As one of the flow-based passive sorting, the hydrodynamic filtration using a microfluidic-chip has shown to effectively separate into different sizes of subpopulations from cell or particle suspensions. Its model framework involving two-phase Newtonian or generalized Newtonian fluid (GNF) was developed, by performing the complete analysis of laminar flow and complicated networks of main and multiple branch channels. To predict rigorously what occurs in flow fields, we estimated pressure drop, velocity profile, and the ratio of the flow fraction at each branch point, in which the analytical model was validated with numerical flow simulations. As a model fluid of the GNF, polysaccharide solution based on Carreau type was examined. The objective parameters aiming practical channel design include the number of the branches and the length of narrow section of each branch for arbitrary conditions. The flow fraction and the number of branches are distinctly affected by the viscosity ratio between feed and side flows. As the side flow becomes more viscous, the flow fraction increases but the number of branches decreases, which enables a compact chip designed with fewer branches being operated under the same throughput. Hence, our rational design analysis indicates the significance of constitutive properties of each stream.