FLOW THEORY DEVELOPMENT ANALYSIS IN THE PIPES
DOI:
https://doi.org/10.31713/vt220196Keywords:
flow theory, laminar flow, laminar flow regime, flow structure, pipesAbstract
In order to improve the reliability of the hydraulic structures, it isnecessary to improve the approach of the hydraulic calculation ofpressure pipes. That is, we need to develop this theory of kinematicflow structure. The article describes the literature analysis about thedevelopment of flow theory in the pipes.It is noted that the graph of the dependence of the friction factor on theReynolds number reveals only the flow regimes, but does not revealthe flow structure, which is necessary when considering the hydrauliccalculations of the pipes. J. Stokes obtained the solution of thedifferential equation of S. Navier. His theoretical results completelycoincide with the data of experiments conducted in small diameterpipes at low velocity (laminar flow regime). To close the differentialequation, he considered the continuity equation and accepted theboundary conditions. J. Stokes found that the result obtainedadequately describes the structure of the laminar flow for all pointson the Nikuradze graph.The results of the analysis and the theoretical studies summarized.The relationship between the flow laminar regime and the flowstructure in the pipes has described. Equations for calculating flowparameters determined: the equation of distribution of the averagedflow velocity in laminar flow regime, the distance from the pipe axis tothe points with average velocities, the value of the maximum flowvelocity, the ratio of the maximum velocity to the average flow velocityin the pipe, the value of the vortex components. It is proved that vortexlines are concentric circles whose centres located on the pipe axis.The equation of the particles rotation components of the flow and themaximum value of the angular velocity of rotation of the particles onthe inner surface of the pipe were obtained. After integrating the Navier-Stokes differential equation, the pressure distribution equationin the pipe obtained.All equations that determine the flow structure expressed byReynolds number and pipe friction factor. Such formulas have adoptedto show the relationship between the flow regime and the flowstructure. The flow structure for turbulent regime is still unknown.Therefore, we will describe the solution of this problem in the futurearticles.References
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