• Title/Summary/Keyword: Velocity slope

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A Case Study on Teaching and Learning of the Linear Function in Constant Velocity Movement: Focus on Integrated Curriculum of Mathematics and Science (등속도 운동에서 일차함수 교수-학습 과정에 관한 사례연구: 수학과 과학의 통합교육 관점을 기반으로)

  • Shin, Eun-Ju
    • Journal of Educational Research in Mathematics
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    • v.15 no.4
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    • pp.419-444
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    • 2005
  • As a theoretical background for this research, the literatures which focus on teaching and loaming of connecting with mathematics and science were investigated. And the rationale of integrated curriculum on the basis of the 7th mathematics curriculum and the goal of mathematics education and the forms of integrated curriculum and the integrated curriculum in foreign school were investigated. Depending on this review, the implement method of the integrated curriculum of mathematics and science in Korea school is suggested as the following: It requires designing inter-disciplinary into-grated problem or various teaching and learning materials which are based upon concept, skill, and principle by commonality found across the subject matter. Based on the analyses upon described above, three inter-disciplinary integrated teaching and learning materials were developed. And then, based on the case stud)', the research questions were analyzed in depth. Students could understand the developing process of linear function, develop the formula and grape representing the relationship between time and velocity, time and distance, and interpret realistic meaning of the slope.

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A Study on the Estimation of Discharge in Unsteady Condition by Using the Entropy Concept (엔트로피 개념에 의한 부정류 유량 산정에 관한 연구)

  • Choo, Tai Ho;Chae, Soo Kwon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.12
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    • pp.6159-6166
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    • 2012
  • A discharge measurement is difficult in flood season which is especially important in the water resources field and the continuous discharge measurement for all rivers is impossible on the present system. So, the stage-discharge curve has been used for a long time to produce discharge data of rivers. However, there has been problems from a reliability angle due to the fact that this method uses only stage-discharge relationship, although the stage-discharge curve has the convenience. Therefore, a new mean velocity equation was derived by using Chiu's 2D velocity formula of the entropy concept in this paper. The derived equation reflected hydraulic characteristics such as the depth, gravity acceleration, hydraulic radius, energy slope, kinematic coefficient of viscosity, etc. and estimated also a maximum velocity. In addition, this method verified the relationship between a mean and maximum velocity and estimates an equilibrium state ${\phi}(M)$ well presenting properties of a river cross section as the results. The mean velocity was estimated by using the equilibrium state ${\phi}(M)$, and then the discharge was estimated. To prove this equation to be accurate, the comparison between the measured and estimated discharge is conducted by using the measured laboratory data in the unsteady condition flow showing loop state and the results are consistent. If this study is constantly carried out by using various laboratory and river data, this method will be widely utilized in water resources field.

Application of Laser Distance Measurer to measure ground surface displacement in slopes (사면의 지표변위 측정을 위한 레이저 거리측정기의 활용)

  • Cho, Yong-Chan;Song, Young-Suk
    • Journal of the Korean Geosynthetics Society
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    • v.13 no.1
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    • pp.23-31
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    • 2014
  • In this study, the method to measure effectively the ground surface displacement of slope was proposed using the Laser Distance Measurer (LDM). Applying the proposed technique is more simple and easier than the complicated and high-priced instrument to measure the ground surface displacement. LDM is an instrument that the red laser aimed at the target and then the reflected laser used for calculating the distance. The advantages of LDM are easy operating method, high measurement precision and lower in price. To check the feasibility, the proposed method applied to the real site that the ground surface displacement of slope was occurred continuously. The ground surface displacements were occurred in various points of the natural and cut slopes located at the lower part of coal mine waste heap due to the load of waste heap. To measure directly the ground surface displacement in this site, 6 measurement sections and 26 measurement points were selected. As the result of the displacement measured by the proposed technique within a certain period time, the accumulative ground surface displacement could be measured as well as the velocity of displacement could be estimated. Also, the progress direction of ground surface displacement can be confirmed and predicted through the analysis of all measured result.

