An analytical model to predict the velocity-dip-position at the central section of open channels is presented in this study. Unlike the previous studies where empirical or semi-empirical models were suggested, in this study the model is derived by using entropy theory. Using the principle of maximum entropy, the model for dip-position is derived by maximizing the Shannon entropy function after assuming dimensionless dipposition at the central section as a random variable. No estimation of empirical parameter is required for calculating dip-position from the proposed model. The model is able to predict the location of maximum velocity at the central section of an open channel with any aspect ratio. The developed model of velocity-dipposition is tested with experimental data from twenty-two researchers reported in literature for a wide range of aspect ratio. The model is also compared with other existing empirical models. The present model shows good agreement with the observed data and provides least prediction error compared to other models.

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Abstract:In the last few decades, a wide variety of instruments with laser-based techniques have been developed that enable experimentally measuring particle velocity and fluid velocity separately in particle-laden flow. Experiments have revealed that stream-wise particle velocity is different from fluid velocity, and this velocity difference is commonly known as "velocity lag" in the literature. A number of experimental, as well as theoretical investigations have been carried out to formulate deterministic mathematical models of velocity lag, based on several turbulent features. However, a probabilistic study of velocity lag does not seem to have been reported, to the best of our knowledge. The present study therefore focuses on the modeling of velocity lag in open channel turbulent flow laden with sediment using the entropy theory along with a hypothesis on the cumulative distribution function. This function contains a parameter η, which is shown to be a function of specific gravity, particle diameter and shear velocity. The velocity lag model is tested using a wide range of twenty-two experimental runs collected from the literature and is also compared with other models of velocity lag. Then, an error analysis is performed to further evaluate the prediction accuracy of the proposed model, especially in comparison to other models. The model is also able to explain the physical characteristics of velocity lag caused by the interaction between the particles and the fluid.

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