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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 Blasius boundary layer ： ウィキペディア英語版 Blasius boundary layer In physics and fluid mechanics, a Blasius boundary layer (named after Paul Richard Heinrich Blasius) describes the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate which is held parallel to a constant unidirectional flow $U$. The solution to the Navier–Stokes equation for this flow begins with an order-of-magnitude analysis to determine what terms are important. Within the boundary layer the usual balance between viscosity and convective inertia is struck, resulting in the scaling argument :$\backslash frac\backslash approx\; \backslash nu\backslash frac+\backslash dfrac=0$ x-Momentum: $u\backslash dfrac+v\backslash dfrac=\backslash dfrac$ (note that the x-independence of $U$ has been accounted for in the boundary-layer equations) admit a similarity solution. In the system of partial differential equations written above it is assumed that a fixed solid body wall is parallel to the x-direction whereas the y-direction is normal with respect to the fixed wall, as shown in the above schematic. $u$ and $v$ denote here the x- and y-components of the fluid velocity vector. Furthermore, from the scaling argument it is apparent that the boundary layer grows with the downstream coordinate $x$, e.g. :$$ \delta(x)\approx \left( \frac \right)^. This suggests adopting the similarity variable :$\backslash eta=\backslash frac=y\backslash left(\; \backslash frac\; \backslash right)^$ and writing :$u=U\; f\; \text{'}(\backslash eta).$ It proves convenient to work with the stream function $\backslash psi$, in which case :$\backslash psi=(\backslash nu\; U\; x)^\; f(\backslash eta)$ and on differentiating, to find the velocities, and substituting into the boundary-layer equation we obtain the Blasius equation :$$ f + \fracf f'' =0 subject to $$ f=f'=0 on $\backslash eta=0$ and $f\text{'}\backslash rightarrow\; 1$ as $\backslash eta\backslash rightarrow\; \backslash infty$. This non-linear ODE can be solved numerically, with the shooting method proving an effective choice. The shear stress on the plate :$\backslash tau\_\; =\; \backslash frac\}\{\backslash sqrt\{Ux\}\}.$ can then be computed. The numerical solution gives $f\text{'}\text{'}\; (0)\; \backslash approx\; 0.332$. ==Falkner–Skan boundary layer== We can generalize the Blasius boundary layer by considering a wedge at an angle of attack $$ from some uniform velocity field $U\_$. We then estimate the outer flow to be of the form: $u\_(x)=\; U\_\; \backslash left(\; x/L\; \backslash right)\; ^$ Where $L$ is a characteristic length and ''m'' is a dimensionless constant. In the Blasius solution, m = 0 corresponding to an angle of attack of zero radians. Thus we can write: $$ = \frac As in the Blasius solution, we use a similarity variable $$ to solve the Navier-Stokes Equations. :$$ = y \sqrt}\left(\frac\right)^} It becomes easier to describe this in terms of its stream function which we write as :$$ \psi=U(x)\delta(x)f(\eta) = y \sqrtL}}\left(\frac\right)^\fracf(\eta) Thus the initial differential equation which was written as follows: :$$ u + v = c^m x^ + . Can now be expressed in terms of the non-linear ODE known as the Falkner–Skan equation (named after V. M. Falkner and Sylvia W. Skan〔V. M. Falkner and S. W. Skan, ''Aero. Res. Coun. Rep. and Mem.'' no 1314, 1930.〕). :$$ \frac+f\frac+ \beta \left(\right )=0 (note that $m=0$ produces the Blasius equation). See Wilcox 2007. In 1937 Douglas Hartree revealed that physical solutions exist only in the range $-0.0905\; \backslash le\; m\; \backslash le\; 2$. Here, m < 0 corresponds to an adverse pressure gradient (often resulting in boundary layer separation) while m > 0 represents a favorable pressure gradient. 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「Blasius boundary layer」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.