engleski

Incompressible Newtonian flow through thin pipes

The aim of this paper is to present some results about asymptotic approximations of the incompressible viscous flow through thin (or long) pipes. The ratio between the length and the cross-section is considered as the samll parameter. Using the asymptotic analysis with respect to the small parameter, the effective behaviour of the flow is found. After a simple case of one straight pipe, we study the fluid flow through a network of intersected pipes with prescribed pressure at their ends. At each junction an explicit formula for computing the value of the pressure is found. The interior layer phenomenon in vicinity of the junction is studied. The effects of the curved pipes on the flow profile are considered. Correctors for the Poiseuille flow, due to the curvedness of the pipe are computed.

Thin pipes, Navier-Stokes equations, Poiseuille flow, junction, Kirchoff law, Leray problem, curved pipes

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