Quantifying the Euphrates Electric Conductivity Depending on Parameters by Dimensional Analysis Method

The searching about methods to connect the variables with each other to reach equations including multi variables. The dimensional analysis is a method to facilitate the solution of difficult mathematic equations and experimental formulas;therefore methods of simplifying the difficult equations and obtaining a new equation with different variables is needed. In this study will use 2 methods (statically with dimensionally analysis) to obtain electric conductivity of water of Euphrates river by multi parameters that are time (t), temperature (Te), density, viscosity, discharge and water depth in upstream of Alhindya barrage which located in Babylon governorate, Iraq during winter 2019. The equations were obtained for EC with Te and t by data were collected from Alhindya barrage office with R2 = 0.999 and R2 = 0.995 by statically ways. Dimension analysis was utilized via 2 stages. In first stage was obtained on equation of EC with respect to Te, water density (ρ) and dynamic viscosity (μ) with constant time, depth of water and discharge and we obtain on R2 was 0.994 and R2 = 0.986. In second stage was obtained formula of EC with respect to Te, water density (ρ), dynamic viscosity (μ), with variable time, depth of water and discharge with we obtain on R2 = 0.945 and R2 = 0.94. The result of research indicates that applying the dimension analysis to connect more than one variable with each other to find best solutions and best methods to facilitate the solving the equations. From dimension analysis gave a clear visualization of the association of several variables to give a result that helps measure the electrical conductivity of water in the absence of a water test device.

Parametric Dimensional Analysis on the Structural Response of An Innovative Subsurface Tension Leg Platform in Ultra-Deep Water

The innovative Subsurface Tension Leg Platform(STLP), which is designed to be located below Mean Water Level(M.W.L) to minimize direct wave loading and mitigate the effect of strong surface currents, is considered as a competitive alternative system to support shallow-water rated well completion equipment and rigid risers for large ultra-deep water oil field development. A detailed description of the design philosophy of STLP has been published in the series of papers and patents. Nonetheless, design uncertainties arise as limited understanding of various parameters effects on the structural response of STLP, pertaining to the environmental loading, structural properties and hydrodynamic characteristics. This paper focuses on providing quantitative methodology on how each parameter affects the structural response of STLP, which will facilitate establishing the unique design criteria as regards to STLP. Firstly, the entire list of dimensionless groups of input and output parameters is proposed based on VaschyBuckingham theory. Then, numerical models are built and a series of numerical tests are carried out for validating the obtained dimensionless groups. On this basis, the calculation results of a great quantity of parametric studies on the structural response of STLP are presented and discussed in detail. Further, empirical formulae for predicting STLP response are derived through nonlinear regression analysis. Finally, conclusions and discussions are made. It has been demonstrated that the study provides a methodology for better control of key parameters and lays the foundation for optimal design of STLP. The obtained conclusions also have wide ranging applicability in reference to the engineering design and design analysis aspects of deepwater buoy supporting installations, such as Grouped SLOR or TLR system.

Dimensional analysis and extended hydrodynamic theory applied to long-rod penetration of ceramics

Principles of dimensional analysis are applied in a new interpretation of penetration of ceramic targets subjected to hypervelocity impact. The analysis results in a power series representation – in terms of inverse velocity – of normalized depth of penetration that reduces to the hydrodynamic solution at high impact velocities. Specifically considered are test data from four literature sources involving penetration of confined thick ceramic targets by tungsten long rod projectiles. The ceramics are AD-995 alumina, aluminum nitride, silicon carbide, and boron carbide.Test data can be accurately represented by the linear form of the power series, whereby the same value of a single fitting parameter applies remarkably well for all four ceramics. Comparison of the present model with others in the literature(e.g., Tate's theory) demonstrates a target resistance stress that depends on impact velocity, linearly in the limiting case. Comparison of the present analysis with recent research involving penetration of thin ceramic tiles at lower typical impact velocities confirms the importance of target properties related to fracture and shear strength at the Hugoniot Elastic Limit(HEL) only in the latter. In contrast, in the former(i.e., hypervelocity and thick target) experiments, the current analysis demonstrates dominant dependence of penetration depth only by target mass density. Such comparisons suggest transitions from microstructure-controlled to density-controlled penetration resistance with increasing impact velocity and ceramic target thickness.Production and hosting by Elsevier B.V. on behalf of China Ordnance Society.

