduct this study, an experimental flume with a 90- degree bend in the Islamic Azad University of Ahwaz was used. In total, 90 experiments were conducted on three different labyrinth- shape stepped spillway models with two different lengths, three different widths, and five different discharges. Analysis of the results showed a greater energy loss reduction in triangular rather than rectangular or trapezoidal labyrinth- shape stepped spillways. In addition, energy loss was greater in labyrinth spillways with two cycles than those with one cycle. Energy loss was increased by raising the Froude number from 0.05 to 0.1; in contrast, energy loss was decreased with increasing the Froude number from 0.1 to 1.0, which was due to the submergence of steps, a decrease in the roughness of steps and an increase in the intensity of aeration.
R. Gharibvand, M. Heidarnejad, H. A. Kashkouli, H. Hasoonizadeh, A. Kmanbedast,
Volume 24, Issue 1 (5-2020)
Abstract
The flow fields over a trapezoidal labyrinth weir (two-cycle) and a piano key weir were simulated using Flow3D, studying the impact of each model on the flow field in the weirs and the coefficient of discharge in comparison with the available experimental data. Moreover, the models were investigated experimentally in a 12.5 m long, 0.3 m wide, and 0.4 m high rectangular flume under clear-water conditions. The results showed good agreement between the data from the numerical and experimental models. The piano key weirs had a higher coefficient of discharged compared with labyrinth weirs. The coefficient of discharge was observed to increase by 26 percent as the height of the PKW was increased by 50 percent (from 5 to 7.5 cm). This increase was 24 percent for labyrinth weirs.
A. Alizadeh, B. Yaghoubi, S. Shabanlou,
Volume 24, Issue 2 (7-2020)
Abstract
In this study, the discharge coefficient of sharp-crested weirs located on circular channels was modeled using the ANFIS and ANFIS-Firefly (ANFIS-FA) algorithm. Also, the Monte Carlo simulations (MCs) were used to enhance the compatibilities of the soft computing models. However, the k-fold cross validation method (k=5) was used to validate the numerical models. According to the input parameters, four models of ANFIS and ANFIS-FA were introduced. Analyzing the numerical results showed that the superior model simulated the discharge coefficient as a function of the Froude number (Fr) and the ratio of flow depth over weir crest to the weir crest height) h/P(. The values of the mean absolute relative error (MARE), root mean square error (RMSE) and correlation coefficient (R) for the superior model were calculated 0.001, 0.002 and 0.999, respectively. However, the maximum error value for this study was less than 2%.
A. R. Bahrebar, M. Heidarnejad, A. R. Masjedi, A. Bordbar,
Volume 25, Issue 2 (9-2021)
Abstract
The combination of a labyrinth weir with an orifice is a proper solution for floating material to pass over the weir and transfer sediment through the orifice. Additionally, creating a slot in the overflow wing leads to higher discharge. This study examined four discharges (5, 10, 15, and 20 liters per second) with channel width and height of 30 and 40 cm in trapezoidal-orifice, square-orifice, and triangular-orifice labyrinth weirs in the laboratory and using Flow3D with RNG k-epsilon (k-ε) turbulence model, the results were compared with one another. Comparing the discharge flow over weirs and measuring the discharge coefficient among the mentioned models showed that the triangular-orifice labyrinth weir had the highest discharge rate. Moreover, the increased Ht/P ratio (Ht represents total hydraulic head; P denotes weir height) for all models resulted in the increased discharge coefficient. Due to the efficiency of this type of weirs, the highest discharge coefficient was obtained at low Ht/P ratios. At lower ratios, since there was free flow, the coefficient of weir discharge increased, and as the ratio increased, the weir was partially submerged. Furthermore, for the weir design, the best Ht/P ratio was between 0.13 to 0.41, and the maximum discharge coefficient (Cd = 1.2) was within this range.
