Entropy and 2‐D Velocity Distribution in Open Channels

Abstract

Equations based on the entropy concept have been derived for describing the two‐dimensional velocity distribution in an openchannel cross section. The velocity equation derived is capable of describing the variation of velocity in both the vertical and transverse directions, with the maximum velocity occurring on or below the water surface. Equations for determining the location of mean velocity have also been derived along with those, such as the entropy function, that can be used as measures of the homogeneity of velocity distribution in a channel cross section. A dimensionless parameter of the entropy function named the M number has been found useful as an index for characterizing and comparing various patterns of velocity distribution and states of open‐channel flow systems. The definition and demonstrated usefulness of this parameter indicate the importance and value of the information given by the location and magnitude of maximum velocity in a cross section, and suggest the need for future experimental and analytical studies about maximum velocity.