Dimensional analysis of earthquake-induced pounding between adjacent inelastic MDOF buildings

In this study the seismic pounding response of adjacent multi-degree-of-freedom(MDOF) buildings with bilinear inter-story resistance characteristics is investigated through dimensional analysis. The application of dimensional analysis leads to a condensed presentation of the response, and the remarkable self-similarity property for bilinear MDOF buildings with inelastic collision is uncovered. It is shown that when the response is expressed in the appropriate dimensionless form, response spectra for any intensity of the excitation collapse to a single master curve. The reduced Π set explicitly describes the interaction between the colliding structures. The effect of pounding on the MDOF building’s response is illustrated using three well-divided spectral regions(amplifi ed, de-amplifi ed and unaffected regions). Parametric studies are conducted to investigate the effects of the story stiffness of structures, the story stiffness ratio and mass ratio of adjacent buildings, the structural inelastic characteristics and the gap size values. Results show that(i) the infl uence of system stiffness ratio to the lighter and more fl exible building is more signifi cant in the fi rst spectral region, where the maximum response of the building is amplifi ed because of pounding; and(ii) the velocity and pounding force of the heavier and stiffer building is unexpectedly sensitive to the mass ratio of adjacent buildings.

Material Equivalent Test Based on Dimensional Analysis for Fragment Penetrating Antenna Target

Phased array radar is the main sensor in a battlefield.Phased array antenna is the main execution unit of the phased array radar,and it greatly affects the reliability of the phased array radar. As a result,the fragment damaged antenna test is important.As the materials of phased array antenna are not easy to get,the fragment damaged antenna test is difficult to carry out. Then we present a study on this problem and introduce the principles of dimensional analysis to solve it. Firstly, the fragments damage antenna target dimensionless model is constructed. Secondly,the finite element analysis software ANSYS / LS-DYNA are used to carry out a large number of different materials simulation test for dimensional analysis. Finally,based on dimensional test analysis,the materials equivalent empirical model between different antennas target is presented in the same damage. The results of this study provide a feasible and valuable solution for different materials' target damaged test.

Quantifying.Associations among Dimensions of Ears and Their Form Factors in Maize(Zea Mays)Using Dimensional Analysis

Ear morphological traits such as volume and shape are important features of maize and the quantitative associations among them can help understand kernel yield determination. 150 mature ears each of 4 maize cultivars were collected from field experiments, and ear length(L), diameter(D), area(S) and volume(V) were recorded for individual ears, kernel weight per ear also recorded for a portion of the examined ears. Following principles of dimensional analysis, 8 theoretical equations of 3 sets,which relate ear higher dimensions to its length and diameter, were developed and parameterized and validated with the field observations. The 3 optimized equations showed that the shape of ears in maize can be featured with 3 dimensionless form factors, namely diameter-to-length ratio(c=D/L), areal form factor(b=S/L/D), and volumetric form factor(a=V/L/D/D). Statistically,all of them were significantly different among cultivars, and a's values varied from 0.582 to 0.612, and b's 0.839-0.868, and c's 0.242-0.308. Volumetric form factor and areal form factor could estimate precisely ear volume and area respectively, but diameter-to-length ratio was not suitable to estimate ear diameter by its length. Ear volume explained almost all variation of ear kernel weight and product L*D*D did the same substantially. Dimensional analysis proved to be promising in understanding relationship among morphological traits of ears in maize. Its application in crop researches should improve our knowledge of the physical properties of crop plants.

Dimensional analysis of the impact toughness test for synthetic diamond grits

The method,in which a few carats of diamond grits are placed inside a capsule together with a steel ball,shaken for a number of times,and the unbroken ratio of the grits is then used to evaluate the quality of the diamond,has been well established for many years.However,the unbroken percentage,in an equivalent view,represents the impact toughness of the grits and cannot reflect the value of the crushing energy.Most of the previous empirical formulas obtained from experiments by scholars cannot be applied to practical tests.In this paper,a dimensional analysis was applied to investigate the impact toughness experiment,and the dimensionless relationship has been built among those variables such as the toughness index,the impact time,the impact frequency and the crushing energy per unit area.According to the results of a large number of experiments with synthetic diamond grits of mesh size 45/50,the percentage of the broken grits H is proportional to the impact time T^（1.14） when the impact frequency is 2400 r/min,and the impact frequency f^（2.576） when the number of impacts is 2000.