J. Meshkavati Toroujeni, A.a. Dehghani, A. ٍemadi, M. Masoudian,
Volume 25, Issue 3 (12-2021)
Abstract
One of the crucial problems that exist in the irrigation networks is the fluctuation of the water surface flow in the main channel and changes in the flow rate of the intake structure. One of the effective methods to decrease these fluctuations is increasing the weir crest length at the given width of the channel with the use of the labyrinth weirs can be achieved for this purpose. The labyrinth weir is the same linear weir that is seen as broken in the plan view. In this study, a labyrinth weir with a length of 3.72 m, three different heights of 15, 17, and 20 cm, three different shapes of dentate (rectangular, triangular, and trapezoidal), and a linear weir were used in a recirculating flume with 15 m length and 1 m width. The result showed that for a given length and height of weir, with the increasing of the upstream water head to the weir height ratio (
), the discharge coefficient decreases. The results showed that by increasing weir height, the discharge coefficient decreases for a given length of the weir. Linear weir and labyrinth weir without dentate create more water depth at the upstream by 3.3 and 1.2 fold compared with dentate labyrinth weir.
H. Elahifar, O. Tayari, N. Yazdanpanah, M. Momeni,
Volume 25, Issue 4 (12-2021)
Abstract
The discharge coefficient of labyrinth weirs increases with increasing the crest length in a certain width range. The present research was carried out in a laboratory flume with a length of 8 m, a width of 0.6 m, and a height of 0.6 m. The discharge coefficient of two-cycle symmetric and asymmetric rectangular labyrinth weirs was experimentally measured. The dimensional analysis by the Buckingham π theorem indicated that the discharge coefficient was dependent on Se, B/Wavg, Ht/P, and WL/WR. According to the results, the discharge coefficient decreased with increasing the hydraulic head in the symmetric and asymmetric labyrinth weirs and the linear weir. Asymmetric labyrinth weirs with a WL/WR of 2.05 outperformed symmetric labyrinth weirs with a WL/WR of 1. Quantitatively, the discharge coefficient of the labyrinth weir with a B/Wavg of 3.1 was respectively 21% and 94% higher than that with a B/Wavg of 2.93 and 2.76. The discharge coefficient of the labyrinth weir with a WL/WR of 2.05 was 10-27% higher than that with a WL/WR of 1. The discharge coefficient of the linear weir was 60-250% higher than that of labyrinth weirs.
A.h. Azimi, S Shabanlou, F. Yosefvand, A. Rajabi, B. Yaghoubi,
Volume 25, Issue 4 (12-2021)
Abstract
In this research, the scour hole depth at the downstream of cross-vane structures with different shapes (i.e., J, I, U, and W) was simulated utilizing a modern artificial intelligence method entitled "Outlier Robust Extreme Learning Machine (ORELM)". The observational data were divided into two groups: training (70%) and test (30%). Then, using the input parameters including the ratio of the structure length to the channel width (b/B), the densimetric Froude number (Fd), the ratio of the difference between the downstream and upstream depths to the structure height (Δy/hst), and the structure shape factor (φ), eleven different ORELM models were developed for estimating the scour depth. Subsequently, the superior model and also the most effective input parameters were identified through the conduction of uncertainty analysis. The superior model simulated the scour values by the dimensionless parameters b/B, Fd, Δy/hst. For this model, the values of the correlation coefficient (R), the variance accounted for (VAF), and the Nash-Sutcliffe efficiency (NSC) for the superior model in the test mode were obtained 0.956, 91.378, and 0.908, respectively. Also, the dimensionless parameters b/B and Δy/hst were detected as the most effective input parameters. Furthermore, the results of the superior model were compared with the extreme learning machine model and it was concluded that the ORELM model was more accurate. Moreover, an uncertainty analysis exhibited that the ORELM model had an overestimated performance. Besides, a partial derivative sensitivity analysis (PDSA) model was performed for the superior model.
M. Sabouri, A.r. Emadi, R. Fazloula,
Volume 26, Issue 2 (9-2022)
Abstract
A compound sharp-crested weir is often used to measure a wide range of flows with appropriate accuracy in open channels. In this study, experiments were performed to investigate the hydraulic flow through a compound weir of circular-rectangular with changes in hydraulic and geometric parameters in free and submerged flow conditions. The characteristics of the weirs include rectangular spans width of 39 cm, a circular radius of 5, 7.5, and 12.5 cm, and heights of 10 and 15 cm. The results showed that by increasing the radius and height of the Weir, upstream water depth increases around 28.4%. At a constant h/p, the discharge coefficient increases with the increasing radius of the circular arc. Also, in the submerged conditions, the discharge coefficient is less (around 40%) than in the free flow condition, which is due to the resistance of the depth of the created stream against the passage of the flow.
