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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 Basset–Boussinesq–Oseen equation ： ウィキペディア英語版 Basset–Boussinesq–Oseen equation In fluid dynamics, the Basset–Boussinesq–Oseen equation (BBO equation) describes the motion of – and forces on – a small particle in unsteady flow at low Reynolds numbers. The equation is named after Joseph Valentin Boussinesq, Alfred Barnard Basset and Carl Wilhelm Oseen. ==Formulation== One formulation of the BBO equation is the one given by , for a spherical particle of diameter $d\_p$, position $\backslash boldsymbol=\backslash boldsymbol\_p(t)$ and mean density $\backslash rho\_p$ moving with particle velocity $\backslash boldsymbol\_p=\backslash text\; \backslash boldsymbol\_p\; /\; \backslash textt$ – in a fluid of density $\backslash rho\_f$, dynamic viscosity $\backslash mu$ and with ambient (undisturbed local) flow velocity $\backslash boldsymbol\_f:$〔With referring to 〕 :$$ \begin \frac \rho_p d_p^3 \frac_p} &= \underbrace_p \right)}_ d_p^3 \boldsymbol p}_ \rho_f d_p^3\, \frac t} \left( \boldsymbol_f - \boldsymbol_p \right)}_ d_p^2 \sqrt \int_} \left( \boldsymbol_f - \boldsymbol_p \right)\, \text \tau}__k}_ This is Newton's second law, with in the left-hand side the particle's rate of change of linear momentum, and on the right-hand side the forces acting on the particle. The terms on the right-hand side are respectively due to the: # Stokes' drag, # pressure gradient, with $\backslash boldsymbol$ the gradient operator, # added mass, # Basset force and # other forces on the particle, such as due to gravity, etc. The particle Reynolds number $R\_e:$ :$R\_e\; =\; \backslash frac\_f\; \backslash right|\; \backslash right\backslash \}\backslash ,\; d\_p\}$ has to be small, , for the BBO equation to give an adequate representation of the forces on the particle. Also suggest to estimate the pressure gradient from the Navier–Stokes equations: :$$ -\boldsymbol p = \rho_f \frac_f} - \mu \boldsymbol\!\cdot\!\boldsymbol \boldsymbol_f, with $\backslash text\; \backslash boldsymbol\_f\; /\; \backslash text\; t$ the material derivative of $\backslash boldsymbol\_f.$ Note that in the Navier–Stokes equations $\backslash boldsymbol\_f(\backslash boldsymbol,t)$ is the fluid velocity field, while in the BBO equation $\backslash boldsymbol\_f$ is the undisturbed fluid velocity at the particle position: $\backslash boldsymbol\_f(t)=\backslash boldsymbol\_f(\backslash boldsymbol\_p(t),t).$ 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「Basset–Boussinesq–Oseen 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.