In environmental impact studies on natural flows, the concept of "complete mixing" linked to the flow's "assimilation capacity" is usually presented in terms of transverse diffusion alone, ignoring the fact that it is a joint mechanism with longitudinal dispersion. This article presents a new approach in which a state function comprehensively describes how the two mechanisms act in unison, facilitating the interpretation and calculation of the "mixing length." The developed equations are applied to the study of three different channels, obtaining satisfactory results, converging with those calculated from Elder's transverse diffusion coefficient.