A new approach for oblique weir discharge coefficient prediction based on hybrid inclusive multiple model

One type of long-crested weir is oblique weir. Oblique weirs are longer than standard weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. The main objective of the present study was to investigate the efficacy of several intelligent models including multiple linear regression (MLR), Gaussian process regression (GPR), artificial neural network (ANN) and multiple models driven by ANN (MM-ANN) methods in estimating oblique weir discharge coefficient (C_d). Different input combinations were predicted using the variables of H/P, P/L_e, and W/L_e and the output coefficient of discharge. Prediction models were analyzed by statistical index, including root mean square error (RMSE), correlation coefficient (R), error percentage chart, relative error (RE%) plot, Kling-Gupta efficiency (KGE), probability density function (PDF) plot, scatter plot, scatter plot of error residuals and Taylor's diagram. Obtained results showed that the ANN model performed best by combining the inputs of the three variables (i.e., H/P, P/L_e, and W/L_e) with R = 0.746 and RMSE = 0.065 among the standalone models. Eventually, the proposed hybrid model MM-ANN was most accurate in estimating the oblique weir C_d by improving the prediction results of the implemented models.     

Investigation of flow characteristics and energy dissipation over new shape of the trapezoidal labyrinth weirs

Labyrinth weirs are mainly used to increase the discharge capacity. The current study adds a new performance to labyrinth weirs as an energy dissipator. The labyrinth weirs' zigzag shape and flow behaviour could benefit energy dissipation. Therefore, the present study aims to investigate the hydraulic characteristics and energy dissipation of the compound labyrinth weir. Sixteen models were used for different sidewall angles (α°) of 6–35 and 90 (linear weir for comparison). The results demonstrated the highest values of the compound coefficient of discharge, C_dc, for a sidewall angle of 35°, and the lowest value of the compound coefficient of discharge for a sidewall angle of 6°. The C_dc increased initially at low H՛_t/P՛ values, and the C_dc showed a decreasing trend for higher values of H՛_t/P՛. For sidewall angles (α°) ranging from 6 to 35, the compound coefficient of discharge C_dc does not significantly change as it approaches a value of H՛_t/P՛ = 1.0. Furthermore, for the range of the relative critical head (y_c/P՛) between 0.07 and 0.95, the results showed that the compound labyrinth weirs could dissipate the energy of flow by 93%, 92%, 89%, 85%, 83%, 79%, and 75% for α° = 6, 8, 10, 12, 15, 20°, and 35, respectively. The amount of improvement in energy dissipation over a compound labyrinth weir was better than a linear weir by 17%, 15%, 14%, 12%, 11%, 10%, and 8% for α° = 6, 8, 10, 12, 15, 20, and 35, respectively. The residual energy (E₁/E_min) at the base of downstream compound labyrinth weirs was closer to the minimum potential amount of residual energy as y_c/P՛ increased. For a given value of y_c/P՛, the relative residual energy at the base of compound labyrinth weirs increased as the sidewall angle (α) increased. An empirical equation has been provided to predict the compound coefficient of discharge when relative energy dissipation data is available.     

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

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

Effect of carbide volume fraction on erosive wear behaviour of hardfacing cast irons

The present work reports the effect of carbide volume fraction on erosive wear behaviour of hardfacing cast irons. Five different grades of weld hardfacing cast irons were selected for the present investigation. The solid particle erosion experiments were carried out with blast furnace sinter, silica sand and alumina particles under mild (53–75 μm, 25 m s⁻¹), moderately severe (125–150 μm/100–150 μm, 50 m s⁻¹) and under severe erosion conditions (300–425 μm, 90 m s⁻¹) at impingement angles of 30 and 90°. The variation in erosion rate with carbide volume fraction was observed to be strong function of the erodent particle hardness, impingement angle and the impact velocity. Under mild erosion conditions, erosion rate decreased with increasing carbide volume fraction (CVF), whereas erosion rate increased with CVF under moderately severe erosion condition with alumina particles. With silica sand particles under moderately severe erosion conditions the beneficial effect of large volume fraction of carbides could only be observed at 30°, whereas at normal impact erosion rate increased with increasing CVF. The erosion rate showed power law relationship with ratio of hardness of erodent particle to that of the target material (H_e/H_t) and expressed as E=c(H_e/H_t)^p.With increasing severity of erosion conditions erosion rate showed stronger dependence on H_e/H_t as compared to those under mild and moderately severe erosion conditions. The mechanism of materials removal from the carbides involved Hertzian fracture with softer sinter particles, whereas harder alumina particles could plastically indent and cause gross fracture of the carbides.     

