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Entropy 2013, 15(4), 1221-1231; doi:10.3390/e15041221

Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory

1
Department of Biological and Agricultural Engineering, Texas A and M University, 2117 TAMU, College Station, TX 77842, USA
2
Department of Civil and Environmental Engineering, Texas A and M University, 2117 TAMU, College Station, TX 77842, USA
3
Dipartimento di Ingegneria, Università degli Studi del Sannio, Piazza Roma 21, 82100, Benevento, Italy
*
Author to whom correspondence should be addressed.
Received: 1 February 2013 / Revised: 1 April 2013 / Accepted: 2 April 2013 / Published: 8 April 2013
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)
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Abstract

The one-dimensional (1D) power law velocity distribution, commonly used for computing velocities in open channel flow, has been derived empirically. However, a multitude of problems, such as scour around bridge piers, cutoffs and diversions, pollutant dispersion, and so on, require the velocity distribution in two dimensions. This paper employs the Shannon entropy theory for deriving the power law velocity distribution in two-dimensions (2D). The development encompasses the rectangular domain, but can be extended to any arbitrary domain, including a trapezoidal domain. The derived methodology requires only a few parameters and the good agreement is confirmed by comparing the velocity values calculated using the proposed methodology with values derived from both the 1D power law model and a logarithmic velocity distribution available in the literature.
Keywords: entropy; flow measurement; open-channel flow; Shannon entropy; streamflow; velocity distribution entropy; flow measurement; open-channel flow; Shannon entropy; streamflow; velocity distribution
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Singh, V.P.; Marini, G.; Fontana, N. Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory. Entropy 2013, 15, 1221-1231.

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