M. Majedi Asl, R. Daneshfaraz, J. Chabokpour, B. Ghorbani,
Volume 26, Issue 2 (9-2022)
Abstract
In the last decade, the use of gabion structures in hydraulic engineering for stabilizing the structure due to its high density and weight has become widespread. Also, the material's roughness and porosity cause it to be used in energy dissipation and drainage projects. This study evaluates the relative energy dissipation of gabion structures downstream of the ogee spillway in the conditions of a submerged hydraulic jump. The evaluated parameters in this study were Froude number, gabion height, gabion thickness, and material diameter. The experiments were performed with three average diameters of 1.5, 2.2, and 3 cm for rock material, three gabion heights of 10 and 20 cm, and Max. The end sill heights were 10, 20, and 30 cm. The operated discharges were regulated from 20 to 40 l/s. The results showed that by decreasing the average diameter of gabion aggregates, the amount of relative energy dissipation increases in all tested models, so that in gabion with a 1.5 cm average diameter of aggregates, the amount of energy dissipation increased by 3.6% in comparison with using the diameter of 3cm for the average diameter of the material. Increasing the height of the gabion to the extent that the flow is entirely inward can have up to 33% more relative energy dissipation than the gabion with a height of 10 cm. Also, by increasing the diameter of the gabion from 10 cm to 30 cm, relative energy dissipation increases up to 15%.
M. Sadeghi, T.o. Naeeni, F. Kilanehei, M. Galoie,
Volume 26, Issue 3 (12-2022)
Abstract
One of the most important hydraulic structures in a dam is the spillway. The design of the ogee spillway crest is based on the lower profile of the free-flow jet passing through the sharp-crested weir. When the downstream ogee spillway profile for the design discharge conforms to the lower profile of the free-jet passing through the sharp-crested weir, the pressure on that surface of the spillway becomes zero. In this study, the design of the ogee spillway was performed initially based on both two- and three-dimensional numerical modeling and then compared to the USBR standard method. The comparison of the final numerical and analytical results showed that although the vertical two-dimensional outputs were completely in agreement with the USBR standard profile, the three-dimensional profiles were different because in this model, guide walls were not considered. According to the analysis, if the flow entering the spillway is parallel to its axis, the lower profile of the sharp-edge spillway will be in complete agreement with the standard profile. Since, the design of guide wall geometry for ogee spillways is carried out using physical modeling which iteratively revises during a high-cost trial and error procedure, this research based on the case study of the spillway of Karun-3 dam has been tried using numerical modeling. The closest geometry to the geometry of the overflow guide wall was obtained which creates the least difference in transverse velocities. In this way, the design of guide walls can be done with more accuracy and low cost in comparison to physical modeling.
H. Noury Hasanabady, M.r. Kavianpour, A. Khosrojerdi, H. Babazadeh,
Volume 26, Issue 3 (12-2022)
Abstract
Using a rough bed for spillway compare to common dissipation methods such as stilling basins, stepped spillways, ski jumps, and bed elements may be more efficient to boost energy dissipation. In this research, the impact of spillway continuous bed roughness on energy dissipation was investigated. For this purpose, a non-dimensional relationship was developed, and by calibrating the numerical model based on the present experimental study, energy dissipation over the spillway for three slopes of 15, 22.5, and 30 (degree) with six roughness sizes of 0.0, 0.005, 0.0072, 0.0111, 0.016, and 0.022 (m) and three discharges of 170, 110, and 90 (lit/s) was investigated. Based on the present results, using a rough bed spillway will increase energy dissipation. Also, the ratio of energy lost per meter length of rough bed spillway to that of smooth spillway increases by chute slope. The results showed that the highest amount of relative energy consumption in the presence of roughness was related to the slope of 22.5 degrees and 22.2 mm for roughness (85%), and the lowest relative energy consumption was observed in the control state (25%). As a result of the present study, a natural rough bed without concrete coating has befitted in terms of environmental aspects, construction cost, and energy loss.
