Aeration of square jets in an open channel: experimental analysis and modeling

ANFIS

adaptive neuro-fuzzy inference system

ANN

artificial neural network

b_depth

bubble penetration depth

CaCl₂

calcium chloride

CC

correlation coefficient

DO

dissolved oxygen

DO_d

dissolved oxygen concentration of downstream

DO_u

dissolved oxygen concentration of upstream

E₂₀

aeration efficiency

GEP

genetic expression programming

GP

Gaussian process

HR

cumulative hydraulic radius

cumulative hydraulic radius of each jet

J_L

jet length

J_pu/pr

jet pump pressure ratio

J_T

jet thickness

J_V

jet velocity

K_La₂₀

volumetric oxygen transfer rate

LS-SVM

least square support vector machine

MAE

mean absolute error

ML

machine learning

MLR

multiple linear regression

Na₂SO₃

Sodium sulfite

N_j

number of plunging jets

O₂

oxygen

OTC

oxygen transfer coefficient

OTE

oxygen transfer efficiency

P/V

jet power per unit volume

PUK

Pearson VII function kernel

Q

water discharge

RBF

radial basis kernel

RF

random forest

RMSE

root means square error

SRM

structural risk minimization

Std. dev.

standard deviation

SVM

support vector machine

SVR

support vector regression

T

water temperature

T_Nj

side length of the square

α

the angle of inclination of the open channel

θ

jet impact angle

Water resource concerns, such as reasoned usage pollution control, are acquiring the interest of scientists around the globe. Numerous sectors already require the use of biological methods to treat wastewater. Treating industrial effluents using aerobic biological methods results in quicker processes, eliminates unpleasant conditions, and yields clear effluents without odor and stability (Metcalf & Eddy 2003). There is much emphasis on water quality and maintaining water quality parameters in the earth's freshwater hydrosphere (rivers, lakes, and reservoirs). Dissolved oxygen (DO) concentration is among the most widely cited parameters. DO is often used as an indicator of the quality of the water used by humans or serving as a habitat for aquatic flora and fauna. Numerous organic, chemical, and biological processes that raise or lower local oxygen concentrations maintain it. Respiration by marine life, biodegradation of organic material, and other oxygen-consuming chemical reactions reduce DO concentration in the natural water. Photosynthesis by aquatic plant life can be a significant source of oxygen to a water body.

Similarly, aeration and other gas transfer activities are crucial in controlling untreated or wastewater pollution. In the aeration process through water jets, more extensive gas–liquid interfaces lead to air entrainment, which enhances the DO concentration in the water. This phenomenon proves effective in various industries, such as environmental sectors, where plunging liquid jets agitate the liquid pool's surface, enhancing the gas–liquid exchange. Two complementary processes commonly bring about air entrainment. The air boundary layer contracts due to contact strain at the intermittent point where air and water meet in the first mechanism.

On the other hand, the second phenomenon is the capture of air around a descending jet upon impact with a liquid pool (Qu et al. 2013; Hassan & Shabat 2023). The presence of air trapped on the water's surface leads to the formation of a sizable void resembling a cylinder at the lower part, which then gets compressed and gives rise to a bubbling column descending beneath the water's point of impact (Qu et al. 2011). The basis for aeration is the development of a sizable air–water interface in the liquid, which leads to the dissolution of O₂ in water from the air being transported by a peculiar speed discharge jet with the free liquid surface. The interaction of an ‘impinging water jet's plume’ of air bubbles with water in a quiescent pool to transfer oxygen mass is called oxygenation by ‘plunging jets’ (Chipongo & Khiadani 2017). The mechanism of plunging overfall jets at hydraulic structures, i.e., weirs (Baylar 2000; Baylar et al. 2001), drop shafts, cascades (Baylar & Emiroglu 2005; Emiroglu & Baylar 2006) as well as floatation in water and wastewater treatment (Deswal 2008), biological aerated filters, bubble floatation of minerals, plunging breakers, chemical mixing, cooling systems in power plants that generate high turbulence activity at the free surface, enhances air–water transfer (Banks et al. 1984). It was observed by Baylar et al. (2009) that self-aeration in stepped cascades is a vital process in water treatment, while Wei et al. (2016) reported that flow turbulence is a critical factor for the self-aeration development process. In addition, the constraint of buoyancy on air bubble diffusion into the chute bottom decreased as the chute slope increased, making the development process for bottom self-aeration more pronounced. Toombes & Chanson (2005) mentioned the design of a stepped cascade specifically for water treatment through reoxygenation.

