• Title/Summary/Keyword: Experimental equation

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A Study on Comparison of the Darcy-Weisbach and Hazen-Williams Equation (Darcy-Weisbach와 Hazen-Williams Equation 비교 연구)

  • Kim, Tae-Kyoungi;Rhee, Kyoung-Hoon;Sun, Byoung-Jin;Chio, Cheong-Ho
    • Journal of Korean Society of Water and Wastewater
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    • v.21 no.4
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    • pp.421-428
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    • 2007
  • Many engineering problems on the pipeline flow use continuity, energy, friction loss head equation. To calculate friction loss head in a pipeline, Darcy-Weisbach and many average velocity equations can be used and Hazen-Williams equation is used frequently in the pipe network for the water supply systems. Darcy-Weisbach equation is a general one acquired from applying Bernoulli's equation in the pipeline flow and Hazen-Williams equation is a experimental one in case that pipe velocity is below 3m/sec and pipe diameter is over 50mm. In this study, comparing Darcy-Weisbach with Hazen-Williams equation, relation f and C that are expressed as roughness coefficients of those equations is explained. Next, head losses calculated from using those equations are compared and those are applied in realistic pipelines. Comparing f with C, the f is decreasing linearly according to increase of the Reynolds number Re and increasing in case the C is decreasing. additionally, the C is increasing up to a point and then is decreasing according to increase of the Re. Next, the C is increasing and Re's range for increase of the C lengthens in case of decreasing of the relative roughness ${\varepsilon}/d$. Comparing head losses acquired from the two equations, head loss appears large in case that the C is decreasing and the ${\varepsilon}/d$ is increasing. additionally, Head loss calculated by the Darcy-Weisbach equation varies larger than one by Hazen-Williams equation in regard of the Re. Next, change aspect of head loss acquired by the C is distinguished more clearly than the one by the ${\varepsilon}/d$.

Experimental Study on Hysteresis Phenomena in Porous Media (다공성 매질에서 이력현상에 대한 실험적 연구)

  • 강우영;박재현
    • Water for future
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    • v.28 no.4
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    • pp.215-222
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    • 1995
  • The water retention function which has the hysteresis phenomena is required to analyze the Richards equation which is a governing equation of the unsaturated flow, and its hysteresis phenomena has influence upon the characteristics of the unsaturated flow. The accuracy of the published hysteresis models is compared by using experimental data of the water retention function. The apparatus to experiment the hysteresis phenomena on the soil is developed, and experimental data for the main wetting process and the main drying process of the water retention function are obtained. The parameters of the van Genuchten equation are calibrated by using experimentally obtained data. As a result of the comparison of the selected hysteresis models which simulate the main drying curve from the main wetting curve, the Model I-1(Mualem) overestimates and the Model II-1(Mualem) underestimates but the Model III-2(Park and Sonu) similarly estimates the experimental data of the main drying curve.

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Development of Adjusted Subcatchment Width Equation in SWMM (SWMM의 수정유역폭식 개발)

  • Bae, Deg-Hyo;Jang, Min-Seok
    • Journal of Korea Water Resources Association
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    • v.42 no.2
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    • pp.105-115
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    • 2009
  • The objectives of this study are to deduce a problem of existing subcatchment width equation in Storm Water Management Model(SWMM) and to analyze the suitability of a new adjusted subcatchment width equation on both ideally assumed watersheds and an actual urban watershed area. The problems of existing subcatchment equation are issued on the theoretical review of the equation and from the model application on different types of simplified assumed watershed. The adjusted equation, proposed in this study, that considers the pipe flows in addition to the surface flows on small subcatchment can improve the limitation of existing equation when applied on the assumed watersheds. Also, Gunja watershed with 96.3 ha is selected and collected rainfall-runoff events for the feasibility study of the proposed equation on actual urban watershed area. The results represent that the simulated flows from adjusted equation rather than the simulated flows from existing equation are well agreed with observed ones.

