Abstract
This paper presents the results of studying the motion of a liquid layer along the walls of a vertically installed pipe under the action of gravity. Two-dimensional boundary layer is formed by the fluid motion relative to the hard wall on surfaces of structures (pipes, turbines, heat-and-mass transfer equipment, aircrafts, ships, etc.), which are of positive interest in engineering practice. Further upgrading of the above-mentioned structures is possible only by increasing accuracy of momentum in the boundary layer, heat and mass transfer rates calculation. It is confirmed that in the boundary layer transfer phenomena intensity (perpendicular to the wall) is due to the fluid particles velocity distribution regularities in the cross-section of the layer. Fluid velocity distribution regularities in turn are conditioned by Reynolds number according to current notions. The principal method of quantitative analysis of turbulent flow in a boundary layer suggested by Reynolds continues to be the velocity and pressure fluctuations averaging method for some timespan. The suggested model of fluid movement enables to prognosticate conditions under which in cross-sections of the boundary layer reshaping of velocity profile takes place, to carry out analytic calculation of such hydrodynamic characteristics as mean velocity of motion, layer thickness and shearing stresses acting on the wall. The difference between the suggested methods developed for calculation of flow parameters from the well-known ones is in that that calculations are made based on an integrated approach regardless of such conceptual definitions as laminar and turbulent regimes widely used in modern hydrodynamics. Obtained results and design formulas known in the literature have been compared. It has been found that the thickness of the sliding layer, determine by the proposed calculation formula, 1.17 times smaller than that determined by the currently used formula
Highlights
In the history of hydrodynamics development an important milestone was boundary layer notion introduced by [1]
For the fluid film the Reynolds number is determined by ReL = G μ, where G = ρ∙u∙δ is the fluid flow for the unit width of the fluid film, u is the mean velocity of the fluid film, δ is the thickness of the film, ρ is the fluid density, μ is the dynamic viscosity index
It is shown that depending on fluid physical properties, velocity of flow and potential flow, fluid motion in the boundary layer range can take place by two different laws of velocity distribution
Summary
In the history of hydrodynamics development an important milestone was boundary layer notion introduced by [1]. According to its approaches fluid flow can be divided into two zones in the effective cross-section. Fluid viscosity has essential influence on a boundary layer being formed only near solid wall where the flow rate gradient is the greatest. In [2] boundary layer theory was developed which enables to reduce hydrodynamics equations without essential losses. To study exchange phenomena in the boundary layer in the last century in a number of countries researchers carried out fundamental theoretical and experimental investigations [3]. Information on the study methods can be found in the following works [4, 5]
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