Similarly, studies of local surface aeration in open channels in association with hydraulic structures such as weirs, spillways, gates, and hydraulic jumps indicate significant water quality improvement due to oxygen transfer (Avery 1976; Avery & Novak 1978; Gulliver & Rindels 1993; Kobus & Koschitzky 2018). Conventional hydraulic structures, including weirs, can be utilized to increase aeration. Still, flumes may enhance the aeration process in a mild or insignificant slope canal where the drop is impossible (Dursun 2016).

Sometimes, a natural gas exchange at the free surface is insufficient to offset the oxygen consumption caused by pollutants in water pollution abatement. Increasing the amount of oxygen transferred into the body of water requires local aeration. Local surface aeration processes in open channel flows mainly occur at hydraulic jumps, drop structures, and weirs, increasing the oxygen transfer by entrained air bubbles. As a result, the air entrainment and oxygen transfer properties are now crucial design parameters for many hydraulic structures. Furthermore, effective water resource management and wastewater treatment system design depend on the aeration process performed by water jets under the static head, which eliminates the cost of electrical energy and enhances the treatment efficiency capability of an open channel flow system.

One of the ways of wastewater treatment is screening, which removes large suspended contaminants from the waste stream to prevent scouring and damage to downstream structures. This procedure removes the larger suspended and floating objects, such as fibers, paper, rags, string, and other materials. The geometry of the holes in a screen can be different; however, they are often rectangular or round. At the entrance of the hydraulic section, e.g., trenches, barrages, water intakes, and pumping stations, trash screens are commonly employed to capture flowing waste that could cause issues downstream. Screens are used in open channels to ensure the removal of coarse pollutants. Screens were first introduced as energy dissipators in the research conducted by Rajaratnam & Hurtig (2000). Their research shows that screens help stabilize the location of hydraulic jumps and dissipate more energy than free hydraulic jumps. Numerous other studies that followed examined the impact of various factors, including porosity and screen location (Rajaratnam & Hurtig 2000), screen location and thickness (Çakır 2003), the effects of sloping screens (Bozkus et al. 2007), different types of hydraulic jumps (Sadeghfam et al. 2015), and the combination of screens with baffle-like structures (Daneshfaraz et al. 2017). Despite all these applications, the utility of screens and their geometry with input parameters such as tilt angle, discharge, number of jets, cumulative hydraulic radius, and Froude number to increase DO concentration in an open channel has created a considerable gap in measuring the aeration efficiency (E₂₀), and the impact of such input parameters on E₂₀ requires detailed investigations.

During the literature review, it was found that the experimental work takes a lot of time, cost, and energy to assess E₂₀ with various input parameters. Therefore, a review of the predictive models was utilized to reduce the experimental work for estimating the E₂₀. Predictive models for E₂₀ are critical for reducing energy costs, optimizing biological processes, maintaining regulatory compliance, and ensuring the long-term sustainability of operations in water treatment, aquaculture, and other aeration-dependent industries. Soft computing has attracted much attention in the engineering field (Govindaraju 2000; Azamathulla 2012; Sihag et al. 2018; Sihag et al. 2019a, 2019b, 2020, 2022; Bhoria et al. 2021; Sepahvand et al. 2021; Singh et al. 2021, 2022, 2023; Nivesh et al. 2022; Sharma et al. 2022, 2023; Upadhya et al. 2022a, 2022b; Yamini et al. 2022; Sazonov et al. 2023; Arora et al. 2024; Singh & Minocha 2024a, 2024b) and hydrological studies (Danboos et al. 2023; Dullah et al. 2023; Latif & Ahmed 2023; Singh & Minocha 2024b, 2024c). Soft computing methods have proved their efficacy in the realm of aeration. In their study, Baylar et al. (2008) effectively utilized adaptive neuro-fuzzy inference system and least square support vector machine to analyze datasets containing the rate of air entrapment and E₂₀ measurements acquired through descending jets emanating through weirs having triangular geometry. Predictive formulas using multiple linear and multiple nonlinear regressions were employed to assess the effectiveness of different modeling techniques. Bagatur & Onen (2014) examined the efficacy of genetic expression programming (GEP) to establish a connection between the variables of a triangle weir and the air entrainment rate and E₂₀. In the studies (Deswal 2011; Bagatur & Onen 2014; Deswal & Pal 2015), support vector machine (SVM) and Gaussian process (GP) regression techniques achieved good predictive performance of the O₂ mass transportation coefficient of N_j plunging into a still water pool. GEP and artificial neural network (ANN) modeling were used to compare the kernel functions based on multiple linear regression and support vector regression (SVR) to model mass transfer by vertical and inclined N_j. Using nonlinear regression and ANN approaches, Kramer et al. (2016) efficaciously assessed the depth of plunging water jets with extended discharge. Kumar et al. (2021) studied plunging jets' O₂ mass transfer characteristics.

