Abstract
The knowledge of the fluid discharge in free surface flows requires a great number of velocity measurements along the whole cross-section, taking up a large amount of time, using expensive equipment, and employing specialized labor. To overcome these obstacles, various models have been developed thus far that show how to estimate the mean velocity through the maximum velocity. In three-dimensional open channels, the maximum velocity can be located below the free surface because of the presence of secondary flows mainly originating by the sidewalls, an occurrence known as dip-phenomenon. In this condition, predicting the maximum velocity position is quite difficult and has always represented a challenge to most hydraulic engineers and researchers. In the present study, a mathematical model derived from the information entropy theory is proposed to evaluate the velocity-dip-position over the entire cross-section of both wide and narrow open channels, thus overcoming the limitations of the existing methods. Large literature measurement sets, collected in uniform and non-uniform flows, were used to test the validity of the model, showing good agreement with the experimental data and providing an accurate estimation of the dip-position.
Highlights
The water discharge of an open channel flow, an essential element for the effective management of water resources, is estimated through the measurement of the cross-section mean velocity
Thereliability reliabilityof of theoretical model here developed is confirmed by the experimental obtained from a wide set of data referring to channels with various characteristics, such as alignment, coefficients obtained from a wide set of data referring to channels with various characteristics, such slope, roughness, geometric shape, and velocity and shear stress distributions
The reliability of the theoretical model here developed is confirmed by the experimental Entropy 2019, 21, 554 coefficients obtained from a wide set of data referring to channels with various characteristics, such as alignment, slope, roughness, geometric shape, and velocity and shear stress distributions
Summary
The water discharge of an open channel flow, an essential element for the effective management of water resources, is estimated through the measurement of the cross-section mean velocity. This paper proposes a theoretical model, stemming from the principle of the maximum informational entropy, to estimate the velocity-dip-position in open channels, knowing only one single entropic parameter, M The latter seemed to keep constant over the entire cross-section despite the varying water discharge in [24,25,26,27] and over the entire reach for rivers with the same morphological characteristics in [28]. The here-proposed model was validated through a detailed error analysis in a wide range of experimental data sets and the results support its application both in the central line and over the entire cross-section of wide and narrow open channels having different bed and sidewall roughness conditions, regular and irregular geometric shapes, and various water discharges and flow depths. Since the model does not depend on specific kinematic or dynamic flow characteristics, it carries fewer limitations compared with most of the methods so far developed in the literature
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