翻訳と辞書 Words near each other ・ Helen Brach ・ Helen Bradley ・ Helen Bray ・ Helen Brewster Owens ・ Hele & Co ・ Hele (disambiguation) ・ Hele baronets ・ Hele Bay ・ Hele Railway Station ・ Hele's School ・ Hele's School, Exeter ・ Hele, Devon ・ Hele, Hainan ・ Hele-On Bus ・ Hele-Shaw clutch ・ Hele-Shaw flow ・ Heleanna ・ Heleanna chloreis ・ Heleanna melanomochla ・ Helebridge ・ Helechawa, Kentucky ・ Helechosa de los Montes ・ Heleen Hage ・ Heleen Jaques ・ Heleen Mees ・ Heleen Sancisi Weerdenburg ・ Heleen van Royen ・ Helegiu ・ Helegiu River ・ Heleia Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hele-Shaw flow ： ウィキペディア英語版 Hele-Shaw flow Hele-Shaw flow (named after Henry Selby Hele-Shaw) is defined as Stokes flow between two parallel flat plates separated by an infinitesimally small gap. Various problems in fluid mechanics can be approximated to Hele-Shaw flows and thus the research of these flows is of importance. Approximation to Hele-Shaw flow is specifically important to micro-flows. This is due to manufacturing techniques, which creates shallow planar configurations, and the typically low Reynolds numbers of micro-flows. The governing equation of Hele-Shaw flows is identical to that of the inviscid potential flow and to the flow of fluid through a porous medium (Darcy's law). It thus permits visualization of this kind of flow in two dimensions. ==Mathematical formulation of Hele-Shaw flows== Let $x$, $y$ be the directions parallel to the flat plates, and $z$ the perpendicular direction, with $2H$ being the gap between the plates (at $z=\backslash pm\; H$). When the gap between plates is asymptotically small : $H\; \backslash rightarrow\; 0,\; \backslash ,$ the velocity profile in the $z$ direction is parabolic (i.e. is a quadratic function of the coordinate in this direction). The equation relating the pressure gradient to the velocity is, : $=\; p\; \backslash frac\; \backslash ,$ where $$ is the velocity , $p(x,y,t)$ is the local pressure, $\backslash mu$ is the fluid viscosity. This relation and the uniformity of the pressure in the narrow direction $z$ permits us to integrate the velocity with regard to $z$ and thus to consider an effective velocity field in only the two dimensions $x$ and $y$. When substituting this equation into the continuity equation and integrating over $z$ we obtain the governing equation of Hele-Shaw flows, : $\backslash frac+\backslash frac=0.$ This equation is supplemented by the no-penetration boundary conditions on the side walls of the geometry, : $p\; \backslash cdot\; \backslash hat\; n=\; 0\; \backslash ,$ where $\backslash hat\; n$ is a unit vector perpendicular to the side wall. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hele-Shaw flow」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.