Buckingham's Theorem Research Articles

The Hydrodynamic Similarity between Different Power Levels and a Dynamic Analysis of Ocean Current Energy Converter–Platform Systems with a Novel Pulley–Traction Rope Design for Irregular Typhoon Waves and Currents

In the future, the power of a commercial ocean current energy convertor will be able to reach the MW class, and its corresponding mooring rope tension will be very good. However, the power of convertors currently being researched is still at the KW class, which can bear less rope tension. The main mooring rope usually has a single cable and a single foundation. To investigate the dynamic response and rope tension of an MW-class ocean current generator mooring system, here, a similarity rule is proposed for (1) coefficients without any fluid–structure interaction (FSI) using the Buckingham theorem and (2) ones with FSI. The overall hydrodynamic drag and moment including the hydrodynamic coefficients in these two situations are represented in a Taylor series. Assuming similarity between the commercial MW-class and KW-class ocean current convertors, all hydrodynamic parameters of the MW-class system are estimated based on the known KW-class parameters and based on the similarity formula. In order to overcome the extreme tension of the MW-class system and to provide good stability, in this paper, we propose a pulley–rope design to replace the traditional single-traction-rope design. The static and dynamic mathematical models of this mooring system subjected to the impact of typhoon waves and currents are proposed, and analytical solutions are obtained. We find that the pulley–rope design can significantly reduce the dynamic rope tensions of the mooring system. The effect of the length ratio of the main traction rope, rope A, to the seabed depth on the dynamic tension of stabilizing converter rope D is significant. The length ratio is within a safe range, and the maximum rope dynamic tension is less than the fracture strength. In addition, if the rope length ratio is over the critical value, the larger the ratio, the higher the safety factor of the rope. In summary, the pulley–rope design can be safely used in an MW-level ocean current generator system.

A Dimensionless Study Describing Heat Exchange through a Building’s Opaque Envelope

The urban environment represents one of the main contexts in which natural resources are exploited to support intensive human activities, especially from an energy perspective. In this context, there is still a lack of general methodologies/tools which can be used to understand the behavior of buildings and to prove their sustainability under real operating conditions, depending on their location, construction characteristics and materials, plants, external conditions, and conduction. In this research, the Buckingham theorem is applied to the thermophysics of buildings, describing the heat transfer of opaque surfaces in a transient regime. The abstraction of dimensionless numbers merges the main phenomena of interest, such as thermal conduction, convection, and radiation, enhanced by consideration of the surface sun–air temperature and the external air temperature. The parameters themselves were mutually matched through a proper equation, whose coefficients were determined by a regression analysis of the measurements from an intensive experimental campaign investigating a building in Florence for 3 years. The resulting correlation shows a good agreement with the available dataset and a determination coefficient of over 70%. Therefore, the proposed approach, owing to the generalization of the dimensionless numbers, suggests the possibility of sustainability estimates, from an energy point of view, of envelope/plant/user systems, including assessments at a higher scale than that of a single building.

Local scour depth at piles group exposed to regular waves: On the assessment of expressions based on classification concepts and evolutionary algorithms

An accurate estimation of local scour depth around piles group is inevitably essential to provide stability of marine structures. Over the past decades, many investigations have been made to understand the scouring process at piles group exposed to waves for field and experimental scales. This study aims to predict the wave-induced local scour depth by various robust Data Driven Models (DDMs) and Machine Learning Models (MLMs) developed by classification and evolutionary concepts: Model Tree (MT), Evolutionary Polynomial Regression (EPR), Multivariate Adaptive Regression Spline (MARS), and Gene-Expression Programming (GEP). From relevant literature, 125 data series were employed to provide empirical relationships for scour depth predictions. The raw variables were related to bed sediment, pile configuration, pile geometry, approaching flow, and wave characteristics. Non-dimensional parameters have been obtained through the Buckingham theorem in order to control local scour depth. In this way, the ratio of spacing between piles to pile diameter (G/D), sediment number (Ns), pile arrangement number (ratio of the number of piles parallel to the flow; m; to the number of piles normal to the flow; n), Shields parameter (θ), and Keulegan-Carpenter (KC) were considered. From the training and testing stages of Artificial Intelligence Models (AIMs), it was found that regression equation given by MARS model provided better performance (e.g., Correlation Coefficient [R] = 0.9297, Root Mean Square Error [RMSE] = 0.3489, and Scatter Index [SI] = 0.2765) than other AI models’ efficiency. Additionally, the performance of AI models was assessed for various ranges of dimensionless parameters (i.e., G/D, Ns, and θ) versus KC variation. MARS model had the best performance for G/D = 0–1 and KC < 10 (R = 0.9917 and RMSE = 0.2198) and 0.4≤θ < 0.5 and 15 < KC < 25 whereas EPR model had promising efficiency in the its highest level for Ns = 1–3 and 10 < KC ≤ 15 (R = 0.9941 and RMSE = 0.0771) than other AI models. For the sensitivity analysis, the mutation rate and number of chromosomes are examined for the GEP model, the K-fold number and number of parameters for the MARS model, and the number of algebraic terms and number of chromosomes for the EPR model. Furthermore, ranking analysis of AI models indicated that MARS model had the best performance (Ranking Performance Index [RPI] = 0.7348) and followed by GEP (0.3412), M5MT (0.2999), and EPR (0.2848).