The literature review established that investigating the effect of screens on E₂₀ has a broad scope of exploration in open channel flow by plunging water through jets of different shapes. In this study, a square-shaped plane was considered to keep its higher HR than a circle. Also, the predictive models were utilized to reduce the experimental work for estimating the E₂₀. Predictive models for E₂₀ are critical for reducing energy costs, optimizing biological processes, maintaining regulatory compliance, and ensuring the long-term sustainability of operations in water treatment, aquaculture, and other aeration-dependent industries.

The objectives of the study were as follows:

• 1. To determine the relationship between the output variable (E₂₀) and input variables (number of jets, discharge, angle of inclination, Froude number, and cumulative hydraulic radius) provided by screens with square jets.

• 2. To calculate the E₂₀ experimentally and predict using an ANN, support vector machine, Gaussian process, and Bagging random forest (RF).

• 3. To compare the results of the optimized models on the basis of correlation coefficient (CC), root means square error (RMSE), and mean square error (MSE).

• 4. A sensitivity analysis for each input parameter is done to find the most influential parameter.

Seven interchangeable acrylic screens with 1, 2, 4, 8, 16, 32, and 64 jets were included in the aeration apparatus (Figure 2). Three values of Q (3.41, 3.84, and 4.75 L/s) and angle of inclination of the open channel (0°, 1.5°, and 3°) were examined for each screen. Every screen was positioned within the tilting flume and adjusted so water could only enter the downstream pool through one or more jet holes. The Wrinkler method was used to determine the DO of the water sample. So, sodium sulfite (Na₂SO₃) and a cobalt chloride (CoCl₂) catalyst were added to the water tank to deoxygenate the water before the testing started. A sample of oxygen-depleted water taken upstream of the screen was used to determine the initial concentration of dissolved oxygen (DO_u) using the azide modification method (APHA 2005). Aeration was carried out for a predefined duration (t = 2 min). Subsequently, a sample of oxygenated water was obtained in order to calculate the DO_d (dissolved oxygen content in the water downstream of the screen) following time ‘t.’ The water temperature was recorded adequately throughout the studies using a laboratory thermometer. Special care was taken to address uncertainty during the experimentations. To avoid error and uncertainty in the DO measurement, the results of the Wrinkler method were compared with the results obtained from the Multimeter (HACH) with the IntelliCAL LDO101 prob. The comparison suggested that there was an uncertainty band of + 0.01 mg/L, which was acceptable. Similarly, for the identification of uncertainty in the measurement of the discharge, the discharge measured from the rectangular weir was calibrated against the results of pitot tubes, and it was found that the error band was ± 0.03 L/s, which was also acceptable.

The present section represents the experimental findings of the tilting flume equipment of the hydraulics lab. The input parameters, such as α, varied from 0° to 3°, Q from 3.41 to 4.75 L/s, N_j from 1 to 64, and HR from 0.0375 to 1.56 cm. The experimental results showed that the parameters studied significantly impact E₂₀.

The increase in E₂₀ is due to higher Q, which enhances the momentum of the flow in jet(s) at elevated velocities, with the amplified surface region of air–water interaction resulting from the increased count of jet orifices and the generation of heightened turbulence at more significant outflows. Conversely, the jets acquire the essential kinetic energy to permeate more profoundly into the reservoir when the outflow surpasses 3.41 L/s, and a larger contact area between air and water forces more oxygen into the pool. It was observed that the higher the Q, the higher the E₂₀.

