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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 Volume viscosity ： ウィキペディア英語版 Volume viscosity Volume viscosity (also called second viscosity or bulk viscosity) becomes important only for such effects where fluid compressibility is essential. Examples would include shock waves and sound propagation. It appears in the Stokes' law (sound attenuation) that describes propagation of sound in Newtonian liquid. ==Derivation and Use== The negative-one-third of the trace of the Cauchy stress tensor is often identified with the thermodynamic pressure, :$-T\_a^a\; =\; p,$ which only depends upon the equilibrium state potentials like temperature and density (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution and another contribution which is proportional to the divergence of the velocity field. This constant of proportionality is called the volume viscosity. Volume viscosity appears in the Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics 〔Happel, J. and Brenner , H. "Low Reynolds number hydrodynamics", ''Prentice-Hall'', (1965)〕, 〔Landau, L.D. and Lifshitz, E.M. "Fluid mechanics", ''Pergamon Press'',(1959)〕 and acoustics 〔Litovitz, T.A. and Davis, C.M. In "Physical Acoustics", Ed. W.P.Mason, vol. 2, chapter 5, ''Academic Press'', NY, (1964)〕, .〔Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", ''Elsevier'', (2002)〕 :$\backslash rho\; \backslash left(\backslash frac\; +\; \backslash mathbf\; \backslash cdot\; \backslash nabla\; \backslash mathbf\backslash right)\; =\; -\backslash nabla\; p\; +\; \backslash mu\; \backslash nabla^2\; \backslash mathbf\; +\; \backslash mathbf\; +(\backslash frac\backslash mu\; +\; \backslash zeta)\; \backslash nabla\; (\backslash nabla\; \backslash cdot\; \backslash mathbf)$ where $\backslash zeta$ is the volume viscosity coefficient. Authors who use the alternative term ''bulk viscosity'' for the same parameter include 〔Morse, P.M. and Ingard, K.U. "Theoretical Acoustics", ''Princeton University Press''(1986)〕, .〔Graves, R.E. and Argrow, B.M. "Bulk viscosity:Past to Present", ''Journal of Thermophysics and Heat Transfer'',13, 3, 337-342 (1999)〕 This additional term disappears for ''incompressible fluid'', when the divergence of the flow equals 0. This viscosity parameter is additional to the usual dynamic viscosity μ. 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「Volume viscosity」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.