ROLE OF PHYSICS IN PHYSICS-INFORMED MACHINE LEARNING

Physical systems are characterized by inherent symmetries, one of which is encapsulated in the units of their parameters and system states. These symmetries enable a lossless order-reduction, e.g., via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machine learning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/or numerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantly enhance the interpretability and generalizability of ML-discovered secondary laws. Our numerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysis enables both deep neural networks and sparse regression to reproduce old results, e.g., Stokes law for a sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction. Our results suggest the need to incorporate other physics-based symmetries and invariances into ML-based techniques for equation discovery.

Experimental study of simple flumes with trapezoidal contraction

There are different devices available for measuring the flow discharge. Static measuring devices such as weirs and flumes (without any moving parts) play a significant role in discharge measurement in open channels. Many researchers have focused on application of flumes in irrigation networks. This investigation set out to study the flow discharge through a trapezoidal cut-throated flume (TCTF). The flume is simply constructed by placing two triangular plates on either side of a rectangular open channel to form a trapezoidal throat. The channel cross section is rectangular while throat cross section of the flume is trapezoidal. The proposed flume is simple, low-cost, easy to install and does not require high maintenance. The present study was designed to determine the effect of different variables on the flume discharge. For this, an experimental study was carried out under free outflow conditions and under upstream subcritical flow regime to formulate the flume discharge. Three models are defined for flume discharge relation based on the Buckingham's theorem of dimensional analysis, and then calibrated using the experimental data collected during this study. The first discharge model has an average error of 1.81%, while the second and third improved models have average errors of 0.96% and 1.44% respectively. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equations with an average error less than 2.23% were presented to estimate the submergence threshold. The results of this study indicate that while the downstream wall slope influences the submergence threshold, the flume discharge is not influenced by this variable. The proposed models are simple and accurate and present appropriate estimation of discharge for flows through the TCTFs. The findings of this study will be of interest for practical hydraulic engineers.

Dimensionless modeling of fine material distribution in an experimental silo during central spout loading

Spout loading results in the accumulation of broken kernel and fine materials below the auger chute with spatial distribution over the radial direction. This hinders the air distribution affecting the proper execution of stored grain management practices with any stored bulk. For their optimal performance, it is necessary to assess the effect of systems characteristics on the fine material distribution.This study investigated a generalized dimensionless model of broken corn and foreign material (BCFM) distribution using the dimensionless analysis of the Buckingham theorem. The model considered practical loading parameters in the proposed equation to predict BCFM after the filling process. Practical filling parameters that were investigated includes fill pipe diameter, material flow rate and initial BCFM. Statistical parameters such as RMSE (root mean square error), Chi-square (χ2), coefficient of determination (R2), and MRDM (mean relative deviation modulus) were determined to assess the suitability of the developed model.The results showed that the generalized dimensionless model predicted fine material distribution in the experimental silo with reasonable accuracy. It predicted the nonlinear sifting effect across the radial direction and showed a higher concentration of fines near the bulk core section. It was observed that the sifting effect in a center-filled silo was more pronounced with a lower broken kernel.

