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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 Crocco's theorem ： ウィキペディア英語版 Crocco's theorem Crocco's theorem is a fluid dynamics theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first enunciated by Alexander Friedmann for the particular case of a perfect gas and published in 1922:〔Friedmann A. An essay on hydrodynamics of compressible fluid (Опыт гидромеханики сжимаемой жидкости), Petrograd, 1922, 516 p., (reprinted ) in 1934 under the editorship of Nikolai Kochin (see the first formula on page 198 of the reprint).〕 :$\backslash frac=T\; \backslash nabla\backslash ,s-\backslash nabla\; \backslash ,h$ However, usually this theorem is connected with the name of Italian scientist Luigi Crocco,〔Crocco L. (Eine neue Stromfunktion für die Erforschung der Bewegung der Gase mit Rotation ). ZAMM, Vol. 17, Issue 1, pp. 1–7, 1937. DOI: 10.1002/zamm.19370170103. Crocco writes the theorem in the form $\backslash scriptstyle\backslash mathrm\backslash ,\backslash mathbf\; u\backslash times\backslash mathbf\; u=T\backslash mathrm\backslash ,S$ for perfect gas (the last formula on page 2).〕 a son of Gaetano Crocco. Consider an element of fluid in the flow field subjected to translational and rotational motion: because stagnation pressure loss and entropy generation can be viewed as essentially the same thing, there are three popular forms for writing Crocco's theorem: # Stagnation pressure: $\backslash mathbf\; u\; \backslash times\; \backslash boldsymbol\; \backslash omega\; =v\; \backslash nabla\; p\_0$ 〔Shapiro, Ascher H. "National Committee for Fluid Mechanics Films Film Notes for 'Vorticity,'" 1969. Encyclopaedia Britannica Educational Corporation, Chicago, Illinois. (retrieved from http://web.mit.edu/hml/ncfmf/09VOR.pdf (5/29/11)〕 # Entropy (the following form holds for plane steady flows): $T\; \backslash frac\; =\; \backslash frac\; +u\; \backslash omega$ 〔Liepmann, H. W. and Roshko, A. "Elements of Gasdynamics" 2001. Dover Publications, Mineola, NY (eq. (7.33)).〕 # Momentum: $\backslash frac\; +\; \backslash nabla\; \backslash left(\backslash frac\; +\; h\; \backslash right)\; =\; u\; \backslash times\; \backslash boldsymbol\; \backslash omega\; +\; T\; \backslash nabla\; s\; +\; \backslash mathbf,$ In the above equations, $\backslash mathbf\; u$ is the flow velocity vector, $\backslash omega$ is the vorticity, $v$ is the specific volume, $p\_0$ is the stagnation pressure, $T$ is temperature, $s$ is specific entropy, $h$ is specific enthalpy, $\backslash mathbf$ is specific body force, and $n$ is the direction normal to the streamlines. All quantities considered (entropy, enthalpy, and body force) are ''specific'', in the sense of "per unit mass". == References == * * * * 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「Crocco's theorem」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.