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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 pulsatile flow ： ウィキペディア英語版 pulsatile flow In fluid dynamics, a flow with periodic variations is known as pulsatile flow. The cardiovascular system of chordate animals is a very good example where pulsatile flow is found. Pulsatile flow is also observed in engines and hydraulic systems as a result of rotating mechanisms belonging to them. == Derivation == To obtain the velocity profile of non-stationary flow, one must solve the equations of motion and continuity. Depending on the complexity of the boundary conditions, the problem's analytic solution may be impracticable and thus numerical simulations would be necessary. An analytical solution is here given assuming the following hypothesis: *Fluid is homogeneous, incompressible and Newtonian; *Tube wall is rigid, circular and cylindrical; *Motion is laminar, axisymmetric and parallel to the tube's axis; *Boundary conditions are axisymmetry at the centre and no-slip condition on the wall; *Pressure gradient drives the fluid; *Gravitation has no effect on the fluid. The field equations Navier-Stokes equation and the equation of continuity are simplified as :$\backslash rho\; \backslash frac\; =\; -\backslash frac\; +\; \backslash mu\; \backslash left(\backslash frac\; +\; \backslash frac\; \backslash frac\backslash right)\; \backslash ,$ and :$\backslash frac\; =\; 0\; \backslash ,\; .$ The pressure gradient is a general periodic function :$\backslash frac\; =\; \backslash sum^N\_C\_n\; e^\; \backslash ,\; .$ Flow velocity profile is driven by the pressure, resulting in :$u(r,t)\; =\; \backslash sum^N\_U\_n\; e^\; \backslash ,\; .$ Substituting the pressure gradient and flow velocity profile in the Navier-Stokes equation gives us :$i\backslash rho\; n\backslash omega\; U\_n\; =\; -C\_n\; +\backslash mu\; \backslash left(\backslash frac\; +\; \backslash frac\; \backslash frac\backslash right)\; \backslash ,\; .$ With the boundary conditions satisfied, the general solution is :$U\_n(r)\; =\; A\_nJ\_0\; \backslash left(\; \backslash alpha\; \backslash frac\; n^i^\; \backslash right)\; +\; B\_nY\_0\; \backslash left(\; \backslash alpha\; \backslash frac\; n^i^\; \backslash right)\; +\; \backslash frac\backslash ,\; ,$ where $J\_0(kr)$ is the Bessel function of first kind and order zero, $Y\_0(kr)$ is the Bessel function of second kind and order zero, being $k$ a constant. $A\_n$ and $B\_n$ are arbitrary constants and $\backslash alpha$ is the dimensionless Womersley number. In order to determine $A\_n$ and $B\_n$ the axisymetic boundary condition is used, i.e. $\backslash partial\; U\_n/\; \backslash partial\; r\; =\; 0$, then the derivatives $J\_0\text{'}$ and $Y\_0\text{'}$ approaches infinity. Hence $B\_n$ must vanish. And the boundary condition at the wall gives us :$U\_n(R)\; =\; 0\; =\; A\_nJ\_0\; \backslash left(\; \backslash alpha\; n^i^\; \backslash right)\; +\; \backslash frac\backslash ,\; .$ Solving this equation for $A\_n$, we obtain the amplitudes of the velocity profile :$U\_n(r)\; =\; \backslash frac\; \backslash left(1\; -\; \backslash frac\; n^i^)\})\}\; \backslash right)\; \backslash ,\; ,$ which leads to the velocity profile itself :$u(r)\; =\; \backslash sum^N\_\; \backslash frac\; \backslash left(1\; -\; \backslash frac\; n^i^)\})\}\; \backslash right)\; e^\; \backslash ,\; .$ The velocity profile depends on Womersley number $\backslash alpha$. 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「pulsatile 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.