Probabilistic modeling of hydraulic conditions of tree pipeline networks under conventional boundary conditions

The paper is concerned with the probabilistic modeling of pipeline network hydraulic conditions that occur due to random impacts of the external environment (load of consumers pressures at sources). The research is focused on a network with a tree configuration under conventional boundary conditions (for pressure at a tree root and flow rates at the other nodes) that are specified probabilistically. We propose a topological method for a probabilistic analysis of such network operation. This method makes it possible to determine mathematical means variances and covariances of state variables (pressures at nodes flow rates and pressure losses in branches) by final formulas when traversing the entire tree without laborious matrix operations or calculations of systems of equations. A numerical case study is used to exemplify the efficiency of the proposed approach adequacy of the obtained results and high speed compared to other more general methods similar to Monte-Carlo methods