Studying the relationship between the hydraulic and geometry characteristics of labyrinth weirs based on the historical memory of reported data

One of the effective ways to increase the efficiency of weirs is to use nonlinear weirs, such as labyrinth weir, which increases the flow capacity by increasing the length of the weir at a fixed width. Given the importance of precisely estimating the flow discharge coefficient of this type of weir and its impact on supplying the safety of water structures, in the present study, the flow coefficient of labyrinth weirs was estimated using data-driven models of Extreme Learning Machine (ELM), Classification And Regression Tree (CART), Chi-square Automatic Interaction Detector (CHAID), and Multiple Linear Regression (MLR). After the modeling process, the predicted results were compared with the observed values using statistical measures and diagnostic analysis. In this study, three input combinations of hydraulic parameters, including the total upstream hydraulic head of weir (H_T), weir discharge (Q), and head to weir height (H_T/P) were used as input vectors. In order to evaluate the accuracy of the models, the statistical indicators of Coefficient of Efficiency (CE), RMSE, MDE, and RSD were employed. The final results showed that the ELM method created with all potential input parameters (H_T, Q, and H_T/P) was highly accurate in determining flow discharge coefficient. Due to having the lowest error (CE = 0.8815, RMSE = 0.0370), it was selected as the superior model.     

Synthesis of multiple degrees-of-freedom spatial-motion compliant parallel mechanisms with desired stiffness and dynamics characteristics

This paper presents a new design method to synthesize multiple degrees-of-freedom (DOF) spatial-motion compliant parallel mechanisms (CPMs). Termed as the beam-based structural optimization approach, a novel curved-and-twisted (C-T) beam configuration is used as the basic design module to optimize the design parameters of the CPMs so as to achieve the targeted stiffness and dynamic characteristics. To derive well-defined fitness (objective) functions for the optimization algorithm, a new analytical approach is introduced to normalize the differences in the units, e.g., N/m or N m/rad, etc., for every component within the stiffness matrix. To evaluate the effectiveness of this design method, it was used to synthesize a 3-DOF spatial-motion (θ_x − θ_y − Z) CPM that delivers an optimized stiffness characteristics with a desired natural frequency of 100 Hz. A working prototype was developed and the experimental investigations show that the synthesized 3-DOF CPM can achieved a large workspace of 8°×8°×5.5 mm, high stiffness ratios, i.e., >200 for non-actuating over actuating stiffness, and a measured natural frequency of 84.4 Hz.     

Flow velocity pattern around trapezoidal piano key side weirs

In general, the side weirs are the structures installed along a channel or river. When the flow depth rises above the weir crest, the overflow passes through these weirs and enters the lateral canal. Nowadays, piano key weirs are considered as an important alternative to labyrinth weirs to modify the weirs encountering with difficulty to pass the maximum flow discharges. The present study investigates the hydrodynamic performance and the effect of the uniformity of velocity field on the resultant kinetic energy in the trapezoidal piano key side weirs with 90° installed laterally in the main channel wall. These weirs are classified as A-Type piano key weirs and two approaches (main: Mode 1 and adverse: Mode 2) were used to investigate the effect of the weirs' placement on their performance. The results showed that for velocity vectors in both modes, on average, the maximum flow discharge through the side weir occurred in the x and y directions (V_x and V_y) at Z*<0.2 and 0.2<Y*<0.7. The results also showed that at the control surface of X* = 1, the maximum values of α occur due to existing the inverse flow and increasing the deflection angle of the velocity vectors. The performance of the weir in Mode 2 was more appropriate Mode 1 due to the lack of weir base at the flow inlet, which is an obstacle for the deflection angle of the velocity vectors.     