α affects E₂₀, as shown in Figure 6. The trend is similar and consistent with all α, i.e., 0°, 1.5°, and 3°. The smallest angle, 0°, has the most minor effect on E₂₀ compared to the α at 1.5° and 3°. The increase in E₂₀ in 3° is up to 37%. This study's most efficient screen model uses N_j 1–64 jets at maximum Q and α = 3°. It can be deduced from Figure 6 that E₂₀ increases as the α increases. The reason for this is due to the high velocity at higher angles. The increase in E₂₀ with α is due to the jet's more incredible momentum at greater speeds, as well as an increase in air–water contact area due to the increased N_j and the creation of more turbulence at higher Q. The jets, on the other hand, acquire the essential kinetic power to delve further into the tank as the discharge exceeds 3.41 L/s. More oxygen is compelled into the pool due to a larger air–water contact area.

The various parameters used in calculating the Froude number are listed in Table 3. The total flow area is 30.75 cm², so the square (⁠⁠) side length reduces with increased N_j values. The Froude number values increase with the increase in Q and a decrease in ⁠.

Table 3

Results of parameters used in Fr. no calculation for square jets

Nj .	The cross-sectional area of each jet (cm2) .	Side length (cm) .	Froude number .
			Q = 3.41 L/s = 110.89 cm/s .	Q = 3.84 L/s = 124.87 cm/s .	Q = 4.75 L/s = 154.47 cm/s .
1	30.75	5.545268	1.503535	1.69313	2.094367
2	15.375	3.921097	1.788014	2.013482	2.490636
4	7.687	2.772634	2.126319	2.394447	2.961882
8	3.843	1.960548	2.528634	2.847494	3.522291
16	1.921	1.386317	3.00707	3.38626	4.188733
32	0.960	0.980274	3.576028	4.026965	4.981271
64	0.480	0.693159	4.252639	4.788895	5.923763

Nj .	The cross-sectional area of each jet (cm2) .	Side length (cm) .	Froude number .
			Q = 3.41 L/s = 110.89 cm/s .	Q = 3.84 L/s = 124.87 cm/s .	Q = 4.75 L/s = 154.47 cm/s .
1	30.75	5.545268	1.503535	1.69313	2.094367
2	15.375	3.921097	1.788014	2.013482	2.490636
4	7.687	2.772634	2.126319	2.394447	2.961882
8	3.843	1.960548	2.528634	2.847494	3.522291
16	1.921	1.386317	3.00707	3.38626	4.188733
32	0.960	0.980274	3.576028	4.026965	4.981271
64	0.480	0.693159	4.252639	4.788895	5.923763

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The primary computational task of SVM involves solving a convex quadratic optimization problem to ensure optimal results (Cortes 1995). The results of SVM are better than other machine learning (ML) techniques that depend on minimizing empirical risks (Thissen et al. 2003). When applying SVM to solve regression problems, three critical factors come into play (Samui 2008). At first, SVM performs regression by employing a collection of linear methods specified within a space of increased dimensions. Additionally, SVM employs Vapnik's ε-regression coefficients calculated using an insensitive loss function. Furthermore, assess the associated risk. Finally, structural risk minimization is a concept that SVM integrates. The goal of SVR is to diagnose an f(t) function for data from the training stage (D) with the most significant margin from the training goal values (N).

The correct choice of kernel determines how well SVM algorithms work. The Pearson VII function kernel (PUK) and radial basis kernel (RBF) were finalized, and their expressions are given in the following equations, respectively (Sihag et al. 2019a, 2019b).

Numerous ensemble methods, including boosting, Bagging, and, more recently, RF, have gained wide popularity (Breiman 1996, 2001; Freund & Schapire 1996; Liaw & Wiener 2002). RF is a structured collection of tree predictors created by sampling random vectors from input vectors. Breiman (2001) developed the RF algorithm, an exceptionally effective tool for classification and regression tasks (Scornet et al. 2015). This approach combines a mixture of successful and unsuccessful attempts by utilizing variables based on optimal divisions. By assembling a cluster of arbitrary trees, the RF technique produces forests driven by chance (Mohanty et al. 2019). In RF, Bagging and random subspace methods are combined, and a majority vote determines the outcome.

A sensitivity analysis was conducted to identify the primary input variable affecting the prediction of E₂₀ in open channel flow for hollow square jets. The dataset that yielded the best performance, GP_PUK, was utilized. Each time, one input variable was removed to create a different training dataset, and the outcomes were measured using CC, MAE, and RMSE. The extent of change observed in these evaluation parameters indicates the variable's influence on E₂₀. Findings from Table 7 indicate that HR depth is the most dominant variable, significantly impacting the prediction of E₂₀ compared to other input variables. The HR is calculated as ⁠.

