To the development of hydraulic regulations of turbulent flows in pipelines

Abstract

The results of the theoretical analysis of the turbulent movement of water in pipelines are given. It is proposed to evaluate the parameters of turbulent flows based on the indicators of molecular and turbulent viscosity with the introduction of the conditional relative thickness of the boundary layer into the calculations. The dependencies of the logarithmic law of the distribution of averaged velocities in the cross-sections of pipelines have been clarified. Unlike similar formulas of the semi-empirical theory of turbulent motion, they correspond to the boundary conditions on the pipeline wall. New theoretical dependencies between the main parameters of turbulent flows in pipelines were obtained. It is proved that the magnitude of the coefficients of hydraulic friction is determined by two parameters: the conditional relative thickness of the boundary layer and the proportionality factor, which takes into account the change in tangential stresses in the turbulent flow. The adequacy of the obtained dependencies is confirmed by their correspondence to the experimental data of the hydraulic dependencies of turbulent flows, on the basis of which the current standards for hydraulic calculations of water pipes were developed. For hydraulically smooth pipes, an explicit dependence was obtained for hydraulic friction coefficients in a wide range of Reynolds numbers (from 7 10³ to 10⁷). It almost completely corresponds to the well-known Prandtl-Colebrook’s formula, which has an implicit form. Numerical values and analytical dependencies between parameters of turbulent flow in hydraulically smooth pipelines are determined. It was established that with an increase in the Reynolds number, the values of both the conditional and absolute thicknesses of the boundary layer decrease, and with the increasing of the pipe diameters, they grow. It is shown that the thickness of the boundary layer depends on the type and magnitude of the roughness of the inner surface of the pipes and it is decisive when other parameters of turbulent flows in pipelines are evaluating.