Fluid flow through a network of thin pipes

We study the fluid flow through a network of intersected thin pipes with pr escribed pressure at their ends. Pipes are either thin or long and the rati o between the length and the cross-section is considered as the small param eter. Using the asymptotic analysis with respect to that small parameter th e effective behaviour of the flow is found. At each junction an explicit fo rmula for computing the value of the pressure is found. The interior layer phenomenon in vicinity of the junction is studied. We generalize the juncti on formula on the case of adiabatic compressible flow. (C) 2001 Academie de s sciences/Editions scientifiques et medicales Elsevier SAS.