Calculation of the flow of a viscous fluid near an inlet and outlet


DOI: 10.34759/trd-2023-129-10

Аuthors

Kaurov P. V.

Saint Petersburg State University of Industrial Technologies and Design, Saint Petersburg, Russia

e-mail: pucmo@mail.ru

Abstract

The article considered and solved the problem on the viscous fluid flow between the source and the drain at small Reynolds numbers. It presents the analytical solution of the Stocks equation when bipolar coordinates utilization. The sought-after function is represented as a sum of the two components, first of which satisfies the boundary conditions, while the application of the other component satisfies the initial Stocks equation in the bipolar system of coordinates. Approximation of the first component the flow function by the simple dependence allows reducing the initial equation with variable coefficients to the three ordinary differential expressions with constant coefficients relative to the second component of the flow function. Analytical solution is presented for the three ordinary differential equations. The examples of the computed flow function in the dimensionless form for various distances between the source and the drain are presented. Comparison of the flow functions calculated values with the experimental data from the literature sources demonstrates reasonable agreement.

Keywords:

laminar flow, viscous fluid, stream function, Stokes equations, bipolar coordinates

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