Prediction of velocity-dip-position over entire cross section of open channel flows using entropy theory

Abstract

An analytical model to predict the velocity-dip-position is presented in this study. Unlike the previous studies where empirical or semiempirical 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 dip-position as a random variable. No estimation of empirical parameter is required for calculating dip-position from the proposed model. The model is capable of predicting the velocity-dip-position at any section from sidewall region (along lateral direction) of an open channel with any aspect ratio. The ratio of mean to maximum value of dip-position is analyzed from data, and it is found that ratio is almost constant for narrow open channels and it increases with aspect ratio for wide open channels. A relation is also proposed to predict this ratio in case of wide open channels. The developed model of velocity-dip-position is tested with existing experimental data for a wide range of aspect ratio and is also compared with other empirical models. The present model shows good agreement with the observed data and is comparable with the existing models.