Stationary Flow Of A Viscous Fluid In A Flat Channel With Permeable Walls ( In The Example Of Blood Circulation )
European Journal of Molecular & Clinical Medicine,
2020, Volume 7, Issue 3, Pages 2731-2738
AbstractThis article is devoted to the study of the stationary flow of a viscous fluid in a flat channel with permeable walls. As is known, in a pulsating flow in pipelines, a pressure wave propagates through its walls, which is called a pulse wave. This wave, as it moves away from the initial cross section, gradually weakens and practically attenuates at the ends. In the present work, stationary flows of a viscous fluid in a plane channel with permeable walls are considered to be sufficiently long for the channel. The problems are solved and calculation formulas for determining the longitudinal and transverse speeds are obtained. Formulas are also found and numerical calculations are made that determine the change in pressure and fluid flow in the direction of the main stream for various values of the permeability coefficient. It is shown that at lower values of the coefficient of permeability, the pressure is distributed along the flow according to linear laws, and the fluid flow rate remains almost constant along the channel length. Other values of the permeability coefficient, it is characteristic that with an increase in the permeability coefficient of the pressure distribution differs significantly from the linear distribution, with the maximum deviation in the middle of the channel. The fluid flow rate with an increase in the permeability coefficient increases several times in the initial section compared to the fluid flow rate, in the same pressure drop in the flow of a viscous fluid in a flat channel with impermeable walls.
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