Modern Dimensional Analysis Based on Fire-Protected Steel Members’ Analysis Using Multiple Experiments

Nowadays, the real structures (considered as prototypes) subjected to fire are analysed by means of the behaviours of some reduced scale structures (defined as models). These prototype–model correlations are governed by the so-called dimensional analysis (DA) methods. These methods, starting from the Buckingham theorem, offer several dimensionless variables and based on them is the so-called Model Law (ML), which is able to foresee the predictable prototype’s answer based on the results of the experimental investigations performed exclusively on the model (usually manufactured at a reduced scale). Based on the MDA principles, in a previous paper the authors elaborated the complete ML for the heat transfer in beams with rectangular-hole cross-sections, considering unprotected as well as thermally protected structural elements. The authors, based on meticulous experimental investigations, obtained the validation of this ML for the unprotected steel members. In this contribution, the authors offer in a similar manner the ML validation for intumescent paint-protected steel members and thus the complete validation of their original ML. In their theoretical and experimental investigations, the authors involved both a real column’s element combined with its models manufactured at 1:2 and 1:4, as well as 1:10 scales too. Consequently, the obtained ML can be considered as generally valid, involving a real structural element and its model manufactured at the desired scale.

Rectangular top-hinged plate as portable flow measuring device

Abstract Most previous studies have focused on adjustable complex flap gates and little research has been carried out on simple inline top-hinged plates for flow measurement. The present study investigates discharge measurement by top-hinged plates located along channels under free flow condition. The proposed simple device is a portable one. Two discharge models are proposed based on Buckingham's theorem of dimensional analysis. The first model (Model I) considers deflection angle as an independent variable while the second model (Model II) considers it as a dependent variable. A series of laboratory experiments (687 runs) were performed to calibrate the proposed models. The results showed that when the slope of the channel increases, the accuracy of the proposed model slightly decreases. The first model has an average error of 2.32%, while the second model has an average error of 3.19%, thus flow discharge through the rectangular channels with longitudinal slopes in range of [0, 0.005] can be accurately estimated using the proposed discharge models. Based on this experimental study, the plate length enhances the performance of the second model when the mass plate is unknown. The proposed device offers a simple and reliable discharge measurement approach for both horizontal and sloping rectangular channels.

The interaction analysis between liquid-solid two-phase flow and equipment components in a molten salt pump

Latent heat energy storage is an important issue in the solar energy engineering. As energy storage materials, molten salts release some of latent heat and crystallize. The particles of salt crystals probably collide and rub with the contact parts in the process of movement, and the colliding and rubbing leads to the abrasion or damage of the contact parts. In this study, a dimensionless analysis of the solid-liquid two-phase flow transported by molten salt pump (MSP) was carried out by Buckingham's theorem and the similarity criterion, and the numerical model verified by the theory was used to analyze the flow field in the pump. To accurately evaluate the wear-prone position of the MSP, dozens of monitoring points were arranged on the blade and near the volute tongue. The effects of multiple factors such as the solid particle size, pump inlet particle volume fraction (IPVF), span, and flow rate on the internal flow field and stability of the MSP were studied. The results show that the solid particles mainly concentrate at the inlet and outlet ends of the suction surface of the blades, as well as near the volute tongue. Under low flow rate conditions, the IPVF has a significant influence on the flow trajectory with large-sized particles, whereas has little influence on that of the small-sized particles; when the solid particle size is large, the occurrence of vortex and back flow decreases with the increase of IPVF. The IPVF, curvature of the blade and span have a certain impact on the pressure load, and the greatly affected areas are mainly distributed near the blade head and tail. The research results have certain reference value for improving the anti-wear performance and stable operation of MPSs.

A Regressive Model for Periodic Dynamic Instabilities during Condensation of R1234yf and R1234ze Refrigerants

