低雷諾係數之薄長方形層流實驗

謝金邦(CHIN-BANG HSIEH)

指導教授 ： 賈至達

國立臺灣師範大學/理學院/物理學系/碩士(2009年)

摘要

流體在流動時分三種類型；分別為層流、穩流及亂流三大類別。雷諾係數(Reynolds number)大於4000是亂流(Rough turbulent)，無法做任何的理論推導計算只有經驗公式而已；大於2000而小於4000是穩流(Transitional turbulent)，也一樣只有經驗公式；小於2000是層流(Smooth turbulent)，有理論公式可推導計算，這是本論文討論的範圍。一般的普通物理學和高中物理課程對僅伯努力現象都有詳細討論，但是黏滯力的作用完全被忽略。任何在有限制範圍流動的流體都帶有黏滯力的作用，這現象不易被觀察後加以計算，所以實驗的設計上必須能觀察到此現象而且能計算。設計一個流體是水而且是層流的實驗裝置，同時包含流體必須是不可被壓縮和雷諾係數(Reynolds number)的限制。理論模擬所推導出來的公式是近似值，在邊界附近忽略了一些，所以才可得到有解的公式。近似值中包含了黏滯的作用力項與伯努力項。理論值與實驗值相當接近，所以邊界附近的忽略是可行。

關鍵字

伯努力方程式 ； 黏滯力 ； 雷諾係數 ； 層流

並列摘要

The flow of fluid can be characterized into three types, i.e. rough turbulent, transitional turbulent and smooth turbulent. The flow of fluid with Reynolds number below 2000 is assigned as smooth turbulent, and it can be described by the theoretical model. We investigated the smooth turbulent experimentally as well as theoretically. Bernoulli principle has been taught in university and senior high school in details while the viscosity of fluid is totally ignored. We add viscosity effect in cooperation with Bernoulli principle for fluid flows in a flat rectangular nozzle-pipe. Experiment setup allows us to determine the pressure along the pipe and average flow rate of the pipe. Assume the incompressibility of water and ignore the boundary effect caused by the height of the flat nozzle-pipe, we can derive a formula contributed by two terms, and one is caused by viscosity and the other is Bernoulli equation. We found the theoretical model can be used to describe the experimental results very well.

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