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Foundations of the Relative Constancy of Mean Velocity for Natural Streams: A General Principle of Steady State Anticipated by L. Prandtl and L. Leopold
International Journal of Mathematical, Engineering and Management Sciences Pub Date : 2020-12-01 , DOI: 10.33889/ijmems.2020.5.6.101
Alfredo José Constaín Aragón , Carlos Peña-Guzmán , Gina Alexandra Peña-Olarte

Mean velocity is a key parameter for understanding, modeling and predicting the complex phenomena of advection and dispersion in natural watercourses, which are threatened by human intervention and river disasters. For this reason, the principles of relative constancy for the value of this parameter, established early by L. Prandtl and L. Leopold in the 20th century, are powerful theoretical tools for those who develop engineering tasks in this field. This article presents updated analyses of these principles, explaining how this constancy depends essentially on the existence of a steady state in the flow, which allows equiprobability in the system, and therefore, a minimum production of entropy. At the same time an equation is developed, as a function of macroscopic parameters, facilitating its interpretation and practical application. This hypothesis is contrasted by reviewing the relative values for those parameters and their effect on the formula, and defining the practical conditions of applicability of the formula. This method of validating the hypothesis is important in hydrometric practice, as flow velocity measurements are the starting point for their description, especially for large rivers where comprehensive assessments are impossible. KeywordsTurbulence, Thermodynamics of irreversible processes, Production of entropy, Hydraulic.

中文翻译:

天然水流平均速度相对恒定的基础:L。Prandtl和L. Leopold预期的稳态一般原理

平均速度是理解,建模和预测自然水道中对流和分散的复杂现象的关键参数,这些自然现象受到人为干预和河流灾害的威胁。因此,由L. Prandtl和L. Leopold于20世纪初期建立的该参数值的相对恒定原理对于那些在该领域开展工程任务的人来说是强大的理论工具。本文介绍了这些原理的最新分析,解释了这种恒定性基本上如何取决于流中是否存在稳态,从而使系统具有等概率,从而使熵的产生最小。同时,根据宏观参数开发了一个方程,有助于其解释和实际应用。通过审查这些参数的相对值及其对公式的影响,并定义公式适用性的实际条件,可以对比此假设。这种验证假设的方法在水文测量实践中非常重要,因为流速测量是描述的起点,特别是对于无法进行全面评估的大型河流。关键词湍流;不可逆过程的热力学;熵产生;水力。特别是对于无法进行综合评估的大河。关键词湍流;不可逆过程的热力学;熵产生;水力。特别是对于无法进行综合评估的大河。关键词湍流;不可逆过程的热力学;熵产生;水力。
更新日期:2020-12-01
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