Mathematical Modeling of Viscous Incompressible Fluid Flow in Tubular Networks: Analysis of Laminar and Turbulent Regimes

The article delves into the mathematical modeling of the flow of viscous, incompressible fluids through a network of tubes enclosed within an outer pipe. It comprehensively examines both laminar and turbulent flow regimes, providing a thorough analysis of the underlying physical phenomena. Specifically, it investigates the fluid dynamics through a configuration consisting of n tubes, each with a length L and radius r situated within the outer tube. The article derives formulae for calculating key parameters such as the maximum velocity of fluid flow, the volumetric flow rate through the tube's cross-section, the coefficient of frictional resistance along the tube's length, and the maximum value of tangential stress.

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