A modified nodal pressure method for calculating flow distribution in hydraulic circuits for the case of unconventional closing relations

We proposed a method for numerically solving the problem of flow distribution in hydraulic circuits with lumped parameters for the case of random closing relations. The conventional and unconventional types of relations for the laws of isothermal steady fluid flow through the individual hydraulic circuit components are studied. The unconventional relations are presented by those given implicitly by the flow rate and dependent on the pressure of the working fluid. In addition to the unconventional relations, the formal conditions of applicability were introduced. These conditions provide a unique solution to the flow distribution problem. A new modified nodal pressure method is suggested. The method is more versatile in terms of the closing relation form as compared to the unmodified one, and has lower computational costs as compared to the known technique of double-loop iteration. The paper presents an analysis of the new method and its algorithm, gives a calculated example of a gas transportation network, and its results.