• 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%.

• Fire Science and Engineering
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• v.32 no.2
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• pp.17-23
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• 2018

In this study, the relations of the wall thermal conductivity and surface temperature in a compartment fire are investigated using Buckingham Pi theorem. The dimensionless parameters of the previous study are analyzed in order to correlate the dimensionless groups of the heat release rate, the thermal conductivity, the volume of compartment and the convective heat transfer coefficient. In addition the reduced scale of compartment, which has 1/6 size of ISO 9705 Room Corner Tester, is manufactured and the oxygen concentration and the maximum temperature in the space are measured for the gasoline pool fire ($10cm{\times}10cm$, $15cm{\times}15cm$ and $20cm{\times}20cm$). Finally, the criterion of the wall temperature increase are suggested in accordance with the thermal conductivity and the convective heat transfer coefficient. In addition, the dimensionless empirical equation using Buckingham Pi theorem considering the heat release rate are presented suggested. The results of this study will be useful especially for the fire phenomenon investigation of the wall thermal conductivity coefficient and shape in the compartment space.

• Journal of Korean Society of Water and Wastewater
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• v.19 no.6
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• pp.827-837
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• 2005

In this study, we derived a new non-dimensional variable including bubble size and air diffusing area by Buckingham's theorem for making a practical correlation with experimental results. Firstly, we drew a relationship between a non-dimensional variable, $NH/u_s$, which has a form of Froude number and destratification efficiency with a simple theoretical consideration. Then we derived two non-dimensional variables by Buckingham's ${\pi}$-theorem and equating them with a form of $Fr_N$ for making single parameter to correlate overall destratification efficiency. As the result, the single parameter Be number shows a correlations with destratification efficiencies obtained from laboratory and pilot experiments. Also, for the practical applications, we conducted multiple regression analysis using Be and tank area to make predictive equations about destratification efficiency. The result also shows a successful correlations with destratification efficiency ($R^2$>0.9, p<0.001). Using this equation, we proposed a new design methodology with respect to bubble diffusing area.

• Journal of the Korean Society for Marine Environment & Energy
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• v.2 no.1
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• pp.34-39
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• 1999

Removal of spilled oil over the sea and the river has become one of the urgent problems in these days. Removing oil using mechanical devices by adhesion method is known to be closely related with the problem of estimating the thickness of film remaining on the surface of solid withdrawn from a quiescent liquid. In the present study a series of experimental results are compared with the analytic estimation for the thickness of film remaining on the solid surface using non-dimensional analysis. For the case of pure water both results show the remarkable agreement. However, discrepancy has been found for the case of Bunker C oil and diesel oil. The analytic estimation over-predicts the experimental value for the case of Bunker C oil and under-predicts it for the case of diesel oil. Further study is required to investigate the real situation including a contact angle and the property difference between oil and water.

• Smart Structures and Systems
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• v.6 no.1
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• pp.57-72
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• 2010

This paper presents the most significant results obtained within a broad-ranging experimental program aiming to evaluate both the effectiveness and the robustness of a Base Isolation (BIS) and a Tuned Mass Damper (TMD) combined control strategy (BI & TMD). Following a brief description of the experimental model set-up and the adopted kinematic scaling technique, this paper describes the identification procedures carried out to characterize the system''s model. The dynamic response of a small-scale model to recorded earthquake excitations, which has been scaled by using the Buckingham pi-theorem, are later presented and discussed. Finally, the effectiveness and robustness of the combined control strategy is evaluated by comparing the model's dynamic response. In particular, reduction in relative displacements and absolute accelerations due to the application of different mass damping systems is investigated.

• 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 Mechanical Science and Technology
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• v.15 no.9
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• pp.1328-1338
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• 2001

The objective of this study is to present flow and pressure drop characteristics of R22 in adiabatic capillary tubes of inner diameters of 1.2 to 2.0mm, and tube lengths of 500 to 2000mm. Distributions of temperature and pressure along capillary tubes and the refrigerant flow rates through the tubes were measured for several condensing temperatures and various degrees of subcooling at the capillary tube inlet. Condensing temperatures of R22 were selected as 40, 45, and 50$^{\circ}C$ at the capillary tube inlet, and the degree of subcooling was adjusted to 1 to 18$^{\circ}C$. Experimental results including mass flow rates and pressure drops of R22 in capillary tubes were provided. A new correlation based on Buckingham II theorem to predict the mass flow rate through the capillary tube was presented considering major parameters which affect the flow and pressure drop characteristcis.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.23 no.4
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• pp.251-258
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• 2011

The objective of this study is to propose two empirical correlations to predict the mass flow rate through an automotive block type thermostatic expansion valve and then to evaluate the correlations. The first correlation is deduced by modifying the basic equation of the orifice meter for the mass flow rate and the second correlation is deduced by using the Buckingham's ${\pi}$ theorem. The first correlation showed very good agreement on the measured data for R134a, given by Monforte. Average relative deviation and standard deviation of it are 2.5% and 1.6%, respectively. The second correlation agreed on the same measured data with a little greater deviations. The two correlations may apply to common expansion valves which have different geometrical sizes of the same shape.

• Journal of Korean Tunnelling and Underground Space Association
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• v.8 no.3
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• pp.205-217
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• 2006

Rock and discontinuities are main factors consisting of a rock mass and the physical properties of each factor have direct effects on the mechanical stability of artificial structures in the rock mass. Because physical properties of the rock and discontinuities change a lot according to the size of test materials, a close attention is needed when the physical properties, obtained from laboratory tests, are used for the design of field structures. In this study, change of physical properties of intact materials due to the change of their size are studied. Six kinds of artificial materials including crystal, instead of an intact rock, are adopted for the study to guarantee the homogeneity of specimen materials even with relatively large size. Uniaxial strength and Young's modulus of each artificial material are checked out for a size effect and compared with the predicted values by Buckingham's theorem - dimensional analysis. A numerical analysis using PFC (Particle Flow Code) is also applied and primary factors influencing on the size effect are investigated.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.1
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• pp.33-44
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• 1982

In Order to study for the aeration characteristics which is one of the most important unit processes for the activated sludge process, a pitched blade type aeration model of octagonal shape with a draft tube in it was made as a pilot plant. Oxygen transfer rates, power consumptions and fluid velocities and behaviers were measured and evaluated with the various turbine shapes. And with these results, the dimensionless model analysis using the Buckingham ${\pi}$ theorem was discussed for a proper turbine shape determination.