Analytical description of the flow of the newtonian liquid in a round tube and on a horizontal plate

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.85468

Keywords:

laminar and turbulent flows, general integral, particular solutions, distribution of velocity, tangential stresses

Abstract

The object of research is obtaining general integrals and some particular solutions for two common flow conditions of incompressible liquid – laminar and averaged turbulent flow. Mathematical description is based on the system of equations of motion in stresses (Navier) and its special case for the Newtonian liquid. A condition of integrating the equations is the constancy of pressure drop and viscosity along the flow.

The block schemes of obtaining the general integrals for flow in a pipe and turbulent flow on a plate are represented.

Are as a result, three new general integrals and four particular solutions, which are compared with the known equations, were found. It was shown that the integrals of the Navier equation describe the distribution of tangential stress for turbulent flow. An analysis of solutions for the distribution of velocity showed that the Poiseuille equation for laminar flow in a pipe and the Blasius curve for laminar flow on a plate are particular solutions of one general integral. An analysis of the particular solutions made it possible to estimate the thickness of the laminar sublayer under turbulent flow condition. The results of the work create prerequisites for a more detailed further analysis of laminar and turbulent flows.

Author Biography

Vitaliy Budarin, Odesa National Polytechnic University Shevchenko ave., 1, Odesa, Ukraine, 65044

PhD, Associate Professor

Department of Theoretical, general and non-conventional energy

References

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Published

2016-12-22

How to Cite

Budarin, V. (2016). Analytical description of the flow of the newtonian liquid in a round tube and on a horizontal plate. Eastern-European Journal of Enterprise Technologies, 6(7 (84), 43–49. https://doi.org/10.15587/1729-4061.2016.85468

Issue

Vol. 6 No. 7 (84) (2016): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2016 Vitaliy Budarin

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