Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory
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 dist...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2013-04-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/15/4/1221 |
| _version_ | 1798005577897476096 |
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| author | Gustavo Marini Nicola Fontana Vijay P. Singh |
| author_facet | Gustavo Marini Nicola Fontana Vijay P. Singh |
| author_sort | Gustavo Marini |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T12:42:33Z |
| format | Article |
| id | doaj.art-da44e57ae0a446f7a07b3745e7b09cc9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:42:33Z |
| publishDate | 2013-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-da44e57ae0a446f7a07b3745e7b09cc92022-12-22T04:23:28ZengMDPI AGEntropy1099-43002013-04-011541221123110.3390/e15041221Derivation of 2D Power-Law Velocity Distribution Using Entropy TheoryGustavo MariniNicola FontanaVijay P. SinghThe 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.http://www.mdpi.com/1099-4300/15/4/1221entropyflow measurementopen-channel flowShannon entropystreamflowvelocity distribution |
| spellingShingle | Gustavo Marini Nicola Fontana Vijay P. Singh Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory Entropy entropy flow measurement open-channel flow Shannon entropy streamflow velocity distribution |
| title | Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory |
| title_full | Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory |
| title_fullStr | Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory |
| title_full_unstemmed | Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory |
| title_short | Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory |
| title_sort | derivation of 2d power law velocity distribution using entropy theory |
| topic | entropy flow measurement open-channel flow Shannon entropy streamflow velocity distribution |
| url | http://www.mdpi.com/1099-4300/15/4/1221 |
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