Derivation of Power Law and Logarithmic Velocity Distributions Using the Shannon Entropy
Publication: Journal of Hydrologic Engineering
Volume 16, Issue 5
Abstract
Employing the Shannon entropy, this note derives the well-known power law and the Prandt–von Kármán universal (or logarithmic) velocity distribution equations for open channel flow. The Shannon entropy yields probability distributions underlying these velocity equations. With the use of this entropy, one obtains an expression for the power law exponent in physically measurable quantities (surface flow velocity and average logarithmic velocity) and an expression for shear flow depth in flow depth, surface flow velocity and shear velocity, thus obviating the need for fitting.
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Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 16 • Issue 5 • May 2011
Pages: 478 - 483
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Nov 9, 2009
Accepted: Sep 25, 2010
Published online: Apr 15, 2011
Published in print: May 1, 2011
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