• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1999.05a
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• pp.157-160
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• 1999

The paper provides the results of failure analysis for the porcelain suspension insulators. The comparisons of characteristics were made as a function of failed and unfailed isulators which had been used in real distribution line. This paper also described the failure modes which could be occurred in the fields. The cracks inside cap were detected though measuring the resistance or the leakage current. The ratio of open porosity was calculated from the Archimedes Method. The failure analyses of porcelain suspension insulators were conducted from the various analysis method.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1981-1986
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• 2004

A cross-flow fan relatively makes high dynamic pressure at low speed because a working fluid passes through an impeller blade twice and blades have a forward curved shape. Therefore, the performance of a cross-flow fan is influenced 25% by the impeller, 60% by the rearguider and the stabilizer, 15% by the heat exchanger. At the low flow rate, there exists a rapid pressure head reduction, a noise increase and an unsteady flow against a stabilizer and a rearguider. Moreover, it is difficult to analyze the reciprocal relations of the cross-flow fan because each parameter is independent. Numerical analyses are conducted with different starting angles of the rearguider. Two-dimensional, unsteady governing equations are solved, using FVM, PISO algorithm, sliding grid system and ${\kappa}-{\varepsilon}$ standard turbulence model.

• Journal of Navigation and Port Research
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• v.28 no.2
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• pp.141-148
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• 2004

The observations of rapid motion of bubbles under water for approximately 50ms or less in high . magnetic fields of 10 T have been carried out successfully for the first time. The observation system constructed is composed of a high-speed video camera, a telescope, a cryostat with a split-type superconducting magnet, a light source, a mirror and a transparent sample cell. Using this system, the influence of magnetic field on the path and shape of single bubbles of $O_2$(paramagnetism) and $N_2$ (diamagnetism) has been examined carefully. Experimental values describing the path are in good agreement with theoretical values calculated on the basis of the magneto-Archimedes effect, despite the effect of magnetism on the bubble. However, no effect of magnetism on the shape of the bubble is observed In addition, the influence of magnetic field on drag coefficient of the bubble is discussed.

• Tribology and Lubricants
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• v.20 no.3
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• pp.157-162
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• 2004

The cam curve of a balance type vane pump consists usually of circular arcs and Archimedes' spirals. However, if they are connected directly together, the curve must have a few discontinuous points of the gradients and the motion of the vanes is no longer smooth. Designing data for an oil hydraulic vane pump used in power steering system were obtained by the acquisition of optimum cam profile data which can be available to reduce noises and vibrations through the minimization of cavitation with the improvement of suctional performance. The performance test is carried on the trial manufactures by measuring the volumetric and the mechanical efficiency. And from that result, maintaining the same characteristic as the conventional one in the relief pressure and noise level, the experimental pump discharges 0.7 $\ell$/min and shows nearly 3.5% enhancement in the total efficiency more than the conventional one.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.17-24
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• 2003

The Pythagorean equation $x^2{＋}y^2{=}z^2$ and Pythagorean triple had appeared in the Babylonian clay tablet made between 1900 and 1600 B. C. Another quadratic equation called Pell equation was implicit in an Archimedes' letter to Eratosthenes, so called ‘cattle problem’. Though elliptic equation were contained in Diophantos’ Arithmetica, a substantial progress for the solution of cubic equations was made by Bachet only in 1621 when he found infinitely many rational solutions of the equation $y^2{=}x^3{-}2$. The equation $y^2{=}x^3{+}c$ is the simplest of all elliptic equations, even of all Diophantine equations degree greater than 2. It is due to Bachet, Dirichlet, Lebesque and Mordell that the equation in better understood.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.407-417
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• 2022

Archimedes proved that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and the chord AB is four thirds of the area of the triangle ∆ABP. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ℝ². As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.

