Existence, Uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations

TL;DR

This paper proves the existence, uniqueness, and monotonic properties of solutions for hydraulic network flow distribution problems with pressure-dependent closures, and investigates the inverse Maxwell matrix structure.

Contribution

It introduces new theoretical results on solution properties and matrix structures for hydraulic networks with pressure-dependent relations.

Findings

Proved existence and uniqueness of solutions.

Established monotonic behavior of solutions.

Analyzed the inverse Maxwell matrix structure.

Abstract

Existence, Uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations was proved. Structure and properties of inverse Maxwell matrix of the problem were investigated