Dimensional Analysis

A relationship between the leakage current and wind velocity, which is the first of its kind, has been proposed in this paper. This relationship has been derived based on Dimensional Analysis technique. The proposed relationship has been applied for prediction of leakage current in the 275 kV insulators of YTL (Yeoh Tiong Lay) Power Station, which situated at the coast of South China Sea, Terrengannu, Malaysia. The calculated results were compared with the measured leakage current data. There was an excellent concordance between the experimental results and those calculated from the mathematical model.

Most of the hydraulic geometry relationships derived under premises that there are direct or indirect relation, at least statistically, between meander geometry characteristics and some hydraulic variables as discharge and velocity. The authors, based on-a-site investigation on Al-Abbasia reach, in the middle of the Euphrates river, Najaf governorate, developed power functions (four models). The study-reach is about six kilometers, it is divided into twenty one cross-sections. These sections represent the meanders and bends in the reach. The recent work is to develop models depending on dimensional analysis and Buckingham Pi theorem. These models are correlate the river width and mean depth with other geometry and hydraulic characteristics. The statistical comparison of the different methods illustrate that the method of dimensional analysis gives higher results in width model comparing with method of power function and lower in mean depth, but acceptable.

In this paper, a combined use of dimensional analysis (DA) and modern statistical design of experiment (DOE) methodologies is proposed for a hydrodynamics experiment where there are a large number of variables. While DA is well-known, DOE is still unfamiliar to most ocean engineers although it has been shown to be useful in many engineering and non-engineering applications. To introduce

Fractal measurements using the Cantor's dust method in a linear one-dimensional analysis mode were made on the fracture patterns revealed on two-dimensional, planar surfaces in four granites. This method allows one to conclude that: (1) The fracture systems seen on two-dimensional surfaces in granites are consistent with the part of fractal theory that predicts a repetition of patterns on different scales of observation, self similarity. Fractal analysis gives essentially the same values of D on the scale of kilometres, metres and centimetres (five orders of magnitude) using mapped, surface fracture patterns in a Sierra Nevada granite batholith (Mt. Abbot quadrangle, Calif.). (2) Fractures show the same fractal values at different depths in a given batholith. Mapped fractures (main stage ore veins) at three mining levels (over a 700 m depth interval) of the Boulder batholith, Butte, Mont. show the same fractal values although the fracture disposition appears to be different at different levels. (3) Different sets of fracture planes in a granite batholith, Central France, and in experimental deformation can have different fractal values. In these examples shear and tension modes have the same fractal values while compressional fractures follow a different fractal mode of failure. The composite fracture patterns are also fractal but with a different, median, fractal value compared to the individual values for the fracture plane sets. These observations indicate that the fractal method can possibly be used to distinguish fractures of different origins in a complex system. It is concluded that granites fracture in a fractal manner which can be followed at many scales. It appears that fracture planes of different origins can be characterized using linear fractal analysis.

We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents theta, whose exact numerical values are given for which x(-theta) or t(theta z) has the dimension of particle size distribution function psi(x,t), where z is the kinetic exponent. We obtained conditions for which the scaling and fragmentation process altogether breaks down, and we give an explicit scaling solution for a special case. Finally, we identify a new class of fractals ranging from random to nonrandom and show that the fractal dimension increases with increasing order and a transition to a strictly self-similar pattern occurs when randomness completely ceases.

The dimensional analysis of an object from an image reduces a lot of burden for a user, like the traditional measuring tape method. Using the dimensions will make reconstruction of the 3D model of the real-time object easier. However, this method is not used in the current implementation. Dimensional analysis can also be helpful in online shopping where the user's availability for fitting is not possible. 3D model replaces the fitting stage in online shopping. Once the dimensions of an object's surface are found, it is easy to calculate surface areas, given surface areas we can calculate volume. But the calculation of volume requires more than one dimension of the object. In this paper, an approach using a reference object, whose real-time dimensions are already known is used. The whole process is divided into three tasks-Object detection using SURF algorithm, Dimensional Analysis of the 2D object using pixel per metric ratio given that there is a reference object on the same plane and 3D reconstruction using Structure from Motion algorithm.

In an attempt to prove Euclid's fifth postulate, Legendre applied the principle of homogeneity. This was apparently the second historical use of dimensional analysis. This paper describes and analyses Legendre's work. It is shown that he assumed as a basis of his argument the inexistence of an absolute length standard-as Lambert did before him. Some reactions against and for Legendre's ideas are presented. It is shown that Legendre's work was premature: his method did not have a solid foundation, and the mathematicians of his time had good reasons to dismiss his arguments as invalid.

