Derivation of Power Law and Logarithmic Velocity Distributions Using the Shannon Entropy Academic Article

abstract

• Employing the Shannon entropy, this note derives the well-known power law and the Prandt-von Krmn 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. 2011 American Society of Civil Engineers.

authors

• Singh, Vijay

published proceedings

• JOURNAL OF HYDROLOGIC ENGINEERING

author list (cited authors)

• Singh, V. P.

citation count

• 21

complete list of authors

• Singh, Vijay P

publication date

• May 2011

publisher

• American Society of Civil Engineers (ASCE)  Publisher

published in

• Journal of Hydrologic Engineering - ASCE  Journal

keywords

• Entropy
• Power Law
• Prandtl-von Karman Universal Velocity Distribution
• Shannon Entropy
• Velocity Distribution
• Von Karman Constant

Digital Object Identifier (DOI)

• 10.1061/(ASCE)HE.1943-5584.0000335

start page

• 478

end page

• 483

volume

• 16

issue

• 5

URL

• http%3A%2F%2Fdx.doi.org%2F10.1061%2F%28asce%29he.1943-5584.0000335