M. Majedi Asl, T. Omidpour Alavian, M. Kouhdaragh, V. Shamsi,
Volume 27, Issue 3 (12-2023)
Abstract
Non-linear weirs meanwhile economic advantages, have more passing flow capacity than linear weirs. These weirs have higher discharge efficiency with less free height upstream compared to linear weirs by increasing the length of the crown at a certain width. Intelligent algorithms have found a valuable place among researchers due to their great ability to discover complex and hidden relationships between effective independent parameters and dependent parameters, as well as saving money and time. In this research, the performance of support vector machine (SVM) and gene expression programming algorithm (GEP) in predicting the discharge coefficient of arched non-linear weirs was investigated using 243 laboratory data series for the first scenario and 247 laboratory data series for the second scenario. The geometric and hydraulic parameters were used in this research including the water load (HT), weir height (P), total water load ratio (HT/p), arc cycle angle (Ɵ), cycle wall angle (α), and discharge coefficient (Cd). The results of artificial intelligence showed that the combination of parameters (Cd, H_T/p, α, Ɵ) respectively in GEP and SVM algorithms in the training phase related to the first scenario (Labyrinth weir with cycle wall angle 6 degrees) were respectively equal to (R2=0.9811), (RMSE=0.02120), (DC=0.9807), and (R2=0.9896), (RMSE=0.0189), (DC=0.9871) in the second scenario (Labyrinth weir with a cycle wall angle of 12 degrees) it was equal to (R2=0.9770), (RMSE=0.0193), (RMSE=0.9768), and (R2 = 0.9908), (RMSE = 0.0128), (DC = 0.9905), which compared to other combinations has led to the most optimal output that shows the very favorable accuracy of both algorithms in predicting the coefficient the Weir discharge is arched non-linear. The results of the sensitivity analysis indicated that the effective parameter in determining the discharge coefficient of the arched non-linear Weir in GEP and in SVM is the total water load ratio parameter (HT/p). Comparing the results of this research with other researchers revealed that the evaluation indices for GEP and SVM algorithms of this research had better estimates than other researchers.
M. Dorfeshan, A.r. Masjedi, M. Heidarnejad, A. Bordbar,
Volume 27, Issue 3 (12-2023)
Abstract
Piano key overflows have a high discharge capacity. Proper design of these overflows requires sufficient accuracy in predicting the type of overflows. In this study, experiments were performed in a rectangular laboratory flume made of Plexiglas to investigate the effect of the relative length and width of the two-cycle piano switch overflow crest on the discharge coefficient. In present research, the flow intensity coefficient was investigated by installing a rectangular piano switch overflow with relative crest lengths of 0.8, 1, and 1.2 and relative crest widths of 0.2, 0.3, and 0.4 in 10 flow intensities in the channel. The results of this study showed that by increasing hydraulic load, the flow intensity coefficient first increases and then decreases. Also, by increasing the relative length of the crest by 50%, the current intensity coefficient increases by 43% in the overflow. Increasing the relative width of the overflow crest by 50% increases the current intensity coefficient by 25% in the overflows. Also, an equation was presented to determine the maximum relative scour depth, and the correlation coefficient of the results of this equation with the laboratory results is about 0.90.
S. Barani, M. Zeinivand, M. Ghomeshi,
Volume 27, Issue 4 (12-2023)
Abstract
In this study the effect of orifice number and dimensions in combined structure sharp crested rectangular weir with multiple square orifice was investigated. For this propose, some experiments in different flow rate, different orifice number and dimensions were done. The results showed that by different orifice numbers and dimensions, flow discharge increased at the same upstream flow head. This increasing trend was observed in all numbers and dimensions of the investigated experiments. The analysis of the quantitative results showed that by increasing the number of orifices, the discharge rate through the combined structure of weir-orifice was increased on average 2.06 liters per second and by increasing each centimeter of orifice dimensions, the discharge was increased by 2.82 liters per second. Also by calculating the percentage of flow rate increase, it was observed that by adding the orifice number, it increases by 18.7% and by increasing the size of the orifice by one centimeter, the flow rate increases by 28.1%.