A Method of Rating Curve Adjustment (수위유량곡선보정방법에 대하여)

  • 박정근
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.18 no.2
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    • pp.4116-4120
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    • 1976
  • With the use of many rivers increased nearly to the capacity, the need for information concerning daily quantities of water and the total annual or seasonal runoff has became increased. A systematic record of the flow of a river is commonly made in terms of the mean daily discharge Since. a single observation of stage is converted into discharge by means of rating curve, it is essential that the stage discharge relations shall be accurately established. All rating curves have the looping effect due chiefly to channel storage and variation in surface slope. Loop rating curves are most characteristic on streams with somewhat flatter gradients and more constricted channels. The great majority of gauge readings are taken by unskilled observers once a day without any indication of whether the stage is rising or falling. Therefore, normal rating curves shall show one discharge for one gauge height, regardless of falling or rising stage. The above reasons call for the correction of the discharge measurements taken on either side of flood waves to the theoretical steady-state condition. The correction of the discharge measurement is to consider channel storage and variation in surface slope. (1) Channel storage As the surface elevation of a river rises, water is temporarily stored in the river channel. There fore, the actual discharge at the control section can be attained by substracting the rate of change of storage from the measured discharge. (2) Variation in surface slope From the Manning equation, the steady state discharge Q in a channel of given roughness and cross-section, is given as {{{{Q PROPTO SQRT { 1} }}}} When the slope is not equal, the actual discharge will be {{{{ { Q}_{r CDOT f } PROPTO SQRT { 1 +- TRIANGLE I} CDOT TRIANGLE I }}}} may be expressed in the form of {{{{ TRIANGLE I= { dh/dt} over {c } }}}} and the celerity is approximately equal to 1.3 times the mean watrr velocity. Therefore, The steady-state discharge can be estimated from the following equation. {{{{Q= { { Q}_{r CDOT f } } over { SQRT { (1 +- { A CDOT dh/dt} over {1.3 { Q}_{r CDOT f }I } )} } }}}} If a sufficient number of observations are available, an alternative procedure can be applied. A rating curve may be drawn as a median line through the uncorrected values. The values of {{{{ { 1} over {cI } }}}} can be yielded from the measured quantities of Qr$.$f and dh/dt by use of Eq. (7) and (8). From the 1/cI v. stage relationship, new vlues of 1/cI are obtained and inserted in Eq. (7) and (8) to yield the steady-state discharge Q. The new values of Q are then plotted against stage as the corrected steadystate curve.

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A Study on Transportation Characteristics of Debris dependent on Geologic Conditions (지질조건에 따른 사태물질 이동특성 고찰)

  • Chae Byung-Gon;Kim Won-Young;Lee Choon-Oh;Kim Kyeong-Su;Cho Yong-Chan;Song Young-Suk
    • The Journal of Engineering Geology
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    • v.15 no.2 s.42
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    • pp.185-199
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    • 2005
  • Properties of sliding materials are dependent on the lithology because debris is the product of rock weathering processes. In order to characterize transportation behavior of debris dependent of debris types, this study selected 26 debris flows over three areas composed with different rock weathering types and topographic conditions. Analyses of lithology, weathering, and topographic characteristics were performed by detailed field survey. Based on the field survey data, transportation behavior of debris was studied at the aspect of the relationship of grain size and volume of debris as well as topographic conditions. According to the study results, change of slope angle is very influential factor on runout distance of debris among the topographic factors. Because the sliding velocity and the energy of debris are frequently changed and more irregular on an undulating slope, the unout distance of debris is larger than that of an uniformly dipping slope. Runout distance of debris is also influenced by volume and grain size of debris. Volume of debris in the gabbro is four or five times larger than that of the granite area because it is controlled by the lithology. Considered with grain size distribution, runout distance of debris is longer in the gabbro area which is composed with irregular grain size bearing large corestones than that in the medium grained granite area.

