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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 Torricelli's law ： ウィキペディア英語版 Torricelli's law Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing out of an opening to the height of fluid above the opening. Torricelli's law states that the speed of efflux, ''v'', of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth ''h'' is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height ''h'', i.e. $v\; =\; \backslash sqrt$, where ''g'' is the acceleration due to gravity (9.81 N/kg near the surface of the earth). This last expression comes from equating the kinetic energy gained, $\backslash fracmv^2$, with the potential energy lost, ''mgh'' , and solving for ''v''. The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle. ==Derivation== Bernoulli's principle states that: :$+gz+=\backslash text$ where ''v'' is fluid speed, ''g'' is the gravitational acceleration (9.81 m/s^2), ''z'' is the fluid's height above a reference point, ''p'' is pressure, and ''ρ'' is density. Define the opening to be at ''z''=0. At the top of the tank, ''p'' is equal to the atmospheric pressure. ''v'' can be considered 0 because the fluid surface drops in height extremely slowly compared to the speed at which fluid exits the tank. At the opening, ''z''=0 and ''p'' is again atmospheric pressure. Eliminating the constant and solving gives: :$gz+=+$ :$\backslash Rightarrow\; v^2=2gz\backslash ,$ :$\backslash Rightarrow\; v=\backslash sqrt$ ''z'' is equivalent to the ''h'' in the first paragraph of this article, so: :$v=\backslash sqrt$ 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「Torricelli's law」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.