A mathematical investigation on the invariance problem of some hydraulic indices

Abstract

In recent decades many mathematical models, both theoretical and computational, have been applied to hydraulic networks with considerable success, and recently this trend appears to be growing exponentially. Yet there are important problems of a mathematical nature that have very often had little consideration in this field, such as that of the invariance of the models with respect to the reference adopted. In this paper, a mathematical framework new in the field is used and, starting from the discussion of the invariance problem of local indices, the behavior of some widespread global ones that evaluate the resilience of a network will be investigated from both a theoretical and computational point of view. The authors also give suitable changing formulas in the local and global case and describe the conditions that ensure invariance. Through a mathematical-like formalization of the hydraulic network concept, the new framework finally allows to find a series of mathematical solutions to problems of this kind, two of which will be provided in the text.