Investigate on milling force of cryogenic cooling processing aluminum honeycomb treated by ice fixation

Aerospace metal honeycomb materials with low stiffness had often the deformation, burr, collapse, and other defects in the mechanical processing. They were attributed to poor fixation method and inapposite cutting force. This paper presented the improvement of fixation way. The hexagonal aluminum honeycomb core material was treated by ice fixation, and the NC milling machine was used for a series of cryogenic machining. Considering the similar structure of fiber-reinforced composite materials, the milling force prediction model of ice fixation aluminum honeycomb was established, considering tool geometry parameters and cutting parameters. Meanwhile, the influence rule on milling force was deduced. The results show that compared with the conventional fixation milling method, the honeycomb processing effect is improved greatly. The machining parameters affect order on milling forces: the cutting depth is the most important, followed by the cutting width, then the spindle speed and the feed. Moreover, too small cutting depth (a_p?=?0.5 mm) will cause insufficient cutting force, while a_p?>?2 mm with higher force will reduce the processing quality of honeycomb. Simultaneously, the honeycomb orientation (θ) has a great influence on processing quality. Using the model, the predicted and measured error values of the feed and main cutting force are all small in θ?<?90°. But, the rate is 33 and 26% for the main cutting force and feed force error in θ?>?90°, respectively, while they all exhibit the smallest error in θ?=?60°. This bigger error mainly is due to unstable cutting force with obtuse angle. In addition, the tool rake angle has little influence on cutting quality in θ?<?90°, but bigger on that in θ?>?90°. Furthermore, the calculation model successfully conforms to the main deformation mechanism and influences parameters of the cutting force in the milling process, and it can accurately predict the cutting force in θ?<?90° and guide the milling process.     

1-N-alkyl -3-methylimidazolium ionic liquids as neat lubricants and lubricant additives in steel–aluminium contacts

The influence of the alkyl chain length and of the anion on the lubricating ability has been studied for the room-temperature ionic liquids (IL) 1-n-alkyl-3-methylimidazolium X⁻ [X = PF₆; n = 6 (L-P106). X = BF₄; n = 2 (L102), 6 (L106), 8 (L108). X = CF₃SO₃; n = 2 (L-T102). X = (4-CH3C6H4SO3); n = 2 (L-To102)]. Neat IL have been used for AISI 52100 steel-ASTM 2011 aluminium contacts in pin-on-disk tests under variable sliding speed. While all IL give initial friction values lower than 0.15, real-time sharp friction increments related to tribochemical processes have been observed for L102 and L-P106, at room-temperature and at 100 °C. Electronic microscopy (SEM), energy dispersive (EDS) and X-ray photoelectron (XPS) spectroscopies show that wear scar surfaces are oxidized to Al₂O₃ and wear debris contain aluminium and iron (for L102) fluorides. For L-P106, the steel surface is covered with a P-containing tribolayer. A change of anion (L-T102; L-To102) reduces friction and wear, but the lowest values are obtained by increasing the alkyl chain length (L106; L108). When the more reactive L102 and L-P106 are used as 1 wt.% base oil additives at 25 °C, tribocorrosion processes are not observed and a friction reduction (69–75% for 1 wt.% L102) and a change from severe (10⁻³ mm³ m⁻¹) to mild wear (10⁻⁴ to 10⁻⁶ mm³ m⁻¹) is obtained with respect to the neat IL. 1 wt.% IL additives also show good lubricating performance at 100 °C.     

