• Water for future
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• v.29 no.4
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• pp.187-198
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• 1996

A numerical model for unsteady dispersion of horizontal line source in turbulent shear flow is developed. A fractional step finite difference method is used which splits the unsteady two-dimensional advective diffusion equation into the longitudinal advection and the vertical diffusion equations, and solves them alternately for half time intervals by the Holly-Preissmann scheme and the Crank-Nicholson scheme, respectively. The developed numerical model is verified using a semi-analytic solution for steady dispersion in turbulent shear flow. Dispersion of an instantaneous plane source in turbulent shear flow is analyzed using the model. The degree of mixing at the same dimensionless time is almost the same regardless of the friction factor, and the travel distance required to reach a certain degree of mixing is inversely proportional to the square root of the friction factor.

• Water for future
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• v.28 no.3
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• pp.205-216
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• 1995

Existing equations for dispersion coefficient are analyzed in depth to select proper dispersion coefficient which can represent dispersion characteristics of natural streams. Several equations are tested with measured data which were collected in 26 streams in the United States. Findings of this study are as follows. Elder's equation should not be used to estimate dispersion coefficient of the one-dimensional dispersion model because it underestimates significantly. McQuivey and Keefer's equation is overestimating, whereas Magazine et al.'s equation is underestimating. However, Iwasa and Aya's equation predicts relatively well. Fischer's equation is generally overestimating. Liu's equation predicts quite well. The performance of Liu's equation is the best of all especially in terms of accuracy. However, Liu's equation is generally overestimating in case of large river because the square of channel width is included in the equation. Therefore, it is recommended not to use Liu's equation in case of large rivers, especially rivers of which channel width is larger than 200m.

• Structural Engineering and Mechanics
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• v.76 no.4
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• pp.551-559
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• 2020

On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

• The Journal of the Acoustical Society of Korea
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• v.22 no.7
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• pp.545-553
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• 2003

This paper is concerned with protecting piezoelectric transducers used in an ultrasonic flowmeter from the high temperature of hot fluid in a pipe by using a waveguide and with improving the propagation of ultrasonic longitudinal vibration in the waveguide. Waveguide material has been chosen for efficient insulation of heat transferred in the waveguide, and the minimum length of the waveguide for protecting piezoelectric transducer has been estimated. Forced response of the longitudinal vibration in a uniform circular rod has been obtained and the length of the waveguide has been selected for maximum amplitude. Longitudinal vibration response of a conically-tapered rod excited at a natural frequency has been obtained to confirm that wave motion is amplified as the cross-sectional size of the waveguide decreases along the axial direction. The fact that dispersion of a pulse wave in a waveguide is reduced as the cross-sectional radius is decreased has been examined theoretically and confirmed experimentally by using a single-rod waveguide. A bundle-type waveguide has proven to be a practical one through the evaluation of the wave propagation performance.

• Journal of Soil and Groundwater Environment
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• v.11 no.6
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• pp.53-60
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• 2006

Single well injection withdrawal tracer tests with bromide were carried out at two wells developed in a horizontally heterogeneous fractured rock. The hydraulic conductivity of TW-1 well was 5 times larger than TW-2 well, and the average linear velocity of TW-2 well was 1.8 times faster than TW-1 well. The difference of hydrodynamic dispersions of two wells in the fractured rock was studied with the analysis of concentration breakthrough curves and cumulative mass recovery curves of bromide with withdrawal time, and the estimation of average travel distance, pore velocity, longitudinal dispersivity and longitudinal dispersion coefficient. The average travel distances of bromide were estimated to be 3.00 m in TW-1 well and 5.62 m in TW-2 well. The average pore velocities for the injection/withdrawal phase were estimated to be $4.31\;{\times}\;10^{-4}\;m/sec$ in TW-1 well and $8.08\;{\times}\;10^{-4}\;m/sec$ in TW-2 well. Average travel distance and pore velocity were higher in TW-2 well because of small effective porosity. Longitudinal dispersivities were estimated to be 28.73 cm in TW-1 well and 18.49 cm in TW-2 well, and bromide transport was 1.55 times faster in TW-1 well. Longitudinal dispersion coefficients were estimated to be $5.14\;{\times}\;10^{-6}\;m^2/sec$ in TW-1 well and $6.06\;{\times}\;10^{-6}\;m^2/sec$ in TW-2 well, and diffusion area was 1.18 times larger in TW-2 well.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.8
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• pp.575-582
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• 2015

