Justification for using scale models for impact response evaluation of the SST Transportation System

Introduction: Side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. Side weirs are also used as an emergency structure. This structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. Lateral outflow takes place when the water surface in the main channel rises above the weir sill. Flow over a side weir is a typical case of spatially varied flow with decreasing discharge. There have been extensive studies on side weir overflows. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. In the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. Materials and Methods: The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. It was set up parallel to the main channel; walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 121 experiments on trapezoidal side weirs were carried out. Results and Discussion: For trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow. in which Fr1= upstream Froude number, P= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and T=top flow width of the trapezoidal side weir. Water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. Different elevations in water surface profile depend on the upstream Froude number in the main channel; depth differences in low Froude numbers are at minimum values, and in high Froude numbers are at maximum amounts. The water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. Afterwards, the water level rises towards the downstream of the weir. According to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. According to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. Finally, the general equation was proposed. The general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. The mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5% , respectively. Conclusion: In this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. The results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. It was found that for trapezoidal side weir, the discharge coefficient depends on the Froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. In this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. For this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equation is 2.6%. Thus this equation is proposed for use in practice by water engineers. Keywords: Control structure, Conventional weir, Discharge coefficient, Spatially varied flow, Trapezoidal side weir, Water surface profile

The spatial variability of subreach denitrification rates in streams was evaluated with respect to controlling environmental conditions, molecular examination of denitrifying bacteria, and dimensional analysis. Denitrification activities ranged from 0 and 800 ng‐N gsed−1 d−1 with large variations observed within short distances (<50 m) along stream reaches. A log‐normal probability distribution described the range in denitrification activities and was used to define low (16% of the probability distribution), medium (68%), and high (16%) denitrification potential groups. Denitrifying bacteria were quantified using a competitive polymerase chain reaction (cPCR) technique that amplified the nirK gene that encodes for nitrite reductase. Results showed a range of nirK quantities from 103 to 107 gene‐copy‐number gsed−1. A nonparametric statistical test showed no significant difference in nirK quantities among stream reaches, but revealed that samples with a high denitrification potential had significantly higher nirK quantities. Denitrification activity was positively correlated with nirK quantities with scatter in the data that can be attributed to varying environmental conditions along stream reaches. Dimensional analysis was used to evaluate denitrification activities according to environmental variables that describe fluid‐flow properties, nitrate and organic material quantities, and dissolved oxygen flux. Buckingham's pi theorem was used to generate dimensionless groupings and field data were used to determine scaling parameters. The resulting expressions between dimensionless NO3− flux and dimensionless groupings of environmental variables showed consistent scaling, which indicates that the subreach variability in denitrification rates can be predicted by the controlling physical, chemical, and microbiological conditions.

Dimensionless groups, the output of a successful dimensional analysis, are usually developed via Buckingham's pi theorem. Because this theorem provides a necessary but not sufficient condition for a solution, such a dimensional analysis may, on occasion, appear to fail. The paper presents the necessary and sufficient conditions in a simple form and builds on them to demonstrate how new physical knowledge can augment a ‘primitive’ set of dimensions to arrive at an optimal number of dimensionless groups. The formulation is used to elucidate the historical Rayleigh-Ria-bouchinsky controversy and a related thermomechanical problem is analysed to demonstrate the complete ‘new knowledge’ algorithm. Mathematica code is appended which incorporates these ideas and generates the complete set of admissible dimensionless groups for any specific problem.

This paper shows the experimental results of the flutter speed of thin-flat plates with free leading edge in axial flow as a function of plates’ geometry, fluid densities, and viscosities, as well as natural frequencies of the plates. The experiment was developed based on similitude theory using dimensional analysis and Buckingham Pi Theorem. Dimensional analysis generates four dimensionless numbers. Experiment was conducted by placing the thin-flat plates in a laminar flow wind tunnel in order to obtain the relationship among those dimensionless numbers. The flutter speed was measured by varying the flow velocity until the instability occurred. The dimensional analysis gives a map of the flutter Reynolds number as a function of a new type of dimensionless number that is hereby called flutter fluid structure interaction number, thickness-to-length, and aspect ratios as the correcting factors. This map is a very useful tool for predicting the flutter speed of thin-flat plates in general. This investigation found that the flutter Reynolds number is very high at the region of high flutter fluid structure and thickness-to-length ratios numbers; however, it is very sensitive to the change of those two dimensionless numbers. The sensitivity is higher at lower aspect ratio.