An Experimental Study on Scour at V-shaped Riffle (V형 여울에서 발생하는 세굴에 관한 실험 연구)

  • Yu, Dae-Young;Park, Jung-Hwan;Woo, Hyo-Seop
    • Journal of Korea Water Resources Association
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    • v.36 no.3 s.134
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    • pp.507-520
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    • 2003
  • A V-shaped riffle is an artificial hydraulic structure haying two wings from the streamside with a narrow opening in between. It is usually made of crushed stones or large boulders. It limits channel width and accelerates the flow through the constricted section causing a local scour just downstream. The V-shaped riffle provides with a unique aquatic habitat by forming a pool and sandbars around the pool edge, increasing local morphologic, hydraulic and sedimentological diversity. This study investigates experimentally the scour characteristics of the V-shaped riffle in the sandbed stream and proposes a predictive equation for the scour. Total 45 cases of experiments were conducted to examine the effect of hydraulic factors and configuration of V-shaped riffle on the geometry of scour holes. From the comparison of the experimental results of this study with the predictive equation of spur dike by Breusers and Raudkivi(1991), it is found that their predictive equation of spur dike underestimates the maximum scour depth downstream of the V-shaped riffle. h new predictive equation for the maximum scour depth was developed using the non-dimensional hydraulic and geometrical variables. The parameters used in the proposed equations were determined using the experimental data. The analysis reveals that the scour depth is dependent dominantly on the Froude number at the opening of the V-shaped riffle, while the angle of riffle and the opening width also affect the scour depth. The proposed equation for the scour of V-shaped riffle well agrees with the experimental data. It can be used for estimating the scour of the V-shaped riffle in sandbed streams.

Examination on the Experimental Prediction of Scour Depths Caused by Jets (\ulcorner㈎\ulcorner의한 세굴깊이의 실험적 예측에 대한 고찰)

  • Son, Kwang-Ik;Yoon, Se-Eui
    • Journal of Korea Water Resources Association
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    • v.30 no.6
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    • pp.743-751
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    • 1997
  • A thorough literatural review of researches on the experimental prediction of scour depths caused by jets was carried out to find out a measure of scour prediction. A new experimental equation for predicting scour depths due to a vortical or an inclined jet was developed from five hundreds of experimental data which were carefully reviewed and adopted from the previous researches. The developed equation shows 0.941 statistical correlation coefficient. It was found that the parameters governing the scour depth were the size of bed material, flow rate through unit width of spillway, and head drop across structure. The predicted scour depth could be expressed as the deepest scouring depth below tail water surface with correlation coefficient ${\gamma}$ = 0.941.

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A Study on the Propagation of Measurement Uncertainties into the Result on a Turbine Performance Test

  • Cho, Soo-Yong;Park, Chanwoo
    • Journal of Mechanical Science and Technology
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    • v.18 no.4
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    • pp.689-698
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    • 2004
  • Uncertainties generated from the individual measured variables have an influence on the uncertainty of the experimental result through a data reduction equation. In this study, a performance test of a single stage axial type turbine is conducted, and total-to-total efficiencies are measured at the various off-design points In the low pressure and cold state. Based on an experimental apparatus, a data reduction equation for turbine efficiency is formulated and six measured variables are selected. Codes are written to calculate the efficiency, the uncertainty of the efficiency, and the sensitivity of the efficiency uncertainty by each of the measured quantities. The influence of each measured variable on the experimental result is figured out. Results show that the largest uncertainty magnification factor (UMF) value is obtained by the inlet total pressure among the six measured variables, and its value is always greater than one. The UMF values of the inlet total temperature, the torque, and the RPM are always one. The uncertainty percentage contribution (UPC) of the RPM shows th, lowest influence on the uncertainty of the turbine efficiency, but the UPC of the torque has the largest influence to the result among the measured variables. These results are applied to find the correct direction for meeting an uncertainty requirement of the experimental result in the planning or development Phase of experiment, and also to offer ideas for preparing a measurement system in the planning phase.

