In this study, theoretical models have been developed to predict the velocity-dip-position in steady and uniform turbulent flow through open channels. Unlike the previous works where empirical or semi-empirical models were suggested, the present models are developed from a mathematical approach based on the concept of entropy theory. Considering dimensionless dip-position as a random variable and starting from the Shannon entropy on probability distribution, models are derived by maximizing the entropy function using the principle of maximum entropy. It has been shown that proposed models are applicable over the whole cross section as well as at the central section of any rectangular open channel. The models are validated with a large number of experimental data sets published in literature for a wide variety of flow conditions. Apart from this, the models are also compared with other similar models existing in literature and the prediction accuracy of the present models are confirmed by computing five different errors for all the models. Out of the two proposed models, the model M2c satisfies the required asymptotic boundary conditions. At the end, model M2c is expressed in terms of a damping function. The non-occurrence of maximum velocity at the free surface, commonly known as dip-phenomenon, is explained in the light of the proposed damping concept.

中文翻译：

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速度-倾角-位置的基于熵的模型

在这项研究中，已经开发了理论模型来预测通过明渠的稳定均匀湍流中的速度倾角位置。与之前建议使用经验或半经验模型的作品不同，目前的模型是从基于熵理论概念的数学方法发展而来的。将无量纲倾角位置作为随机变量，从概率分布的香农熵出发，利用最大熵原理使熵函数最大化，推导出模型。已经表明，所提出的模型适用于整个横截面以及任何矩形明渠的中央部分。这些模型通过文献中发表的大量实验数据集进行了验证，适用于各种流动条件。除此之外，这些模型还与文献中存在的其他类似模型进行了比较，通过对所有模型计算五个不同的误差来确认当前模型的预测准确性。在提出的两个模型中，模型 M2c 满足所需的渐近边界条件。最后，模型 M2c 用阻尼函数表示。自由表面不出现最大速度，通常称为倾角现象，根据所提出的阻尼概念进行解释。模型 M2c 用阻尼函数表示。自由表面不出现最大速度，通常称为倾角现象，根据所提出的阻尼概念进行解释。模型 M2c 用阻尼函数表示。自由表面不出现最大速度，通常称为倾角现象，根据所提出的阻尼概念进行解释。