Entropy and Probability Concepts in Hydraulics

Abstract

The concept of entropy based on probability has been applied in modeling the vertical distributions of the velocity, shear stress, and (suspended) sediment concentration in open‐channel flows. A velocity distribution equation derived by the entropy‐maximization principle has advantages over the Prandtl‐von Karman universal velocity distribution equation. The (maximized) entropy functions derived for the velocity distribution and sediment transport are effective in reflecting the effects of the size of suspended sediment, coarseness of bed material, and sediment concentration. They can, therefore, be used as variables for characterizing and comparing various open‐channel flows. Through their sensitivities to the various parameters needed to describe the flow and sediment transport characteristics, the entropy functions can also be used to obtain much‐needed, new equations for the estimation of parameters difficult to determine owing to insufficient numbers of equations available. The entropy concept provides an excellent vehicle for introducing probability into hydraulics, and such an introduction makes dealing with uncertainties inherent in hydraulic processes possible and help developing sampling schemes, in addition to the modeling and parameters estimation mentioned earlier.