Where ‘A’ is the cross-sectional area and ‘P’ is the wetted perimeter, P will be lower if R is greater. It means less water is in contact with the channel section, resulting in less resistance to the flow and allowing more discharge to pass through it. As a result, higher HR results in greater efficiency. The second influential parameter to affect E₂₀ is α. It adds the horizontal component of water weight, which enhances water velocity. The higher velocity tends to increase E₂₀. Apart from α, N_j significantly influences E₂₀ to a greater extent.

Screens have been used in open channels for a long time to ensure the removal of coarse pollutants. Screens were first introduced as energy dissipators in the research studies. Furthermore, water treatment facilities make extensive use of screens. As the incoming water is subjected to additional treatment procedures, screens are used in these facilities as a first treatment step to remove oversized particles and solids. Specific mesh sizes are integrated into the screens used in water treatment plants so that varied-sized particles can be successfully captured and retained. Screens lessen the strain on downstream structures and enhance the effectiveness of ensuing treatment operations by removing these bigger particles early on. However, their performance in providing aeration and increasing the DO concentration has recently been realized. In the current work, seven acrylic screens with N_j values of 1, 2, 4, 8, 16, 32, and 64 and a flow area of 30.75 cm² were used to study aeration in open channel flow. In order to permit water to flow through the perforations in the screens, each screen was positioned and fastened to the three sides of the tilting flume cross section except the top width.

The input parameters, such as α, N_j, Q, HR, and Froude number, were considered for the study. Each parameter studied had a significant effect on E₂₀. Single jets transmit oxygen at a rate that is much lower than that of multiple jets. The results of the current investigation also suggest that E₂₀ increases along with discharge. A higher jet impact angle may boost oxygenation by causing more bubbles to interact with the water in the pool due to deeper jet penetration and a higher jet angle, which would increase oxygen transfer. According to the current study, aeration improves as the flume tilting angle rises, reaching a maximum of 0.37 (or 37%) at a 3° angle. Deswal & Verma (2007a, 2007b) found that the oxygen transferred by multiple jets is much higher than that of a single plunging jet. Shukla & Goel (2018) reported that a solid jet aerator's oxygenation performance is enhanced when it employs several jets instead of a single plunging jet. They also demonstrated how better oxygenation is brought about by higher discharge. When the N_j falls between 1 and 64 and the Q falls between 3.41 and 4.75 L/s, E₂₀ performs best. The most efficient range is from N_j 1 to 16.

Furthermore, the current study's findings showed that a higher discharge tent amounts to higher E₂₀ in the open channel flow system. It also indicated that higher α boosts oxygenation, presumably due to enhanced bubble contact with the water in the pool brought on by deeper jet entry and higher jet angle resulting in higher O₂ transfer (Kumar et al. 2018a, 2018b). The current study found that as the α increases, the E₂₀ also improves, reaching up to 0.37 (or 37%) at the highest angle of 3°. Cihat Tuna et al. (2014) showed that the Froude number and the relationship between the cross-sectional areas of the water flow and the conduit had a particularly substantial impact on E₂₀. Another literature by Puri et al. (2023a, 2023b) suggested that there has been an increase in the Froude number with higher Q and O₂ transfer. The present study's findings also confirm that E₂₀ and the Froude number directly relate to each other. Soft computing techniques include fuzzy logic, genetic algorithms, ANN, ML, and expert systems. E₂₀ prediction is a high-priority study for densely polluted water management resources. The prediction of E₂₀ was the focus of the study; therefore, the efficacy of soft computing models of ANN, RF_Bagging, SVM (PUK and RBF kernels), and GP (PUK kernel) to estimate square jet aeration in an open channel flow was investigated in the current study. The selection was based on the type of classifiers of soft computing models, such as NN, decision trees, ML, such as support vector machines, and a Gaussian process. Accordingly, the aforementioned soft computing models were applied to assess the prediction capabilities of such classifiers. Five input parameters, α, Q, N_j, HR, and Froude number, were utilized to obtain the predicted values of E₂₀. The effectiveness of models was compared using several statistical criteria such as CC, MAE, and RMSE. It has been observed that the CC value of RF_Bagging drops from 0.9848 to 0.9295 during the testing stage and hence declines its performance. The highest CC value exhibited by GP_PUK during the testing stage was 0.9644. The results showed that the GP_PUK model was found to be outperforming other models in prediction capability for E₂₀ due to its CC value in the testing stage. In the testing stage, the CC values found in ANN, RF_Bagging, SVM_RBF, and SVM_PUK were 0.9595, 09295, 0.9637, and 0.9624. GP is an ML method frequently employed for quantitative issue forecasting (Sihag 2018; Puri et al. 2023a, 2023b). The performance of GP_PUK has been found to be the best in various studies, such as the prediction of river discharge (Nivesh et al. 2022) and the prediction of infiltration rates in permeable stormwater channels (Yaseen et al. 2021). The sensitivity analysis revealed that the input parameter HR is highly sensitive to E₂₀ in aeration through square jets in an open channel flow system. Earlier, the prediction for E₂₀ was devoid of input parameters such as tilt angle, discharge, number of jets, cumulative hydraulic radius, and Froude number in an open channel with square jets (Malik & Kumar 2015; Mahdiyar et al. 2019; Natarajan & Sudheer 2020; Sihag et al. 2020; Yaseen et al. 2021; Essam et al. 2022; Nivesh et al. 2022; Ehteram et al. 2023; Ibrahim et al. 2023) by developing GP_PUK, ANN, RF_Bagging, SVM_RBF, and SVM_PUK soft computing models.