Airflow distribution law of multi-branch pipe of pneumatic rice direct seeder based on dimensional analysis

In order to investigate the flow characteristics and distribution law of airflow in multi-branch pipe of pneumatic rice precision direct seeder and obtain the mathematical model between airflow parameters and pipe geometry structure.In this study,the airflow flow law of the multi-branch pipeline of the pneumatic system was studied,the mechanism of airflow flow in the multi-branch pipe was analyzed,and it was clarified that the main factors affecting the airflow flow in the pipe,namely,air density,air dynamic viscosity,the total flow rate of the inlet branch pipe,the length of the closed end of the header,the inner diameter of the outlet branch pipe,and the outlet branch pipe spacing.Numerical simulations were carried out using Fluent simulation software to elucidate the cause of multi-branch pipes of uneven distribution of airflow in multi-branch pipes,the empirical equation among these factors and the flow velocity of the outlet branch pipe are established by dimensional analysis method.The bench test results show that the established empirical equations are applicable in the following ranges:0.018 m3/s≤Q≤0.054 m3/s,0.045 m≤d≤0.05 m,0.075 m≤L≤0.125 m,0.7 m≤Y 1≤0.875 m(0.5 m≤Y 2≤0.75 m,0.36 m≤Y 3≤0.45 m),the prediction accuracy can be controlled within 10%of the empirical formula,which can provide a reference for the prediction and optimization design of outlet velocity of the multi-branch pipe.

Process analysis for an alfalfa rotary dryer using an improved dimensional analysis method

All parameters in terms of wet alfalfa input capacity,dry alfalfa output capacity,alfalfa stem length,rotary speed,heated air temperature,air flow velocity and number of lifting flights fixed at the interior wall of rotary dryer were integrated and derived into fourπterms based on Jiang’s principle.The drying temperature was a significant factor influencing the drying rate and the post-drying quality of alfalfa hay.An improved G.Murphy theorem with high confidence was used to design an experimental program for alfalfa drying in a rotary dryer.Aπequation was derived by using the multiplication of component equations involving the drying parameters and most of its correlation coefficients were higher than 0.99.The validation results show that most of the relative errors ofπterms were lower than 10%and are acceptable in engineering practice.This empirical equation may be used to investigate the parameter interactive effects on conveyor performance,which may be useful in the design and selection of rotary dryers for drying alfalfa hay.

Magnetic field assisted fluidization—Dimensional analysis addressing the physical basis

This paper originates a discussion on dimensional analysis and scaling in magnetically assisted fluidized beds. Basic examination of process variables, merging mechanical and magnetic units, allows the conversion of mixed sets of variables into unified terms representing surface forces as effects of the fields contributing to the assisted fluidization behaviour. This transformation is termed ＂pressure transform＂ since the new variables are all characteristic pressures generated by three basic fields： gravity, magnetic and fluid flow. This approach addresses the physical basis in terms of dimensionless groups rather than formal algebraic manipulations pertinent to classical dimensional analysis. Basic dimensionless group termed granular magnetic Bond number is introduced as the ratio of characteristic pressures of gravity and of magnetic field. This analysis also provides a set of named dimensionless numbers characterizing magnetic field assisted fluidization such as Filippov number, Rosensweig number, Kwauk number and Siegell number, derived as ratios of characteristic pressures.

Blast wave characteristics of multi-layer composite charge:Theoretical analysis,numerical simulation,and experimental validation

