Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

Abstract

This paper investigates the structural changes in the turbulent motion of an incompressible fluid in the hydrodynamic entrance region of plane-parallel pressure motion. Movement in pressure hydromechanical systems usually occurs in a turbulent regime. Studying the patterns of changes in hydrodynamic parameters under conditions of stationary turbulent pressure motion in the inlet region is a very urgent task. The study was carried out on the basis of boundary layer equations. Taking into account the dependence of changes in the kinematic viscosity coefficient that occur between layers of fluid, a boundary value problem was formed. Analytical solutions have been obtained that make it possible to obtain patterns of changes in velocity and pressure in any effective flow section. Based on the general conclusions of the study, solutions were found for two cases: a) the velocity of the fluid entering the cylindrical pipe is constant; b) the velocity of the incoming fluid has a parabolic distribution. For these cases, using computer analysis of the data obtained, general graphs of velocity changes were constructed in various sections along the hydrodynamic entrance region. These graphs, which display the change in velocity along the entire length of the inlet, make it possible to obtain the velocity of fluid movement at any point along the inlet length and estimate the length of the transition zone. The results obtained are among the least studied issues of classical fluid mechanics and are of important theoretical interest. The results obtained are applicable for the correct construction of the hydrodynamic entrance region of machinery. A calculation formula has been obtained to determine the length of the hydrodynamic inlet region