M. Majedi Asl, T. Omidpour Alavian3, M. Kouhdaragh,
Volume 27, Issue 4 (12-2023)
Abstract
Weirs of the labyrinth have some advantages including the high coefficient of the irrigation of weir and the low fluctuation of water when the flow passes over the crest of the weir. In this research, the flow rate coefficient has been investigated by changing the weir geometry in terms of wall slope, arc cycle angle, and nose length change in the upstream and downstream of each cycle of the trapezoidal arc labyrinth weir. A total of 240 tests have been performed on 16 different physical models in a channel with a width of 120 cm and a narrowing of 20 cm from each wall. All models have been compared with the control model (normal labyrinth weir) (80A). The results showed that the 80B weir with an arc cycle angle of 20 degrees and without wall slope has a better performance than other weirs. Also, the weir with an arc cycle angle and a wall slope of 20 degrees in a divergent form (D20B) in the area (Ht/P) <0.31 has a better performance than other weirs with an arc cycle angle of 20 degrees, and after this area, the weir with a wall slope of 10 degrees has performed better in divergent form (D10B). In weirs with different cycles at an arc cycle angle of 20 degrees, the labyrinth weir with 5 cycles (N5) has performed better up to the point (Ht/P)=0.36. Also, at the maximum point, the difference is 13 and 17%, respectively, compared to the 4-cycle and 3-cycle weirs.
R. Sargholi, A. Bordbar, A. Asareh, M. Heidarnejad,
Volume 28, Issue 1 (5-2024)
Abstract
In the past, various methods have been proposed to control beach heel scouring. For shallow rivers (such as mountain rivers), various types of overflows are used. Therefore, the development of scour in cross-vane and w-weir structures for coastal protection was investigated in this study. The results showed that by installing a w-weir structure in a 90-degree position compared to a 30 and 60-degree position, a 37.9% and 19.7% reduction of scouring was observed, respectively. Also, by installing the cross vane structure in the 90-degree position compared to the 30 and 60-degree position, a 35.4% and 21.2% reduction of scouring was observed, respectively. With increasing width (L / B) (ratio of the width of structure to the width of flume), the w-weir structure decreased from 1.5 to 2, scour rate of 7.9%. Also, with increasing width (L / B) (ratio of the width of structure to the width of flume), the cross-vane structure has decreased from 1.3 to 1.7, and the scour rate has decreased by 4.7%. The w-weir structure had an average of 7.3% less scouring than the cross-vane structure.
Y. Neamah Abdulhasan, A. Khoshfetrat,
Volume 28, Issue 3 (10-2024)
Abstract
Piano key weirs are a type of non-linear weir that have a higher discharge coefficient than similar linear weirs. These hydraulic structures have a lightweight foundation and a simple structure is designed and installed on dams and drainage channels. Due to the high efficiency of these weirs, the investigation of downstream scour and ways to reduce it has been the focus of engineers in recent years. In the present study, a trapezoidal type C piano key weir, three discharges, and three tailwater depths were used. Two obstacles with heights of 0.02 and 0.04 meters were also used at the end of the weir exit keys. The results showed that the presence of an obstacle reduces scour at the toe of the weir. The amount of reduction in scour at the toe of the weir was greater in the weir with a larger obstacle height than in the weir with a smaller obstacle height, and in both cases was less than in the simple weir. The presence of an obstacle reduces the maximum depth of scour and moves the distance of the maximum depth of scour away from the toe of the weir. In the weir with obstacle heights of 0.02 and 0.04 meters, compared to the weir without an obstacle, the amount of maximum scour depth is approximately 16.4% and 26.9% less, and the distance of the maximum scour depth is approximately 8.7% and 19.1% more than the weir without an obstacle. The scour index in weirs with obstacles is less than in weirs without obstacles, which can reduce the risk of weir overturning. The lowest value of the scour index was observed in the weir with an obstacle height of 0.04 meters, which is approximately 41.2% less than the weir without an obstacle.