Investigation on solid particle erosion behaviour of polyetherimide and its composites

The present investigation reports about, the solid particle erosion behaviour of randomly oriented short E-glass, carbon fibre and solid lubricants (PTFE, graphite, MoS₂) filled polyetherimide (PEI) composites. The erosion rates (ERs) of these composites have been evaluated at different impingement angles (15–90°) and impact velocities (30–88 m/s). Mechanical properties such as tensile strength (S), ultimate elongation to fracture (e), hardness (H_V), Izod impact strength (I) and shear strength (S_s) seems to be controlling the erosion rate of PEI and its composites. Polyetherimide and its glass, carbon fibre reinforced composites showed semi-ductile erosion behaviour with peak erosion rate at 60° impingement angle. However, glass fibre reinforced PEI composite filled with solid lubricants showed peak erosion rate at 60° impingement angle for impact velocities of 30 and 88 m/s, whereas for intermediate velocities (52 and 60 m/s) peak erosion rate observed at 30° impingement angle. It is observed that 20% (w/w) glass fibre reinforcement helps in improving erosive wear resistance of neat PEI matrix. Erosion efficiency (η) values (0.23–8.2%) indicate micro-ploughing and micro-cutting dominant wear mechanisms. The morphology of eroded surfaces was examined by using scanning electron microscopy (SEM). Possible erosion mechanisms are discussed.     

Experimental study of discharge coefficient of trapezoidal arced labyrinth weirs of widened middle cycle

Arced labyrinth weir is a certain type of nonlinear weirs with a very high discharge capacity. Thanks to the increased effective length and the ensuing increased discharge capacity of these weirs, they can be used in dam spillways and water regulating structures. This study focused on trapezoidal Arced labyrinth weirs (TALW) of widened middle cycle. Various experiments were performed to evaluate the effect on discharge coefficient of various geometric parameters, including the ratio of inside apex width of the end cycles to that of the middle cycle (w₂/w₁) and the ratio of the length of labyrinth weir (Apron) in flow direction to the width of the middle cycle (B/w₁). Results of this study showed that with a decrease in w₂/w₁ from 0.42 to 0.30, discharge coefficient (C_d) would increase by 13–33%.     

Effect of the inlet-to-outlet key width ratio of Piano Key Weir on its hydraulic behaviour

The Piano Key Weir (PKW) is an ungated type of spillway, i.e., a novel evolution over the traditional labyrinth weir. It allows the reservoirs to operate with elevated supply levels without causing any damage to the dam structures, thereby providing additional storage. It is designed to improve the hydraulic performance of linear weirs by increasing pass discharge and energy dissipation. In this study, an experimental investigation has been carried out to assess the effect of the inlet-to-outlet width ratio (W_i/W_o) on PKW hydraulic behaviours viz hydraulic efficiency and energy dissipation. To this end, nine different width proportions (1 ≤ W_i/W_o ≤ 2) type-A PKW models were tested and examined. The findings revealed that the W_i/W_o ratio significantly impacts the hydraulic performance of PKW, and the results indicate that the efficiency of the PKW increases as the width ratio increases at a certain limit and then starts decreasing. The discharge coefficient was the highest for the given discharge and head, resulting in the best hydraulic performance with a W_i/W_o ratio between 1.25 and 1.30. However, the energy dissipation across the PKW decreases as the width ratio increases. Moreover, the discharge coefficient of different width ratios (W_i/W_o) ranging between 1.28 and 1.30 is 7–17% higher than W_i/W_o = 1 and 8–13% higher than W_i/W_o = 2.0. However, the energy dissipation across the weir for W_i/W_o = 2.0 indicates 15–29% less energy dissipation than W_i/W_o = 1. It means the energy dissipation across the weir decreases as the W_i/W_o ratio increases.     

