Abstract The measurement of the velocity distribution and discharge in the open channels has always been an important issue in hydraulics. Unfortunately, flow measurement in the open channel is often expensive and sometimes produces poor results. There are many empirical methods to estimate the velocity distribution in a conduit, however, these methods are often applicable only to a narrow range of open channel conditions. In this paper, considering velocity as a random parameter, one-dimensional velocity distribution in open-channel has been derived based on the entropy concept and the principle of maximum entropy (POME). The entropy indexes (M, G, λ2 and λ*) are important parameters in entropy method to estimate velocity distribution and discharge in a conduit. A new approach is presented in this work for estimating the entropy parameters based on two-point velocity measurements. The approach for estimating the entropy parameters is tested for laboratory observations and velocity distribution and discharge are determined using Shannon, Renyi and Tsallis entropy methods. The present approach has shown good agreement with measured data. Also, the results showed that Tsallis entropy method is more accurate than other forms of entropy and the calculated values of NRMSE for estimated velocity profile and discharge are 7.86 and 8.8% respectively, showing a good simulation.

中文翻译：

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通过测量两点速度估计一维速度分布

摘要 明渠中流速分布和流量的测量一直是水力学中的一个重要问题。不幸的是，明渠中的流量测量通常很昂贵，有时会产生较差的结果。有许多经验方法可以估计管道中的速度分布，但是，这些方法通常仅适用于狭窄范围的明渠条件。在本文中，将速度作为一个随机参数，基于熵的概念和最大熵（POME）原理，推导出了明渠中的一维速度分布。熵指数（M、G、λ2 和 λ*）是熵方法中用于估计管道中速度分布和流量的重要参数。在这项工作中提出了一种基于两点速度测量来估计熵参数的新方法。估计熵参数的方法在实验室观察中进行了测试，速度分布和流量是使用香农、Renyi 和 Tsallis 熵方法确定的。本方法已显示出与测量数据的良好一致性。此外，结果表明，Tsallis 熵方法比其他形式的熵更准确，估计速度剖面和流量的 NRMSE 计算值分别为 7.86 和 8.8%，显示出良好的模拟。本方法已显示出与测量数据的良好一致性。此外，结果表明，Tsallis 熵方法比其他形式的熵更准确，估计速度剖面和流量的 NRMSE 计算值分别为 7.86 和 8.8%，显示出良好的模拟。本方法已显示出与测量数据的良好一致性。此外，结果表明，Tsallis 熵方法比其他形式的熵更准确，估计速度剖面和流量的 NRMSE 计算值分别为 7.86 和 8.8%，显示出良好的模拟。