M. Neisi, M. Sajadi, M. Shafai Bejestan, J. Ahadiyan,
Volume 28, Issue 3 (10-2024)
Abstract
Side weirs are hydraulic structures employed in irrigation and drainage channels as diversion devices or head regulators. The increasing efficiency of the structure of side weirs for constant head has been one of the concerns of researchers in the last decade. The use of different forms of sharp crest, labyrinth, piano key, and increasing the length of the overflow by changing the geometry of the crest have been investigated. In this research, a new type of triangular-shaped side weir has been studied in the laboratory under different hydraulic conditions in sub-critical flow conditions. The results demonstrated that by inclining the crests of the triangular side weir, the amount of vortex created at the entrance of the opening was reduced. So the discharge coefficient and the flow volume over the side weir showed an increase of up to 27% and 48%, respectively, compared to the normal triangular and rectangular side weirs. Also, after analyzing the data, a non-linear equation was presented to estimate the discharge coefficient with the dimensionless parameters of the ratio of the upstream depth to the weir height (y1/p) and the upstream Froud number (Fr1) with an accuracy of ±15% and NRMSE=0.134.
M. Niroubakhsh, A.r. Masjedi, M. Heidarnejad, A. Bordbar,
Volume 28, Issue 4 (12-2024)
Abstract
The application of flip bucket and triangular launchers with different shapes has been given more attention due to safety and better energy consumption to protect the downstream bed of water structures, as well as economic benefits compared to other energy consumers. The objective of this research was to investigate the energy loss of the passing flow in the dentated flip bucket and dentated triangular sill spillways in laboratory and numerical conditions. Physical and numerical modeling was used in a rectangular flume with a length of 9 meters, a width of 0.5 meters, and a height of 0.5 meters, flip bucket, and triangular spillways with dentated with specific dimensions according to the USBR standard in different discharges intensities in laboratory and numerical conditions. The amount of energy loss in the dentated flip bucket spillway was 71.4% and the dentated triangular sill spillway was 74.8% in laboratory conditions, which showed that the dentated triangular sill spillway has a better performance in terms of energy loss than the flip bucket and triangular spillway. The results showed that the shape of the spillway geometry and the presence of the dentated at the end of the structure is an important and influential factor in the amount of energy loss of the currents passing through the dentated flip bucket and dentated triangular sill spillways, which causes more broken and compressed flow lines and, as a result, an increase in speed at the moment. The launch and finally the relative loss of energy is more downstream of the structure. After determining the better performance of the dentated triangular sill spillway in energy loss, the numerical simulation of the dentated triangular sill spillway was performed using the numerical calculation method in Flow-3D software. The results of the analyses indicated that the amount of energy loss in the dentated triangular sill spillway in the numerical calculations was 87.5%, which showed the alignment and correctness of the tests performed with the laboratory conditions.
R. Daneshfaraz, M. Majedi Asl, T. Omidpour Alavian,
Volume 29, Issue 1 (4-2025)
Abstract
Weirs play a crucial role in flood management and dam safety, accounting for a significant portion of the construction costs of dams. The selection of floods with long return periods for flood design is of utmost importance. However, in some cases, increasing the weir capacity by widening it may be impossible due to topographical limitations. One solution to enhance the flow capacity of weirs is the application of labyrinth weirs. These weirs increase the effective length of the weir crest within a given width, allowing for the passage of higher flow rates while maintaining similar hydraulic conditions. In this study, the hydraulic performance of labyrinth weirs is investigated using the Flow3D numerical model and laboratory data. Since laboratory experiments are time-consuming and costly, employing numerical simulations to achieve more accurate and reliable results for evaluating the hydraulic behavior of labyrinth weirs is prioritized. The results of the simulations indicate that the Flow3D software, utilizing statistical parameters such as R², DC, and RMSE, achieves values of (0.9805, 0.9725, and 0.0142), respectively. This demonstrates its capability to model the flow passing through weirs with high accuracy. The obtained values of the discharge coefficient in Flow3D show a high agreement with the laboratory data from Crookston. The approximate alignment of these results indicates the high accuracy of the numerical model. Additionally, in comparison to different discharges, the relative computational error observed for flow rates of 0.35, 0.6, and 0.44 (cubic meters per second) was approximately 0.5 percent, while for flow rates of 0.3, 0.4, and 0.57, the corresponding errors were 8, 6, and 4 percent, respectively. The results indicate that these tools can be effectively utilized in precise hydraulic analyses and the optimization of weir designs, irrigation systems, and fluid dynamics phenomena.
