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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 Rayleigh–Plesset equation ： ウィキペディア英語版 Rayleigh–Plesset equation In fluid mechanics, the Rayleigh–Plesset equation is an ordinary differential equation which governs the dynamics of a spherical bubble in an infinite body of liquid. Its general form is usually written as :$\backslash frac\; =\; R\backslash frac\; +\; \backslash frac\backslash left(\backslash frac\backslash right)^2\; +\; \backslash frac\backslash frac\; +\; \backslash frac$ where :$P\_B(t)$ is the pressure within the bubble, assumed to be uniform :$P\_\backslash infty(t)$ is the external pressure infinitely far from the bubble :$\backslash rho\_L$ is the density of the surrounding liquid, assumed to be constant :$R(t)$ is the radius of the bubble :$\backslash nu\_L$ is the kinematic viscosity of the surrounding liquid, assumed to be constant :$S$ is the surface tension of the bubble Provided that $P\_B(t)$ is known and $P\_\backslash infty(t)$ is given, the Rayleigh–Plesset equation can be used to solve for the time-varying bubble radius $R(t)$. The Rayleigh–Plesset equation is derived from the Navier–Stokes equations under the assumption of spherical symmetry.〔 Neglecting surface tension and viscosity, the equation was first derived by John Strutt, 3rd Baron Rayleigh in 1917. The equation was first applied to traveling cavitation bubbles by Milton S. Plesset in 1949. == Derivation == The Rayleigh–Plesset equation can be derived entirely from first principles using the bubble radius as the dynamic parameter.〔 Consider a spherical bubble with time-dependent radius $R(t)$, where $t$ is time. Assume that the bubble contains a homogeneously distributed vapor/gas with a uniform temperate $T\_B(t)$ and pressure $P\_B(t)$. Outside the bubble is an infinite domain of liquid with constant density $\backslash rho\_L$ and dynamic viscosity $\backslash mu\_L$. Let the temperature and pressure far from the bubble be $T\_\backslash infty$ and $P\_\backslash infty(t)$. The temperature $T\_\backslash infty$ is assumed to be constant. At a radial distance $r$ from the center of the bubble, the varying liquid properties are pressure $P(r,t)$, temperature $T(r,t)$, and radially outward velocity $u(r,t)$. Note that these liquid properties are only defined outside the bubble, for $r\; \backslash ge\; R(t)$. 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「Rayleigh–Plesset 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.