Theoretical Aspects of Turbulent Flows in Pipeline

Abstract

Abstract The paper presents the results of theoretical studies on turbulent water motion in pipelines, obtained by the analysis of experimental data regarding hydraulic patterns of turbulent flows. The authors suggest to evaluate the relevant parameters on the basis of the molecular and turbulent viscosity indicators, with the introduction of the conditional relative thickness of the boundary layer on the pipeline walls into the calculations. On this basis, the authors specified semi-empirical relationships for the distribution of averaged velocities in the pipe cross-sections, and revealed new theoretical relationships between the main parameters of turbulent pipe flows. The research confirmed the adequacy of these relationships given the good agreement of the calculated averaged velocity values with the experimental data which formed a basis for the current standards for hydraulic calculations of water supply pipes. For hydraulically smooth pipes, the authors derived an explicit dependence of the hydraulic friction coe cient on the Reynolds number, which almost completely corresponds to the well-known Prandtl-Colebrook equation that has an implicit form. The presented research allowed to determine numerical values and analytical relationships between parameters, which enabled evaluating turbulent flows in hydraulically smooth pipes in a new way.