Structures in various industries are exposed to dynamic loads. The dissipative properties of adhesively bonded joints can contribute to the damping of dynamically stressed structures. Dynamic hysteresis tests are carried out to determine the damping properties of adhesively bonded overlap joints by varying the geometry and test boundary conditions. The dimensions of the overlap joints are full-scale and thus relevant for steel construction. Based on the results of experimental investigations, a methodology is developed for the analytic determination of the damping properties of adhesively bonded overlap joints for various specimen geometries and stress boundary conditions. For this purpose, dimensional analysis is carried out using the Buckingham Pi Theorem. In summary, it can be stated that the loss factor of adhesively bonded overlap joints investigated within this study is in the range between 0.16 and 0.41. The damping properties can particularly be increased by increasing the adhesive layer thickness and reducing the overlap length. The functional relationships of all the test results shown can be determined by dimensional analysis. An analytical determination of the loss factor considering all identified influencing factors is enabled by derived regression functions with a high coefficient of determination.

The problem of propeller-ice interaction is very important for ice going vessels, and this phenomenon is not cleared yet. Since the classical works of Jagodkin in 1963, some calculation models have been presented, but none of them can be widely accepted. One of this reason is that quite a few full-scale measurement data used to verify a model can be seen. Besides, the nozzle propeller has been used for propulsion system of icebreaker recently because of its excellent features, but full-scale measurement data of the nozzle propeller are rare.This paper describes the results of full-scale data of nozzle propeller concerning propeller-ice interaction. These data were obtained in the full-scale trials of the patrol icebreaker “TESHIO”, which were conducted in the sea of Okhotsk in February 1996. Some strain gauges were attached on the port side shaft, so the regular component and the fluctuations component of shaft thrust, shaft torque and shaft revolution were measured while the ship was going in ice sea. The maximum fluctuations component of shaft horsepower (SHP) was almost as same as the regular component of SHP. The interval of interaction was also proportional to the regular component of SHP. The comparison on the interval of interaction between full scale data and model test data were also shown. It shows the same tendency that the interval of interaction was shorter as the ice thickness become thicker.

Dimensional analysis is taught early in an undergraduate curriculum for mechanical engineering, usually during the very first course in fluid mechanics. Such analysis has its roots in the work of Lord Rayleigh, and the mechanics of the process as typically taught to undergraduates follows directly from the classic paper due to Buckingham on what is now known as the Pi Theorem. Students are meant to learn that dimensional analysis is a powerful tool for: developing insight with respect to flow physics, creating new models of physical processes, guiding the performance of experiments and flowfield simulations, aiding the sensible presentation of technical results, and fostering the replication of experiments and simulations. Unfortunately, the usual method for finding non-dimensional products taught to undergraduates requires the selection of scaling variables that can seem arbitrary and the solution of a number of sets of simultaneous equations that is typically tedious and prone to simple errors of arithmetic. As a consequence, students often fail to gain the intended appreciation for the usefulness of dimensional analysis. Fortunately, another technique for forming Π products that does not suffer from these same drawbacks was presented by the late Prof. B. S. Massey of University College London. This paper is intended to disseminate his so-called “step-by-step method” to a wider audience and thus to encourage the adoption of the technique for use in undergraduate curricula.

Dimensional analysis is one of the most fundamental tools for understanding physical systems. However, the construction of dimensionless variables, as guided by the Buckingham-π theorem, is not uniquely determined. Here, we introduce IT-π, a model-free method that combines dimensionless learning with the principles of information theory. Grounded in the irreducible error theorem, IT-π identifies dimensionless variables with the highest predictive power by measuring their shared information content. The approach is able to rank variables by predictability, identify distinct physical regimes, uncover self-similar variables, determine the characteristic scales of the problem, and extract its dimensionless parameters. IT-π also provides a bound of the minimum predictive error achievable across all possible models, from simple linear regression to advanced deep learning techniques, naturally enabling a definition of model efficiency. We benchmark IT-π across different cases and demonstrate that it offers superior performance and capabilities compared to existing tools. The method is also applied to conduct dimensionless learning for supersonic turbulence, aerodynamic drag on both smooth and irregular surfaces, magnetohydrodynamic power generation, and laser-metal interaction.