AIR ENTRAINMENT AND ENERGY DISSIPATION AT STEPPED DROP STRUCTURE

  • Kim Jin Hong
    • Water Engineering Research
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    • v.5 no.4
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    • pp.195-206
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    • 2004
  • This paper deals with oxygen transfer by air entrainment and energy dissipations by flow characteristics at the stepped drop structure. Nappe flow occurred at low flow rates and for relatively large step height. Dominant flow features included an air pocket, a free-falling nappe impact and a subsequent hydraulic jump on the downstream step. Most energy was dissipated by nappe impact and in the downstream hydraulic jump. Skimming flow occurred at larger flow rates with formation of recirculating vortices between the main flow and the step comers. Oxygen transfer was found to be proportional to the flow velocity, the flow discharge, and the Froude number. It was more related to the flow discharge than to the Froude number. Energy dissipations in both cases of nappe flow and skimming flow were proportional to the step height and were inversely proportional to the overflow depth, and were not proportional to the step slope. The stepped drop structure was found to be efficient for water treatment associated with substantial air entrainment and for energy dissipation.

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A Study on the Behavior of Brine Lumps Caused by Dropping Brine (염수투하에 따른 염수괴 거동에 관한 연구)

  • ;K. Nakatsuji
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.3 no.1
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    • pp.21-28
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    • 1991
  • this paper, two-dimensional behaviors of the brine lumps moving along the inclined boundaries are investigated experimentally and theoretically. It was investigated these factors in the brine lumps which are behaviors. shape. length change. height change. and moving velocity change. The results were compared the above factors with thermal theory. The shape of the brine lumps is well apporximated by a half-ellipse. The shape of the brine lumps was similar with the slope thermal and the moving characteristics were found to reappear with the turbulent thermal theory.

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A Study of Seepage in Earth Structure of Zone Types (이형제체의 침투에 관한 연구)

  • Shin, Bang Woong;Lee, Bong Jik
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.11 no.1
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    • pp.135-144
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    • 1991
  • The phreatic surface in earth embankment of zone types are investigated in this thesis. Also the shape of phreatic surface are analyzed according to rising velocity and slope angle. In order to verify the validity of experimental results, the results are compared with theoretical result. From this comparison, the shape of phreatic surface in multi-layer is predicted by heat transfer equation.

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A Parabolic Wave Model Applicable to Large Area (광역에 적용가능한 포물선형 파랑모형)

  • 이정렬
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.8 no.3
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    • pp.246-255
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    • 1996
  • A mild slope equation of parabolic type is derived with the revision of the 2nd order differential term and a new approach for the application to large area is presented. The replacement with long waves can overcome the numerical difficulty due to small waves over the system of large grid sizes. No matter how long the replaced wave length is, the refraction and shoaling are maintained by toeing its own wave speed and group velocity, respectively. However, the diffraction effect is modified by means of Eikonal equation. The developed numerical model was applied to the shoal of Ito and Tanimoto (1972) to yield the satisfactory results.

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Numerical Study on the Wind Flow Over Hilly Terrain (언덕지형을 지나는 유동의 수치해석적 연구)

  • 김현구;이정묵;경남호
    • Journal of Korean Society for Atmospheric Environment
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    • v.13 no.1
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    • pp.65-77
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    • 1997
  • A theoretical and numerical investigation on the boundary-layer flow over a two- or three-dimensional hill is presented. The numerical model is based on the finite volume method with boundary-fitted coordinates. The k-$\varepsilon$ turbulence model with modified wall function and the low-Reynolds-number model are employed. The hypothesis of Reynolds number independency for the atmospheric boundary-layer flow over aerodynamically rough terrain is confirmed by the numerical simulation. Comparisons of the mean velocity profiles and surface pressure distributions between the numerical predictions and the wind-tunnel experiments on the flow over a hill show good agreement. The linear theory provides generally good prediction of speed-up characteristics for the gentle-sloped hills. The flow separation occurs in the hill slope of 0.5 and the measured reattachment points are compared with the numerical prediction. It is found that the k- $\varepsilon$ turbulence model is reasonably accurate in predicting the attached flow, while the low- Reynolds-number model is more suitable to simulate the separated flows.ows.

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