This paper presents the results of experimental research and mathematical modelling in terms of the influence periodic dynamic instabilities have on condensation phase change in R1234yf and R1234ze refrigerants in tubular minichannels. The main reason for this research was the fact that under the Montreal Protocol (1986), as well as Regulation No 517/2014 of the European Parliament and of the Council of 16 April 2014, the F-gases such as hydrofluorocarbons (HFC), perfluorocarbons (PFC), sulphur hexafluoride, and other agents containing fluorine have to be withdrawn. This includes one of the most commonly used refrigerants—R134a—which, since 1 January 2017, has already been withdrawn. It also includes the R404A refrigerant. R1234ze and R1234yf are suggested as substitutions for R134a. The basic parameters determining the application of those agents are their global warming potential (GWP) indicator, which is below 150, and reduction in fluorinated greenhouse gases emission by a third, simply by withdrawing them (with 2010 as a reference level). The current state of knowledge enables researchers to foresee the influence of some hydrodynamic instabilities on the condensation of fluorinated refrigerants in minichannels. Therefore, an expansion of this knowledge regarding the suggested substitutes is absolutely necessary. Research concerning the condensation in minichannels under dynamic instabilities was already conducted for the refrigerants currently being withdrawn. However, the influence of those instabilities on a phase change in the suggested pro-ecologic substitutes is not known. It is known that during the condensation of refrigerants under dynamic instabilities, the propagation of instabilities occurs in a waveform. Two-phase media are particularly susceptible to this phenomenon. Propagation of instabilities in the form of acoustic wave or wave change in other parameters such as temperature, the density of mass, or heat flux plays a special role. All of them have their own characteristics, with evidently different propagation velocities. Both mechanisms include irreversible dissipation and dispersion. The dissipative effects, by their irreversibility, cause entropy generation and dump the instability propagation in a two-phase medium. The dispersive effects influence the instability propagation that is a function of the generation frequency. Besides the experimental results, the paper contains a dimensional analysis procedure based on the Π–Buckingham theorem that has allowed for the development of a regressive model for the velocities of pressure dynamic instabilities. The experimental part of this paper was conducted using tubular minichannels with an internal diameter of dID = 1.40–3.3 mm.

Kinematics and geometrical admissibility conditions of balanced vane pumps with twin lip vanes

The present work is devoted to analyze the kinematics of twin lip vanes adopted in balanced vane pumps. The work provides the analytical description of the vane motion according to its geometrical parameters and the cam ring profile. Attention is given to the duality of the solution, an intrinsic property of twin lip vanes that may be considered as followers with two symmetrical half-circular tips. Based on the linkage kinematics, the analytical dissertation is further deepened to define the geometrical admissibility of the vane design and its mathematical domain. In order to evaluate the proposed approach, an extended parametric study is performed on the basis of the Buckingham theorem, detailing how the twin lip configuration affects the machine kinematics. Additional calculations are proposed to determine the vane design configurations that satisfy the fundamental law of cam design and to highlight how this requirement dramatically reduces the subset of available choices in presence of cam ring with a precompression profile. Finally, design guidelines are proposed in order to overcome these drawbacks and expand the admissibility domain.

Energy Analysis of the Propulsion Shaft Fatigue Process in a Rotating Mechanical System Part III Dimensional Analysis

Abstract This article presents the third and last part of the problem of diagnosing the fatigue of marine propulsion shafts in terms of energy with the use of the action function, undertaken by the authors. Even the most perfect physical models of real objects, observed under laboratory conditions and developed based on the results of their research, cannot be useful in diagnostics without properly transferring the obtained results to the scale of the real object. This paper presents the method of using dimensional analyses and the Buckingham theorem (the so-called π theorem) to determine the dimensionless numbers of the dynamic similarity of the physical model of the propulsion shaft and its real ship counterpart, which enable the transfer of the results of the research on the energy processes accompanying the ship propulsion shaft fatigue from the physical model to the real object.

Tire dimensionless numbers for analysis of tire characteristics and intelligent tire signals

It is essential to understand and analyze the characteristics of the tire. This paper focuses on analyzing tire characteristics using intelligent tires based on physical tire models. The flexible ring tire model has been selected as the tire model. The flexible ring tire model is analyzed and simplified based on modal analysis. Four tire dimensionless numbers have been proposed to represent tire characteristics using the Buckingham theorem. Tire dimensionless numbers were estimated using intelligent tire sensor signals. The estimation algorithm was designed based on the standing wave characteristics of the tire. The proposed estimation algorithm has been validated through experiments on various tire conditions. The physical correlation between the estimated tire dimensionless numbers and the tire state dimensionless numbers were analyzed. The experimental results verify the physical meaning and estimation performance of the proposed tire dimensionless numbers.