Discharge coefficient in the combined weir-gate structure

The present study investigated the flow discharge coefficient (C_dt) in the combined rectangular broad crested weir-gate structure. To this end, the effect of the following dimensionless parameters on the C_dt were investigated: the width ratio of the central weir to the width of the total structure (B/B_o), the height ratio of the central weir to the height of the central weir floor (Z/P), the ratio of the gate width to the width of the total structure (b/B_o), the ratio of the gate opening height to the height of the central weir floor (d/P), and the ratio of the head on central weir to the total head behind the structure (h₁/H). The Flow-3D numerical model, artificial intelligence models such as linear multilayer perceptron (MLP), Canfis network (CNN), recurrent network (RNN), modular neural network (MNN), and regression equation, were used to estimate the C_dt. The results indicated that increasing d/P and b/B_o ratios led to a decline in this coefficient. In the case of h₁/H ≤ 0.4, an increase in B/B_o ratio resulted in decreasing the turbulence intensity and C_dt while the impact of enhancing the size of B/B_o was not significant if h₁/H > 0.4. Besides, increasing Z/P ratio caused an increase in resistance against the flow and thus a decline in C_dt. Further, the results of artificial intelligence models and regression equation demonstrated that the MNN model with an RMSE and R² of 0.03 and 0.97, respectively, could have an accurate estimate of the C_dt values.     

Tribological Properties of Spark-Plasma-Sintered ZrO2(Y2O3)–Al2O3–Ba x Sr1?x SO4 (x?=?0.25, 0.5, 0.75) Composites at Elevated Temperature

Self-lubricating ZrO₂(Y₂O₃)–Al₂O₃–Ba _x Sr_1−x SO₄ (x = 0.25, 0.5, 0.75) composites have been fabricated by spark plasma sintering (SPS) method. The tribological properties have been evaluated using a high-temperature friction and wear tester at room temperature and 760 °C in dry sliding against alumina ball. The composites exhibit distinct improvements in effectively reducing friction and wear, as compared to the unmodified ZrO₂(Y₂O₃)–Al₂O₃ ceramics. The ZrO₂(Y₂O₃)–Al₂O₃–Ba _x Sr_1−x SO₄ (x = 0.25, 0.5, 0.75) composites have great low and stable friction coefficients of less than 0.15 and wear rates in the order of 10^− 6mm³/Nm at 760 °C. Delamination is considered as the dominating wear mechanism of the composites at room temperature. At elevated temperature, the formation and effective spreading of Ba _x Sr_1−x SO₄ (x = 0.25, 0.5, 0.75) lubricating films during sliding play an important role in the reduction of the friction and wear.     

A combined cold extrusion for a drive shaft: experimental assessment on dimensional compatibility

A combined cold extrusion process is experimentally visualized to manufacture a drive shaft. Due to the requirements of a face width of about 92.00 mm for the spur gear section and a groove depth of roughly 22.70 mm for the internal spline region, a preform is adopted to prevent excessive accumulation of plastic deformation. AISI 1035 medium carbon steel material is spheroidized and annealed to use as the initial billet workpiece. In order to verify the deformed configuration and the dimensional accuracy, both shoulder angles of (θ₁, θ₂) are selected to be (30°, 30°) and (45°, 45°) on each extrusion die for the preform forging and the combined extrusion. Using the prepared tool components, experimental investigations on the dimensional relevancy of the cold forged drive shaft are performed. When the shoulder angle set of (30°, 30°) is applied, the required dimensions with respect to the face width and the groove depth are sufficiently satisfied, but unpredictable forging defects are observed. With the shoulder angles of (45°, 45°), the drive shaft is well deformed and fabricated without any cold forging defects. As a result, it is confirmed that the drive shaft can successfully be actualized with the dimensional precision satisfied by the combined cold extrusion.