This paper deals with the dispersion relation of the waves sustained in a cylindrical shell submerged in the fluid. The waveguide finite method and the boundary element method are used to predict the dispersion characteristic of the cylindrical shell. The dispersion diagram of the cylinder is estimated from the eigenvalue problem and the forced vibration response. It follows that the water-loading leads to the decrease of the cut-on frequencies and the phase speeds of the bending waves. On the contrary, the longitudinal waves and the torsional waves are hardly affected by the fluid, and therefore the order of the cut-on frequencies of the waves is changed. The acoustic dispersion diagram is also estimated from the forced acoustic response to identify the characteristics of the wave radiated to the fluid. It follows that the acoustic waves on and near the surface of the cylinder are the same as those in the structure. But at the far field the acoustic waves caused by subsonic waves e.g., the bending waves disappear as the increase of the distance. Conclusively, the characteristics of waves in cylindrical shells are significantly affected by water-loading in terms of the cut-on frequency, the wave speed, the order of the cut-on and radiation.

• Coupled systems mechanics
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• v.12 no.1
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• pp.41-68
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• 2023

The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discrete-analytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.

• Journal of Soil and Groundwater Environment
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• v.12 no.6
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• pp.17-25
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• 2007

Convergent flow tracer test for 2 m (IW-1 well) and 5 m (IW-2 well) of test scale was conducted at the alluvial aquifer with high permeability and storativity. Pumping rate for convergent flow tracer test were $2,500m^3/day$, and the chloride tracer of 5 kg was instantaneously injected into IW-1 and IW-2 wells. Differences of first arrival time and peak concentration were analyzed by using the concentration breakthrough curves of chloride. Recovered chloride mass were analyzed by recovered cumulative mass curves. And, increment and decrement for chloride concentration were analyzed through chloride concentration versus recovered cumulative mass ratio graphs. Also, increment and decrement ratios of chloride concentration were estimated through linear regression analyses for increment and decrement intervals of chloride concentration. Longitudinal dispersivities were estimated by quot;Converging Radial Flow With Instantaneous Injectionquot; method using CATTI code. Longitudinal dispersivities estimated by CATTI code were 0.4152 m between pumping well and IW-1 well, and 3.2665 m between pumping well and IW-2 well. Longitudinal dispersivity was increased according to far distance from the pumping well. The longitudinal dispersivity according to distance were estimated as 0.21 between pumping well and IW-1 well, and 0.65 between pumping well and IW-2 well.

• Water for future
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• v.12 no.1
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• pp.56-59
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• 1979

A prompt subsurface runoff producing mechanism whih creaters a depletion curve of direct runoff hydrograph is simulated by a dead zone dispersion model technique. Runoff processes are carried out by routing of the outflow resulted from previous linear channel and effective rainfall from its corresponding subwatershed through a series of conceptual linear channels representing subwatersheds of a catchment. Working rules are explained for evaluation the model parameters such as translatory velocity, diffusive factor, and parameters concerning the infiltration and relative magnitude of the prompt subsurface flow region.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.6
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• pp.388-395
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• 1986

Dispersion characteristics of shielded single, coupled and edge-offset microstrip structures are investigated by using hybrid mode analysis with Galerkin's method in the spectral domain. Two new basis functions for the longitudinal strip current are proposed and convergence rates of the solutions for the basis functions are compared. Current distribution of the coupled line is obtaind from that of the single line by using shift theorem of the Fourier transform. In addition, effects of off-centered inner strip conductor on dispersion are also discussed Numerical results include various structual parameters and are compared with other available data and good agreements are observed.