Abstract
The article considers the issue of velocity distribution in a turbulent flow. The logarithmic velocity profile obtained on the basis of semiempirical theory of turbulence by L. Prandtl is given. A comparison of the calculations of the velocity distribution for various dependencies with the measurement data is performed. It is shown that the calculated dependencies show discrepancy with each other and experimental data. The study of the hydraulic characteristics of water flows is required to solve problems of water supply and water disposal, engineering problems of hydraulic construction, regulation of riverbed processes and environmental monitoring of water bodies. The characteristics of the turbulence of a uniform and uneven flow need to be clarified, that will be possible due to the study of the theoretical background of hydraulics and hydrodynamics. Despite the usage of modern computer technologies, the creation of an actual theory of turbulence is still not complete. The separation of the fluid motion into molar and basic motion led to a non-closed system of equations of turbulent motion, that slowed down further progress in the search for a solution for turbulent flow. The most widely used theory is the semi-empirical theory of turbulence by L. Prandtl, based on a phenomenological approach that links turbulence with the characteristics of the averaged flow. The use of modern technology has allowed us to obtain new experimental data that require analysis and generalization. The calculated dependences for the velocity distribution developed on the basis of various phenomenological models, including the well-known logarithmic profiles of L. Prandtl, are compared with the measurement data. The calculations of the velocity distribution for various dependencies are compared with the measurement data. A significant quantitative, and sometimes qualitative, discrepancy of the calculated dependences with each other and with the experimental data was revealed. The discrepancy between the results of calculating the velocity distribution for different dependencies requires an additional critical analysis of the accuracy and reliability of the experimental data of other authors and performing experimental studies under different conditions using a mutually agreed method. The low effectiveness of the considered statistical approaches leads to the need to develop new approaches that represent a combination of some theoretical concepts and experimental data.
Highlights
The study of the hydraulic characteristics of water flows is required to solve problems of water-supply and water disposal, engineering problems of hydraulic construction, regulation of riverbed processes and environmental monitoring of water bodies
The velocity distribution has a wider top due to the alignment of the velocities in the main mass of the flow caused by the mixing of liquid masses
The separation of the fluid motion into molar and basic motions has created a non-closed system of equations of turbulent motions that slowed down further progress in the search for a solution for the turbulent flow
Summary
The study of the hydraulic characteristics of water flows is required to solve problems of water-supply and water disposal, engineering problems of hydraulic construction, regulation of riverbed processes and environmental monitoring of water bodies. The velocity distribution in the laminar flow of a liquid represents a parabolic dependence. The velocity distribution has a wider top due to the alignment of the velocities in the main mass of the flow caused by the mixing of liquid masses. Reynolds applied the principle of superposition and divided the fluid motion into the main (time-averaged) and molar (pulsation) motions. The latter is summed up with the averaged motion at every moment of time, forming the current turbulent fluid motion. The problem of velocity distribution in a turbulent flow is being studied by both foreign and national specialists [2,3,4,5].
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