This article investigates the characteristics of shock wave overpressure generated by multi-layer composite charge under different detonation modes.Combining dimensional analysis and the explosion mechanism of the charge,a peak overpressure prediction model for the composite charge under singlepoint detonation and simultaneous detonation was established.The effects of the charge structure and initiation method on the overpressure field characteristics were investigated in AUTODYN simulation.The accuracy of the prediction model and the reliability of the numerical simulation method were subsequently verified in a series of static explosion experiments.The results reveal that the mass of the inner charge was the key factor determining the peak overpressure of the composite charge under single-point detonation.The peak overpressure in the radial direction improved apparently with an increase in the aspect ratio of the charge.The overpressure curves in the axial direction exhibited a multi-peak phenomenon,and the secondary peak overpressure even exceeded the primary peak at distances of 30D and 40D(where D is the charge diameter).The difference in peak overpressure among azimuth angles of 0-90°gradually decreased with an increase in the propagation distance of the shock wave.The coupled effect of the detonation energy of the inner and outer charge under simultaneous detonation improved the overpressure in both radial and axial directions.The difference in peak overpressure obtained from model prediction and experimental measurements was less than 16.4%.

Application of coupled analysis methods for prediction of blast-induced dominant vibration frequency

Blast-induced dominant vibration frequency （DVF） involves a complex, nonlinear and small sample system considering rock properties, blasting parameters and topography. In this study, a combination of grey relational analysis and dimensional analysis procedures for prediction of dominant vibration frequency are presented. Six factors are selected from extensive effect factor sequences based on grey relational analysis, and then a novel blast-induced dominant vibration frequency prediction is obtained by dimensional analysis. In addition, the prediction is simplified by sensitivity analysis with 195 experimental blast records. Validation is carried out for the proposed formula based on the site test database of the first- period blasting excavation in the Guangdong Lufeng Nuclear Power Plant （GLNPP）. The results show the proposed approach has a higher fitting degree and smaller mean error when compared with traditional predictions.

Dimensional Synthesis of a 3-DOF Parallel Manipulator with Full Circle Rotation

Parallel robots are widely used in the academic and industrial fields. In spite of the numerous achievements in the design and dimensional synthesis of the low-mobility parallel robots, few research efforts are directed towards the asymmetric 3-DOF parallel robots whose end-effector can realize 2 translational and 1 rotational（2T1R） motion. In order to develop a manipulator with the capability of full circle rotation to enlarge the workspace, a new 2T1 R parallel mechanism is proposed. The modeling approach and kinematic analysis of this proposed mechanism are investigated. Using the method of vector analysis, the inverse kinematic equations are established. This is followed by a vigorous proof that this mechanism attains an annular workspace through its circular rotation and 2 dimensional translations. Taking the first order perturbation of the kinematic equations, the error Jacobian matrix which represents the mapping relationship between the error sources of geometric parameters and the end-effector position errors is derived. With consideration of the constraint conditions of pressure angles and feasible workspace, the dimensional synthesis is conducted with a goal to minimize the global comprehensive performance index. The dimension parameters making the mechanism to have optimal error mapping and kinematic performance are obtained through the optimization algorithm. All these research achievements lay the foundation for the prototype building of such kind of parallel robots.

Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis

We present recent work of harmonic and signal analysis based on the complex Hardy space approach.

Flow and penetration behavior of submerged side-blown gas

To assess the widely used submerged side-blowing in pyrometallurgy,a high-speed camera-digital image processing-statistical approach was used to systematically investigate the effects of the gas flow rate,nozzle diameter,and inclination angle on the space-time distribution and penetration behavior of submerged side-blown gas in an air-water system.The results show that the gas motion gradually changes from a bubbling regime to a steady jetting regime and the formation of a complete jet structure as the flow rate increases.When the flow rate is low,a bubble area is formed by large bubbles in the area above the nozzle.When the flow rate and the nozzle diameter are significant,a bubble area is formed by tiny bubbles in the area above the nozzle.The increased inclination angle requires a more significant flow rate to form a complete jet structure.In the sampling time,the dimensionless horizontal and vertical penetration depths are Gaussian distributed.Decreasing the nozzle diameter and increasing the flow rate or inclination angle will increase the distribution range and discreteness.New correlations for a penetration depth with an error of±20%were obtained through dimensional analysis.The dimensionless horizontal penetration depth of an argon-melt system in a 120 t converter calculated by the correlation proposed by the current study is close to the result calculated by a correlation in the literature and a numerical simulation result in the literature.

