Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes (CROSBI ID 227058)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Marušić-Paloka, Eduard ; Pažanin, Igor
engleski
Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes
We consider the incompressible fluid with a pressure-dependent viscosity flowing through a multiple pipe system. The viscosity-pressure relation is given by the Barus law commonly used in the engineering applications. Assuming that the ratio between pipes thickness and its length is small, we propose a rigorous asymptotic approach based on the concept of the transformed pressure. As a result, we obtain new macroscopic model describing the effective behavior of the fluid in the system. In particular, the generalized version of the Kirchhoff's law is derived giving the explicit formula for the junction pressure. The error estimate for the asymptotic approximation is also provided. Mathematical analysis presented here can be applied to a general viscosity- pressure relation satisfied by other empiric laws.
pipe network ; pressure-dependent viscosity ; transformed pressure ; Kirchhoff's law ; asymptotic analysis
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Podaci o izdanju
37 (1)
2018.
297-305
objavljeno
0101-8205
1807-0302
10.1007/s40314-016-0345-5