Mean velocity is a key parameter for understanding, modeling and predicting the complex phenomena of advection and dispersion in natural watercourses, which are threatened by human intervention and river disasters. For this reason, the principles of relative constancy for the value of this parameter, established early by L. Prandtl and L. Leopold in the 20th century, are powerful theoretical tools for those who develop engineering tasks in this field. This article presents updated analyses of these principles, explaining how this constancy depends essentially on the existence of a steady state in the flow, which allows equiprobability in the system, and therefore, a minimum production of entropy. At the same time an equation is developed, as a function of macroscopic parameters, facilitating its interpretation and practical application. This hypothesis is contrasted by reviewing the relative values for those parameters and their effect on the formula, and defining the practical conditions of applicability of the formula. This method of validating the hypothesis is important in hydrometric practice, as flow velocity measurements are the starting point for their description, especially for large rivers where comprehensive assessments are impossible.

From the Chezy-Manning equation, considered valid for the "steady state" of a natural channel, as an extension of the condition of "uniform flow," it is interesting to determine the degree of variation of the average flow velocity, depending on the variations of the factors involved. That is why this article presents a theoretical analysis which yields a first approximation of the sensitivity of the variation of the magnitude of the average speed to changes in the geometry or geomorphology of a section of the channel. It is found that the concept of "stable state" for the thermodynamic state of a natural channel can be assimilated to that of "dynamic equilibrium," in which the values of the state parameters vary slowly, in a "regional" sense.

A basic topic in river studies, whether in hydrodynamics or water quality, is the accurate estimation of both geomorphological and geometric characteristics in cross sections in streams or channels. Many measurements or methodologies that are within the state of the art, are not direct or easy by several aspects. For this reason, this article analyses the application of a state function, Ф (t), which, acting as a thermodynamic potential, allows the magnitudes of the cross sections, depth of the water sheet, slope and longitudinal dispersion coefficient to be obtained directly, using NaCl as a tracer. In order to apply and validate this new method properly, an experiment conducted in 1966 by H.B. Fischer in the W.M. Keck Laboratory of Caltech in USA was studied on two points of the canal. It found average differences of 0.016 m2 (with reference) in the area of the canal, 0.015 m of the height of the water sheet and an average difference of -0.00015 in the slope of the canal