Application of Entropy Concept in Open‐Channel Flow Study

The use of the variational principle to maximize the entropy is illustrated for possible applications in open‐channel flow study. The illustrations include those in: (1) Modeling of velocity distribution by probabilistic formulation and entropy maximization; (2) relating the entropy to the parameters of velocity distribution models; (3) relating the entropy to the energy and momentum coefficients; (4) relating the mean velocity given by the Manning's equation to the velocity distribution and the entropy; and (5) relating the entropy to the locations of the mean and maximum velocities in a channel cross section. The “entropy parameter” M and the maximum velocity $u_{\max }$ are emphasized as important new parameters. Many flow properties can be expressed in terms of M. Knowledge of $u_{\max }$ is equivalent to knowing the range of flow velocity in a channel cross section, an important statistical parameter, which along with the mean velocity can completely describe the probability‐density function of flow velocity and, hence, the velocity distribution and other related flow properties. Such a concept is new to open‐channel hydraulics.