Scaling up of suspension dosage form is considered a challenge as pharmaceutical suspensions are thermodynamically unstable. During the scale-up process, the effect of operational variables on the dispersion process, and physical properties affecting overall attributes need systematic evaluation. Though the scale up process can be studied using dimensional analysis, mathematical modeling, and computer simulation, most of the work in the field of suspension manufacturing still depends on empirical studies and the principles of geometric similarities. Various aspects of the scale up process, technology transfer, and process analytical technology (PAT) applications in suspension manufacturing are discussed.

This book provides readers with the most current, accurate, and practical fluid mechanics related applications that the practicing BS level engineer needs today in the chemical and related industries, in addition to a fundamental understanding of these applications based upon sound fundamental basic scientific principles. The emphasis remains on problem solving, and the new edition includes many more examples.

Mathematical modeling considered as one of the influencing means for drip irrigation improvement to develop efficient and economical system designs. Inadequate mathematical models may lead to an underestimation of head losses calculations. This study concerns the factors affect friction head losses in lateral line and to establish the relationship between them.  The accurate design of drip irrigation laterals needs to determine the total energy losses that include the pipe friction losses along the lateral line and minor losses due to emitter connections. Laboratory experiments were conducted to measure friction head losses for emitter spacing from 0.3 to 2.4 m, pipe inner diameter 13.1, 15.6, and 17 mm, protrusion barb area 14.49, 21.375, 28.78 mm2 (for on-line emitters), emitter cylinder length from 30 to 68 mm, and emitter inner diameter from 11.2 to 15.5 mm (for built-in emitters) at values of Reynolds number varied from 6000 to 21000. Two mathematical models were developed to predict the friction head losses in lateral equipped with on-line and integrated built-in emitters. The parameters affecting the friction head losses in lateral defined in dimensionless terms using Buckingham’s Π theorem. The developed models were accounted for 98% of the variation in measured data. The friction head losses were calculated using the developed models and there was an acceptable accuracy comparing with the previously proposed models. A friendly user interface computer program named EGY-DRIP SYSTEMS had developed for drip irrigation system design. The program had written in Microsoft visual basic 2013. EGY-Drip SYSTEMS program carries out hydraulic calculations of a sub-unit design for drip irrigation system. The hydraulic calculation based on data inputs about water supply, soil, evapotranspiration, crop (vegetables, fruit, and field crops), and irrigation system components (drippers, pipes, and fittings). The program supported with an up-gradable Microsoft access database to facilitate data input by the user. EGY-DRIP SYSTEMS program is outfitted with an open source computer aided drafting program (QCAD) for pipeline network layout drafting.

" No book has been devoted to the dimensional analysis until 1922 –a hundred years after the appearance of Fourier's Traité – as P.W. Bridgman published the course he taught at Yale University. " This is what Monod-Herzen (1976, p. 25) affirms. Between both books, Fourier's 1822 and Bridgman's 1922, James Clerk Maxwell paved the way for the consolidation of this discipline, and his seed did not fall on barren ground. In Spain, without going any further, Maxwell's work took root very soon. So much history belies the French epistemologist. Yes, there is a book on dimensional analysis between Fourier and Bridgman. It is Physical Units written by the Spanish physicist José Muñoz del Castillo, who published it in 1890, that is thirty-two years before the publication of the book by Bridgman. Physical Units thus becomes the first treatise devoted to dimensional analysis. Naturally I will not question that Bridgman's Dimensional Analysis has been the first complete treatise on this discipline. But it is not the first book in which the theory of dimensions is presented, as it could be known in the nineteenth century, twenty four years before the proposal by Buckingham of his famous theorem π. The purpose of this article is to highlight the acceptance and development of dimensional analysis in Spain in the 19th century, a circumstance so far not sufficiently appreciated by the specialized historiography.

Geotechnical centrifuge modelling has been a world-wide used technology in
physical tests. In this papers a derivation of scaling laws by dimensional analysis for the
centrifugal modelling is presented. Basic principles of centrifuge modelling are described.
Scaling laws for slow events like consolidation and fast events like dynamic loads are
shown. The differences in scale factors for both processes are noticed. The aim of this paper
is to introduce geotechnical centrifuge technology to a wider Polish audience.