STUDY OF THE DESIGNS OF BOTTOM BLOWING DEVICES FOR OXIDATIVE BLOWING IN TEEMING LADLES

It is discussed in the article the concept proposed for the production of ultra-low carbon steel, which involves the production of crude steel in basic oxygen furnace followed by oxidative blowing with an oxygen-argon mixture in a teeming ladle to decrease a carbon content in steel to less than 0.03%. High efficiency of the proposed technology is possible only under the intensive process of metal decarburization, which consists of the three stages: supply of reagents to the gas bubble, chemical interaction of reagents on the interfacial surface and removal of reaction products. At low carbon concentrations in the metal, the limiting link of the process is carbon mass transfer to the interfacial surface, which can be intensified by melt stirring. The objective of this article is to study the influence of design of the blowing devices, namely, the position and shape of the pores, on the efficiency of metal homogenization in the teeming ladle. Blowing devices with a circular hole, a slit and undirectional porosity were considered. To perform physical simulation by Buckingham's theorem, similarity numbers were chosen to describe the considered process. In particular, it is proposed to use dimensionless volume flow and a modified homochronicity number. Based on the physical simulation on the “water” model, it was found that the best results of homogenization of the chemical composition of the liquid metal in the teeming ladle show blowing devices with undirected porosity. They are ideal for oxidative purging in a crowded ladle with a mixture of argon and oxygen required for the production of ultra-low carbon steel with an oxygen content of less than 0.03%. The purpose of further research is to develop the design of the mixing chamber of the purge device, in which oxygen and argon are pre-mixed before injection into the liquid metal.

Stage-discharge relationship for slide gates installed in partially full pipes

Sluice/slide gates are widely used for flow depth control and flow discharge measurements in open channels. The hydraulic behavior of the sluice gates located in the rectangular open channels is well documented in the literature. This study reports the results of an investigation conducted to establish the stage-discharge relationship for the sluice gates located in horizontal, circular open channels/pipes under free outflow conditions. Different stage-discharge models were proposed based on the Buckingham's theorem of dimensional analysis and orifice theory. A comprehensive series of laboratory experiments (729 runs) were performed to study the sluice gates located at the middle, and at the end of two circular pipes. Using the data collected from two circular open channels of nominal diameters 20 and 30 cm, the proposed models were calibrated. For the middle slide gates, the experimental results showed that the discharge prediction can be improved by introducing the Reynolds number. For the slide gates located at the middle of the channel, the best proposed model has an average error of 1.40% with a maximum error of 7.12%. For the slide gates located at the end of the channel, the Reynolds number has no significant effect and best proposed model has an average error of 2.47% with a maximum error of 6.59%. The results also showed that the flow discharge of the end slide gate (with unconfined free jet under gravity) is higher than the flow discharge of the middle slide gate for the same gate opening areas and upstream flow depths. The proposed sluice/slide gate for circular open channels offers a simple and reliable discharge measurement approach with acceptable accuracy.

A dimensionless study on thermal control of positive temperature coefficient (PTC) materials

Positive temperature coefficient (PTC) material is widely used in the field of thermal control due to its unique temperature sensitive characteristics. However, there is no general criterion about PTC material thermal control at present due to the lack of theoretical analysis in the previous works. Thus, in this paper, the dimensionless method is used to study PTC material adaptive thermal control and finally, a fitting formula is obtained to estimate the equilibrium temperature of controlled device. First, a one-dimensional and steady-state heat transfer model was proposed to calculate the equilibrium temperature of controlled device under thermal control of PTC materials, and it was verified by experiment. Then, the model has been nondimensionalized and four dimensionless numbers are introduced by Buckingham theorem, in which the Wr number is presented to represent the heating characteristics of PTC materials. Finally, by fitting all the data, a form of fitting equation of equilibrium temperature of controlled device is obtained. The results show that this form proposed in this paper can be applied to the widely used ceramic PTC materials. The criterion equation fitted by this form can effectively estimate the equilibrium temperature of the controlled devices with good accuracy and wide application.

