Апроксимаційна форма замикального співвідношення

Abstract

Modern analysis tool of modes engineering networks is the theory of hydraulic circuits. To determine the flux-distribution is applied formal methods, which are based on Kirchhoff's laws. Accepted hydraulics Darcy–Weisbach equation to determine the pressure loss (closing relation) is not applicable, since the definition of hydraulic friction coefficient used hundreds of dependencies. Therefore, the theory of hydraulic circuits use approximating dependencies. The paper analyzes the various approximation dependencies. The best form of dependence was determined by the method of least squares. The accuracy of the approximation assessed relative performance: the coefficient of variation and the maximum relative error. Shown that the quadratic form closing relation is acceptable in structural optimization problems, but its accuracy is not enough to improve problems modes. Proved that the closing relation should be submitted in the form of a polynomial of the third degree. To continue, depending on the third quadrant in dependent introduced signum function.