This study presents a statistical and dimensional approach as a simple and efficient means to characterise the effects of individual mixture variables on the performance behaviour resulting from the laboratory tests of hot-mix asphalt (HMA) mixtures. The approach is to find the material and/or mixture variables that significantly affect the performance test results and to further assess the level of significance of variables, with the goal of improving the current understanding of HMA performance tests and their practical applications. To demonstrate the approach, two sets of asphalt pavement analyser (APA) test data from Nebraska and one set of data from Kentucky are statistically analysed based on the multiple linear regression technique. A dimensional analysis based on the Buckingham π-theorem is also performed, and the analysis results are compared with the statistical analysis results. Both analyses present comparable results in that the binder stiffness of HMA mixtures is the most significant variable affecting APA performance test results when the mixtures meet volumetric requirements.

This experimentation explores the utilization of argon-assisted electrical discharge machining (AAEDM) of high-carbon high-chromium die steel. High-pressure argon gas in conventional EDM was utilized to assess the surface roughness (SR). Analysis of variance was connected to decide the critical parameters influencing SR. In this study, a mathematical model has been instigated to get to know SR by using Buckingham pi-theorem while applying the AAEDM process. The fit summary confirmed that the quadratic model is statistically appropriate, and the lack-of-fit is insignificant. Root-mean-square error and absolute standard deviation, obtained through response surface method, were also used for developing the model and for its predicting abilities through ANN. The experiment and anticipated estimates of SR during the process, obtained by dimensional analysis and ANN, were found to be in accord with each other. However, the ANN technique proved to be more fitting to the response as compared to the dimensional analysis.

Establishment of mathematical model to predict the dehulling efficiency in miniature pulse splitter machine energized by human powered flywheel motor using dimensional analysis

Experimental investigation and dimensional analysis of friction drilled hole on 6082 aluminium pipe using hardened M2 centre drill

The results obtained from this project will fundamentally change the way we look at computer performance analysis. These results are made possible by the precise definition of a consistent system of measurement with a set of primary units designed specifically for computer performance analysis. This system of units, along with their associated dimensions, allows us to apply the methods of dimensional analysis, based on the Pi Theorem, to define scaling and self-similarity relationships. These relationships reveal new insights into experimental results that otherwise seems only vaguely correlated. Applying the method to cache-miss data revealed scaling relationships that were not seen by those who originally collected the data. Applying dimensional analysis to the performance of parallel numerical algorithms revealed that computational force is a unifying concept for understanding the interaction between hardware and software. The efficiency of these algorithms depends, in a very intimate way, on the balance between hardware forces and software forces. Analysis of five different algorithms showed that performance analysis can be reduced to a study of the differential geometry of the efficiency surface. Each algorithm defines a set of curvilinear coordinates, specific to that algorithm, and different machines follow different paths along the surface depending on the difference in balance between hardware forces and software forces. Two machines with the same balance in forces follow the same path and are self-similar. The most important result from the project is the statement of the Principle of Computational Least Action. This principle follows from the identification of a dynamical system underlying computer performance analysis. Instructions in a computer are modeled as a classical system under the influence of computational forces. Each instruction generates kinetic energy during execution, and the sum of the kinetic energy for all instructions produces a kinetic energy spectrum as a function of time. These spectra look very much like the spectra used by chemists to analyze properties of molecules. Large spikes in the spectra reveal events during execution, like cache misses, that limit performance. The area under the kinetic energy spectrum is the computational action generated by the program. This computational action defines a normed metric space that measures the size of a program in terms of its action norm and the distance between programs in terms of the norm of the difference of their action. This same idea can be applied to a set of programmers writing code and leads to a computational action metric that measures programmer productivity. In both cases, experimental evidence suggests that highly efficient programs and highly productive programmers generate the least computational action.

Linear die filling is currently widely employed in industries. However, there is no comprehensive and systematic model to describe the powder die filling process. This paper utilizes dimensional analysis to extract and analyze various factors that affect the flow characteristics of powder based on DEM-CFD simulations. Several dimensionless parameters including the ratio of particle size to die depth (), solid density number (), shoe speed number (), and force number () were proposed based on the Pi theorem. The results showed that the filling ratio δ increased with the increase in and due to rising. But it decreased with the increase in due to the shortening of effective filling time. Finally, a semi-empirical modeling of linear die filling was developed, taking the critical value as the dependent variable and the solid density number () and shoe speed number () as independent variables. Hence, this model provides a new approach to computing the smallest shoe speed and designing the sizes of dies based on measurable material properties under complete die filling.

Generation of synthetic full-scale burst test data for corroded pipelines using the tabular generative adversarial network