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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Young–Laplace equation ： ウィキペディア英語版 Young–Laplace equation In physics, the Young–Laplace equation () is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It is a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness): :$\backslash begin$ \Delta p &= -\gamma \nabla \cdot \hat n \\ &= 2 \gamma H \\ &= \gamma \left(\frac + \frac\right) \end where $\backslash Delta\; p$ is the pressure difference across the fluid interface, γ is the surface tension (or wall tension), $\backslash hat\; n$ is the unit normal pointing out of the surface, $H$ is the mean curvature, and $R\_1$ and $R\_2$ are the principal radii of curvature. (Some authors refer inappropriately to the factor $2H$ as the total curvature.) Note that only normal stress is considered, this is because it can be shown〔(Surface Tension Module ), by John W. M. Bush, at MIT OCW.〕 that a static interface is possible only in the absence of tangential stress. The equation is named after Thomas Young, who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young–Laplace–Gauss equation, as Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions using Johann Bernoulli's virtual work principles. ==Soap films== (詳細はminimal surface. Note that this is not valid for a soap bubble, because its inner volume is enclosed and has a different pressure from the outside. 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「Young–Laplace equation」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.