The practical implication of the study is that the DO level in the water has been raised to the level at which the square geometry of plunging jets is quite helpful in achieving E₂₀ to the extent of 37%. This increase can be useful for cultivating sericulture, which is helpful for progressive aquatic life sustainability. On the other hand, the stakeholders can cut the cost of treatment by using oxygenated water to supply water to civic bodies. The enriched, oxygenated water can also be congenial to the agricultural and horticultural produce. The oxygenated water is produced by utilizing the square geometrical plunging jets under gravity in open channel flow, for which no electrical power supply is required. Thus, no energy cost is involved.

In order to ascertain the effectiveness of aerating deoxygenated water with a square plunging jet made from acrylic screens, the current study investigates the effects of tilt angle, discharge, number of jets, cumulative hydraulic radius, and Froude number. The experimental results showed that increased tilt angle and discharge helped E₂₀ positively. The increase of discharge from 3.41 to 4.75 L/s, tilt angle from 0° to 3°, and number of jets (N_j) from 1 to 64 increased E₂₀ from 20 to 76%. In an open channel with a modest Q and a comparatively smooth surface, the most significant E₂₀ reached was about 37%. The aeration with achieved efficiency is good enough for sustainable sericulture and water bodies requiring continuous aeration. The simplicity of an open channel system with simple acrylic screens does not require skilled artistry. It is easily manageable by the end users of the rural population, where sophisticated systems may not be feasible. If used, the cost of an automated system can be reduced to a greater extent due to the availability of already treated water with higher E₂₀. Focusing on simple and easily manageable systems significantly contributes to sustainable water management practices.

• The study was further expanded to predict the E₂₀ obtained experimentally by developing suitable soft computing models. The following ML algorithms, ANN, RF_Bagging, GP_PUK, SVM_PUK, and SVM_RBF, were utilized to develop soft computing models. The GP model with the PUK kernel function outperformed all other models with statistical indices such as CC value of 0.964, MAE value of 0.0159, and RMSE value of 0.019 in the testing stage.

• According to sensitivity analysis, the cumulative hydraulic radius was most sensitive to E₂₀ out of five input parameters.

• There is ample scope for conducting studies related to volumetric oxygen transfer (K_La₂₀), OTE, and standard oxygen transfer efficiency for open channel water flow systems for studying oxygen transfer. In addition, the effect of hydraulic jump and Reynolds number can also be explored in such an open channel flow system. Head loss was not measured; future recommendations can be to study head loss. Multivariate polynomial regression can be done on the current data to study the effect of interactions among input variables.

The authors thank the deanship of scientific research at King Khalid University for funding this work through a large group project under grant number (RGP. 2/94/44). The authors duly acknowledge with thanks the contribution of the authors from the literature whose research articles have been cited in this study.

The data have been taken from the experimental work performed by authors in the Hydraulics Lab of Shoolini University, Solan, Himachal Pradesh, India, 173229.

No funding source is available for the current study.

D.P. collected the experimental data, wrote the draft preparation. P.S. reviewed and edited the article. M.S.T. supervised the article, B.S. proofread edited.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.