engleski

Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with $r_{; ; ; \ep}; ; ; (x_{; ; ; 1}; ; ; )=(x_{; ; ; 1}; ; ; , a\cos\frac{; ; ; x_{; ; ; 1}; ; ; }; ; ; {; ; ; \ep}; ; ; , a\sin\frac{; ; ; x_{; ; ; 1}; ; ; }; ; ; {; ; ; \ep}; ; ; )$, where the small parameter $\ep$ stands for the distance between two coils of the helix. The pipe has small cross-section of size $\ep$. Using the asymptotic analysis of the microscopic flow described by the Navier-Stokes system, with respect to the small parameter $\ep $ that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe.

Fluid mechanics ; helical pipe ; Navier-Stokes equations

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