Influence of Process Parameters on Countercurrent Reactor Reduction of Oxidized Mill Scale Waste and Its Co-relationship with Mathematical Model

Mill scale is treated as a waste product by the steel industry, so it is essential to recycle and reuse this waste for recovery of metallic iron and its single oxide derivative. Most of the study in the field of mill scale reduction focuses on the static mill scale reduction. Optimizing the process in dynamic conditions becomes more difficult because of the complexity involved inside the process. In the present method, mill scale having particle size ranges from 106 to 53 µm was converted to single-phase oxide Fe2O3 by blowing pure oxygen at 1100 °C and then it was subjected to a reducing atmosphere of 50% H2 and 50% N2 (1:1) at 875 ± 5 °C at a varying reactor angle from 2° to 5° and different mass flow rates varying from 0.037 to 0.148 kg/min. A generalized experimental model (GEM) has been formulated for the degree of reduction of oxide, which encompasses twelve parameters consisting of reactor design and process parameters. A Buckingham theorem was used to obtain dimensionless parameter for the degree of reduction, and a logical correlation using the proposed model has been established.

Performance Improvement of Helical Downhole Gas-Oil Separator Using Experimental Approach

Summary Growing demand for a subsurface pump application to perform artificial lift in low-pressure wells increases the necessity of a high-efficiency downhole separator to prevent gas entrance in the pump. The purpose of this study is to empirically investigate the efficiency of a helical downhole separator and provide suggestions for improving its performance. To make the results more practical, dimensionless numbers governing the problem were specified using dimensional analysis and the Buckingham theorem, and a laboratory-scale separator was built. Oil and air were selected as the working fluids for this experiment. The results of the experiments showed that the separator performance was divided into three regions: inefficiency region, rapid-growth region, and nongrowth region. To increase the separator efficiency, the separator was modified by blocking the initial holes of the inner tube to provide a region for developing the prerotational effect. The modified separator showed an increase in efficiency as much as 7%. In the third step, the number of holes that were blocked at the entrance region in the first modification were distributed in the rest of the inner tube so that the total hole area remains constant. The separator efficiency, in this case, was significantly increased compared with the previous two cases by as much as twofold. It was found that the inlet design of the separator significantly affects its performance.

Mathematical Modeling Buckingham's Theorem and Optimization Technique on Mechanically Alloyed Nanocomposite Materials

This research work is focused to develop and investigate the mathematical linear and non-linear modelling techniques for mechanically alloyed nanocomposites materials. These conventional and non-conventional artificial intelligent models could predict the both physical and mechanical properties of some nanocomposites materials. The conventional techniques such as dimensional analysis using Buckingham -theory, regression analysis and its hybrid approach; and non-conventional approaches like neural networks, fuzzy theory and adaptive fuzzy theory have addressed through this research work. The most significant input parameters which would affect the mechanical alloying processes, namely, milling time (t, min), ball-to-powder ratio (B), milling speed (N, rpm), ball size (D, mm), percentage of reinforcement (R, %) sintering temperature (T, K), sintering time (ts, min) and consolidation pressure (P, MPa) can be used for the various models. The various responses as physical and mechanical properties to be used are crystallite size (d, nm), bulk hardness (H, MPa), bulk density (ρ, kg/m3 ), tensile strength (σy , MPa), matrix particle size (Z, μm), compressive strength (σu, MPa), and percentage of elongation (e, %). Through this research work, we can select an optimum input parameter as per our required output properties, predicting the physical and mechanical behavior of nanocomposites and select the best linear &amp; non-linear methods.

Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments

In the field of hydrology, stage–discharge relationships are commonly used to estimate the discharge at the basin outlet or by experimental plots. Many experimental efforts have been made in order to derive stage–discharge relationships, according to the Buckingham theorem and dimensional analysis, for a multiplicity of gauge geometry. However, these relationships require experimental and physical meaningless numerical coefficients, thus they need extended calibration. The latter issue merits attention, since the empirical coefficients can be applied when the experimental conditions are strictly reproduced in the field. The aim of this paper is to derive a theoretically based stage–discharge relationship of a non-linear water reservoir that requires limited calibration, by using the continuity equation and the principle of conservation of energy. An analysis was performed using a rectangular water tank with a hole at the bottom. However, the suggested approach can be similarly used for tank geometries that differ from the example used in this study. Since the proposed approach is purely hydraulic, only limited calibration of the physical meaningful discharge coefficient characteristic of the hole is needed. A tank design procedure is suggested, and different theoretical and experimental applications of the proposed methodology are performed and discussed. For the considered cases, the mass water balance was also checked.