engleski

On the viscous flow through a long pipe with non- constant pressure boundary condition

We investigate the flow of a viscous incompressible fluid through a straight long pipe with circular cross-section. The flow is driven by the prescribed pressures at pipe's ends, where pressure $p_0$ on the pipe's entry is assumed to be non-constant. Using asymptotic analysis with respect to the small parameter (being the ratio between pipe's radius and its length), we replace the non-constant pressure boundary condition with the effective one governing the macroscopic flow. We also derive the optimal boundary pressure $p_0$ such that the fluid velocity through a pipe is maximal.

incompressible fluid ; long pipe ; non-constant pressure boundary condition ; asymptotic approximation ; optimal pressure

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