Automated Dynamic Cellular Analysis in Time-Lapse Microscopy

Analysis of cellular behavior is significant for studying cell cycle and detecting anti-cancer drugs. It is a very difficult task for image processing to isolate individual cells in confocal microscopic images of non-stained live cell cultures. Because these images do not have adequate textural variations. Manual cell segmentation requires massive labor and is a time consuming process. This paper describes an automated cell segmentation method for localizing the cells of Chinese hamster ovary cell culture. Several kinds of high-dimensional feature descriptors, K-means clustering method and Chan-Vese model-based level set are used to extract the cellular regions. The region extracted are used to classify phases in cell cycle. The segmentation results were experimentally assessed. As a result, the proposed method proved to be significant for cell isolation. In the evaluation experiments, we constructed a database of Chinese Hamster Ovary Cell’s microscopic images which includes various photographing environments under the guidance of a biologist.

Determination of Parameters Affecting the Estimation of Iceberg Draft

Recent offshore oil and gas loading facilities developed in the Arctic area have led to a considerable awareness of the iceberg draft approximation, where deep keel icebergs may gouge the ocean floor, and these submarine infrastructures would be damaged in the shallower waters. Developing reliable solutions to estimate the iceberg draft requires a profound understanding of the problem’s dominant parameters. As such, the dimensionless groups of the parameters affecting the iceberg draft estimation were determined for the first time in the present study. Using the dimensionless groups recognized and the linear regression(LR) analysis, nine LR models(i.e., LR 1 to LR 9) were developed and then validated using a comprehensive dataset, which has been constructed in this study. A sensitivity analysis distinguished the premium LR models and important dimensionless groups. The best LR model, as a function of all dimensionless parameters, was able to estimate the iceberg draft with the highest level of precision and correlation along with the lowest degree of complexity. The ratio of iceberg length to iceberg height as the “iceberg length ratio” and the ratio of iceberg width to iceberg height as the “iceberg width ratio” was detected as the important dimensionless groups in the estimation of the iceberg draft. An uncertainty analysis demonstrated that the best LR model was biased towards underestimating the iceberg drafts. The premium LR model outperformed the previous empirical models.Ultimately, a set of LR-based relationships were derived for estimating the iceberg drafts for practical engineering applications, e.g., the early stages of the iceberg management projects.

Dilution characteristics of dual buoyant jets in wavy cross-flow environment

Due to the difference in density between the discharge effluent and coastal water,partially treated wastewater is often discharged into the marine environment as a buoyant jet via submarine outfalls with multiport diffusers.The dilution characteristics of effluent discharge(dual buoyant jets)in a wavy cross-flow environment were studied in a laboratory.The planar laser-induced fluorescence technique was used to obtain the concentration data of the jets.The effects of different environmental variables on the diffusion and dilution characteristics of the jets were examined through physical experiments,dimensional analysis,and empirical formulations.It was found that the dilution process of the dual jets could be divided into two components:the original jet component and the effluent cloud component.The jet-to-current velocity ratio was the main parameter affecting the concentration levels of the effluent cloud.The merging of the two jets increased the jet concentration in the flow field.When the jets traveled further downstream,the axial dilution increased gradually and then increased significantly along the axis.Under the effects of strong waves,the concentration contours branched into two peaks,and the mean dilution became more significant than under the effects of weak waves.Therefore,the dilution of the effluent discharge was expected to be significant under strong wave effects because the hydrodynamic force increased.A dilution equation was derived to improve our understanding of the dilution process of buoyant jets in a wavy cross-flow environment.This equation was used to determine the influences of the jet-to-current velocity ratio,wave-to-current velocity ratio,and Strouhal number on the minimum jet dilution.It revealed that the wave and buoyancy effects in effluent discharges were significant.

A model to determine hole spacing in the rock fracture process by non-explosive expansion material

The application of the non-explosive expansion material （NEEM） is widely used as the controlled fracture method in quarry min- ing, especially in hard rocks. The pressure of NEEM is an important parameter in causing rock fracture. An empirical model based on hole spacing was developed to determine the pressure of NEEM in the rock fracture process. Primarily, the empirical model was developed by the mathematical method, utilizing dimensional analysis. Then, the Phase2 code, which is based on the finite element method, was utilized to predict crack growth in rocks. The results of numerical analysis show slight deviations from the empirical model. Hence, the polynomial re- gression analysis was used to modify the model. Finally, the modified model shows a good agreement with the results gained from numerical modeling.