Analysis on Dynamic Characteristics for Moving-Magnet Linear Oscillatory Actuator with Cylindrical Halbach Array (원통형 Halbach 배열 영구자석을 갖는 가동자석형 LOA의 동특성 해석)

  • Jang, Seok-Myeong;Choi, Jang-Young;Cho, Han-Wook
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.54 no.11
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    • pp.533-539
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    • 2005
  • In the previous work, we performed the analysis of a tubular type moving-magnet linear oscillatory actuator (LOA) with cylindrical Halbach array by using 2-d analytical formulas and confirmed validity of analytical results by comparison of those with both finite element (FE) computation and experimental results. This paper deals with the dynamic characteristic analysis of the moving-magnet LOA with cylindrical Halbach array. Control parameters such as the thrust constant, the back-emf constant, resistance and inductance are obtained from both analytical and experimental results. And then, the dynamic simulation algorithm is established by the state and output equation obtained from voltage and motion equation. Finally, for various values of frequency, the dynamic simulation and experimental results for the characteristics of the voltage, current and displacement of moving-magnet LOA are presented. The simulation results are validated extensively by experiments. The experimental and simulation results for the variation of stroke according to control voltage are also presented for various values of frequency.

Development of Effluent Concentration Estimation Equation from Treatment Wetland Experimental Data (수질개선용 인공습지 실험자료에 의한 유출수 농도 추정식 개발)

  • 윤춘경
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.41 no.5
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    • pp.86-92
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    • 1999
  • Effluent concentration estimation equations for wetland system were developed throught statistical analysis of treatment wetland experimental data. Existin g empirical equations were reviewed for thier accuracy with experimental data, and compared with the estimatin equations. About 70 experimental data sets were used for multiple regression, and variables include influent concentration, hydraulic loading rate, average daily air temperature , and plant coverage. The estimatin equations developed for BOD5 , SS ,T-P, and T-N predicted effluent concentrations moderately well, and coefficient fo determination ($R^2$) for them was 0.74 , 0.60, 0.59 and 0.58 respectively. The equations obtained from same data but excluding plant coverage showed relatively lower $R^2$ than the former case, and it was 0.66, 0.52, 0.41 and 0.57 respectively. The EPA, WPCF , and Kadlec and Knight equations worked poorly and $R^2$ for them was significantly lower than the estimation equation developed in the study. The reason might be that the existing equations were oversimplified that they did ot include important parameters such as air temperature and plant coverage. Therefore, developing reasonable estimation equations from experiment under realistic condition is highly recommended rather than using exiting estimation equations.

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Modified sigmoid based model and experimental analysis of shape memory alloy spring as variable stiffness actuator

  • Sul, Bhagoji B.;Dhanalakshmi, K.
    • Smart Structures and Systems
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    • v.24 no.3
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    • pp.361-377
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    • 2019
  • The stiffness of shape memory alloy (SMA) spring while in actuation is represented by an empirical model that is derived from the logistic differential equation. This model correlates the stiffness to the alloy temperature and the functionality of SMA spring as active variable stiffness actuator (VSA) is analyzed based on factors that are the input conditions (activation current, duty cycle and excitation frequency) and operating conditions (pre-stress and mechanical connection). The model parameters are estimated by adopting the nonlinear least square method, henceforth, the model is validated experimentally. The average correlation factor of 0.95 between the model response and experimental results validates the proposed model. In furtherance, the justification is augmented from the comparison with existing stiffness models (logistic curve model and polynomial model). The important distinction from several observations regarding the comparison of the model prediction with the experimental states that it is more superior, flexible and adaptable than the existing. The nature of stiffness variation in the SMA spring is assessed also from the Dynamic Mechanical Thermal Analysis (DMTA), which as well proves the proposal. This model advances the ability to use SMA integrated mechanism for enhanced variable stiffness actuation. The investigation proves that the stiffness of SMA spring may be altered under controlled conditions.

Wind-induced random vibration of saddle membrane structures: Theoretical and experimental study

  • Rongjie Pan;Changjiang Liu;Dong Li;Yuanjun Sun;Weibin Huang;Ziye Chen
    • Wind and Structures
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    • v.36 no.2
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    • pp.133-147
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    • 2023
  • The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.