Flow distribution and pressure drop in 2D meshed channel circuits

The present paper investigates some families of simple 2D circuits or grids of intersecting tubes or channels (thus forming meshes) from the point of view of the fluid distribution and hydraulic characteristics in slow laminar flow. Square grids with a single inlet and a single outlet, and comprising from 4 to 100 meshes are considered, either with all channels identical, or with different channels along the borders of the circuit. Analytical resolution of the mesh and node relations to obtain the steady flow distributions are convenient up to 5×5 meshes, and formal computation furnishes numerical solutions for higher order circuits. This paper discusses some details of the flow and pressure distributions, in particular the symmetries, and also the behavior of some global properties such as overall or internal resistance and flow heterogeneity, as a function of the ratio of resistances of the two types of channels.