• Advances in Computational Design
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• v.8 no.2
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• pp.133-145
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• 2023

Scaling and similitude large scale structural member to small scale model is considered the most important matter for the experimental tests because of the difficulty in controlling, lack of capacities and expenses, furthermore that most of MSc and PhD students suffering from choosing the suitable specimen before starting their experimental study. The current study adopts to take large scale slab with opening as a case study of structural member where the slab is squared with central squared opening, the boundary condition is fixed from all sides, the load represents by four concentrated force in four corners of opening, as well as, the study adopts Buckingham theorem which has been used for scaling, all the parameters of the problem have been formed in dimensionless groups, the main groups have been connected by a relations, those relations are represented by force, maximum stress and maximum displacement. Finite element method by ANSYS R18.1 has been used for analyzing and forming relations for the large scale member. Prediction analysis has been computed for three small scale models by depending on the formed relations of the large scale member. It is found that Buckingham theorem is considered suitable way for creating relations among the parameters for any structural problem then making similitude and scaling the large scale members to small scale members. Finally, verification between the prediction and theoretical results has been done, it is observed that the maximum deviation between them is not more than 2.4%.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• International Journal of Air-Conditioning and Refrigeration
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• v.12 no.4
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• pp.192-197
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• 2004

A capillary tube, which is a common expansion device in small sized refrig-eration and air-conditioning systems, should be redesigned properly to establish an optimum operation cycle of a refrigerating system with alternative refrigerants. Based on experimental data for R-22, R-290, and R-407C, an empirical correlation is developed to predict mass flow rate through capillary tubes. Dimensionless parameters are derived from the Buckingham Pi theorem, considering the effects of operating conditions and capillary tube geometry on mass flow rate. Approximately $97\%$ of the present data are correlated within a relative deviation of $\pm\;10\%.$ The present correlation also predicts the data obtained from open literature within $\pm\;15\%.$ In addition, rating charts of refrigerant flow rate for R-12, R-22, R-134a, R-152a, R-407C, R-410A, R-290, and R-600a are developed.

• Journal of Environmental Health Sciences
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• v.45 no.2
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• pp.192-202
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• 2019

Objectives: According to the central limit theorem, the samples in population might be considered to follow normal distribution if a large number of samples are available. Once we assume that toxicity dataset follow normal distribution, we can treat and process data statistically to calculate genus or species mean value with standard deviation. However, little is known and only limited studies are conducted to investigate whether toxicity dataset follows normal distribution or not. Therefore, the purpose of study is to evaluate the generally accepted normality hypothesis of aquatic toxicity dataset Methods: We selected the 8 chemicals, which consist of 4 organic and 4 inorganic chemical compounds considering data availability for the development of species sensitivity distribution. Toxicity data were collected at the US EPA ECOTOX Knowledgebase by simple search with target chemicals. Toxicity data were re-arranged to a proper format based on the endpoint and test duration, where we conducted normality test according to the Shapiro-Wilk test. Also we investigated the degree of normality by simple log transformation of toxicity data Results: Despite of the central limit theorem, only one large dataset (n>25) follow normal distribution out of 25 large dataset. By log transforming, more 7 large dataset show normality. As a result of normality test on small dataset (n<25), log transformation of toxicity value generally increases normality. Both organic and inorganic chemicals show normality growth for 26 species and 30 species, respectively. Those 56 species shows normality growth by log transformation in the taxonomic groups such as amphibian (1), crustacean (21), fish (22), insect (5), rotifer (2), and worm (5). In contrast, mollusca shows normality decrease at 1 species out of 23 that originally show normality. Conclusions: The normality of large toxicity dataset was not always satisfactory to the central limit theorem. Normality of those data could be improved through log transformation. Therefore, care should be taken when using toxicity data to induce, for example, mean value for risk assessment.