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The Third Invariant Form of hydrodynamic equations and Application for Definition of Water Hammer Characteristics in Pipe

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Journal of Mechanics Engineering and Automation 2014年第1期4卷 85-90页

作者： Nguyen An Nien Nguyen Binh Duong Department of Hydraulics & Hydraulic Structures Southern Institute for Water Resources Research

There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms had important roles in the development of theoretical and practical applications of hydro-aerodynamics and related industries. The third invariant form of hydrodynamic equations is one for the dimensions of spaces. For this goal, the hyper quantities （space and physics） are introduced. Then these are created we can easily cover all problems in arbitrary dimensions （3D, 2D, 1D, separate space for liquids or constituent matters）. In particularly, when they are applied to water hammer problem, which is an especially problem, we can receive immediately celerity and pressure of the event.

关键词： hydrodynamic equations invariant form water hammer.

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Effect of Ion Concentrations on the Characteristics of a Multi-Component Magnetized Plasma Sheath

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Plasma Science and Technology 2009年第6期11卷 642-646页

作者： M.M.HATAMI B.SHOKRI Laser-Plasma Research Institute of Shahid Beheshti University G.C.EvinTehranIran Physical Department and Laser-Plasma Research Institute of Shahid Beheshti University G.C.EvinTehranIran

A hydrodynamic approach is used to investigate a three-component magnetized plasma sheath which consists of electrons and two species of positive ions. Assuming a phase space of one-dimensional spatial coordinate system and three-dimensional velocity coordinate system, the effect of different concentrations of positive ion species on some characteristics of the plasma sheath such as the velocity and density distribution of positive ion species and the electrostatic potential of this region is investigated. The calculated results show that the increase in the density ratio of positive ion species causes a decrease in both the ion velocities and the electrostatic potential of the sheath region. Also, it is shown that in the sheath region of a magnetized plasma consisting of only one positive ion species the bumps of the net density of charged particles disappears much faster. In addition, three-dimensional velocity of each positive ion species in the sheath region is plotted for different concentrations of positive ion species.

关键词： magnetized plasma plasma and electropositive plasma sheath hydrodynamic equations multi-component sheath

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