     

Discharge equation for the gabion weir under through flow condition

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

Structure and dynamics of the turbulent flow through a central baffle

Central baffle flume (CBF) can be utilized as a control structure to measure flow discharge in irrigation channels under free and submerged flow conditions. Stage-discharge relationship has been extensively studied for various geometrical parameters and flow conditions, whereas internal structure of the flow around a baffle has not been investigated in the literature. To address this need, the present work investigates the turbulent flow around a central baffle through high-resolution numerical simulations using an open source computational model. Velocity measurements were conducted in a laboratory flume to setup and validate the numerical model. Comparison of the numerical results with the experimental measurements proves that the present numerical model can predict water depth and velocity field. Longitudinal distance from the apex to the intersection point of water and critical depths can be estimated as L_xc = 2L_e, where L_e is the longitudinal length of the guide walls. A horseshoe vortex system identified in front of the baffle produces a significant bump on the free-surface and rib vortices generated from the baffle extend up to the sidewalls of the channel. The vertical separation layer observed downstream of the baffle results in a reverse flow and a vortex pair is formed by the impingement of the resulting reverse flow on the back of the baffle. Reverse flow, plunging flow structure, splash and rebounding wave events observed at the downstream produce substantial hydrodynamic effects on the baffle. Geometry of the central baffle was modified to suppress recirculation effects based on the insights into the complete flow structure around the baffle. Eventually, vortex structures were suppressed and the length of the recirculation zone was reduced by 76%.     

Accurate theoretical calculation of the discharge coefficient for sonic nozzle using geometric parameter measurements in Re=(7.33×104–1.26×106)

In order to improve the measurement accuracy and efficiency of sonic nozzles (SNs) in laminar boundary layer, a correlation model for theoretical discharge coefficient of sonic nozzle taking into account the viscous effects on the boundary layer along the nozzle wall (C_d,th,1), and the multi-dimensional characteristic effect of the core region (C_d,th,2) was proposed. The theoretical discharge coefficient is related to the measurement of geometric parameters, such as the throat diameter, d, and curvature radius, R_c. The detailed geometric measurements of sonic nozzle by 3D coordinate measuring machine were conducted. Then, the evaluation procedures of parameters d and R_c including roundness and waviness profile for designed SNs of d = 7.453 mm and d = 1.919 mm were presented in detail. The effect of waviness profile on the discharge coefficient and boundary layer transient was investigated. It indicated that waviness effect is quite complex. Finally, the validation of the theoretical calculation model of discharge coefficient was verified by the experimental data of National Institute of Metrology (NIM) and National Metrology Institute of Japan (NMIJ) based on the accurate measurements of the geometric parameters. The result showed that the consistency between the C_d,exp and the C_d,th is better than 0.11% when the effect of the heat transfer was considered within the range of Re= (7.33 × 10⁴–1.26 × 10⁶).     

Pressure measurement technique and installation effects on the performance of wafer cone design

The present study explores novel pressure averaging technique for wafer cone flowmeter design and its robustness in the presence of double 90° bend (out-of-plane) and gate valve as a source of upstream flow disturbance. The wafer cone flowmeter is tested in a circular pipe (inside diameter of 101 mm) with water as the working medium for the flow Reynolds number ranging from 1.19×10⁵ to 5.82×10⁵. Influence of the half cone angle (α) on the coefficient of discharge (C_d) of wafer cone flowmeter is studied with this new pressure averaging technique. Half cone angles considered in this study are 30° and 45° with a constant constriction ratio (β) of 0.75. The upstream static pressure tap is located at 1D upstream of the wafer cone. The downstream pressure averaging technique comprises eight circumferential holes of diameter 2 mm on the maximum diameter step of the wafer cone. The pressure taps are communicated through the support strut which serves as a downstream static pressure tap. The disturbance causing elements are individually placed at 1.5D, 5.5D, 9.5D and 13.5D upstream to the wafer cone flowmeter. The wafer cone flowmeter is also tested with gate valve opening of 25%, 50% and 75% for all the arrangements considered. The 30° cone is found to be better than 45° cone for the range of Reynolds number covered in the present study. The results show that the 30° wafer cone flowmeter with novel downstream pressure averaging technique is insensitive to the swirl flow created by a double 90° bend (out-of-plane) and requires an upstream length of 9.5D with a gate valve as a source of flow disturbance.     

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

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