• School Mathematics
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• v.7 no.4
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• pp.391-402
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• 2005

The purpose of this study is to resolve misunderstanding for centroid of a triangle and to clarify several logical problems in finding the centroid of a Polygon. The conclusions are the followings. For a triangle, the misunderstanding that the centroid of a figure is the intersection of two lines that divide the area of the figure into two equal part is more easily accepted caused by the misinterpretation of a median. Concerning the equilibrium of a triangle, the median of it has the meaning that it makes the torques of both regions it divides to be equal, not the areas. The errors in students' strategies aiming for finding the centroid of a polygon fundamentally lie in the lack of their understanding of the mathematical investigation of physical phenomena. To investigate physical phenomena mathematically, we should abstract some mathematical principals from the phenomena which can provide the appropriate explanations for then. This abstraction is crucial because the development of mathematical theories for physical phenomena begins with those principals. However, the students weren't conscious of this process. Generally, we use the law of lever, the reciprocal proportionality of mass and distance, to explain the equilibrium of an object. But some self-evident principles in symmetry may also be logically sufficient to fix the centroid of a polygon. One of the studies by Archimedes, the famous ancient Greek mathematician, gives a solution to this rather awkward situation. He had developed the general theory of a centroid from a few axioms which concerns symmetry. But it should be noticed that these axioms are achieved from the abstraction of physical phenomena as well.

• Journal of computational fluids engineering
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• v.13 no.4
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• pp.72-79
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• 2008

This study is to investigate the air flow around a sirocco fan which is used in a range hood. The main object of the study is to improve the flow rate of the fan by analysis of unsteady 3-dimensional incompressible flow. Overall analysis is carried out using CFD method. For this, we used a commercial code, SC/Tetra, and used a sliding mesh method to give the same condition as an actual state. First, verification of the CFD results is done by comparing the experimental data with the numerical data for the suction flow rate. It is confirmed that two results are well consistent. Then for the improvent of flow rate, the effect of shape factors such as diameter ratio of fan, geometry of case, cut-off aperture and guide angle of case exit on the suction flow rate was considered. Especially, for a new design of housing, the principle of Archimedes spiral was used. The overall analysis was applied to a new design of housing, and the result showed an increase of flow rate by 10.7%.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.19-30
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• 2008

Cavalieri is chiefly remembered for his work on the problem "indivisibles." Building on the work of Archimedes, he investigated the method of construction by which areas and volumes of curved figures could be found. Cavalieri regarded an area as made up of an indefinite number of parallel line segments and a volume of an indefinite number of parallel plane areas. He called these elements the indivisibles of area and volume. Cavalieri developed a method of the indivisibles which he used to determine areas and volumes. We call this Cavalieri's principle which states that there exists a plane such that any plane parallel to it intersects equal areas In both objects, then the volumes of the two objects are equal. Cavalieri's principle and method of the indivisibles are very important to understand of volume of a pyramid for gifted students.

• 한국신재생에너지학회:학술대회논문집
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• 2010.11a
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• pp.89.1-89.1
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• 2010

본 연구는 세라믹 연결재로 사용되는 Perovskite 구조의 LSTO조성의 실제 SOFC stack 적용을 위한 소결온도를 낮출 수 있는 방법에 관해 연구하였다. SOFC 단전지에서 IC 소재는 $1300{\sim}1400^{\circ}C$에서 소결이 이루어져야만 하나 현재 사용하고 있는 LCO계 조성의 경우 $1500{\sim}1600^{\circ}C$의 높은 온도에서 소결이 이루어지며 고온에서 $Cr_2O_3$의 휘발로 인해 낮은 전기전도성을 갖는 문제점을 가지고 있다. 이러한 문제점을 해결하기 위해 IC 소재에 소결조제를 첨가하여 소결특성을 평가하였고, SEM과 XRD분석을 통하여 perovskite 단일상이 합성된 것을 확인하였다. 또한 Archimedes법을 사용하여 흡수율 및 겉기공율을 측정하였고, DC analyzer를 사용하여 전기전도도를 측정한 결과 대기분위기 $750^{\circ}C$에서 높은 값을 나타냄을 확인할 수 있었다.