This contribution reports on an ongoing study focusing on reduced order models for incompressible viscous fluid flow in two dimensional channels. A finite difference solver was developed using a simple implementation of the immersed boundary method to represent the channel geometry. The solver was validated for unsteady flow by comparing the obtained two-dimensional numerical solutions with analytical profiles computed from the Womersley solution. For the flow in planar branching channels it was validated using reference solutions obtained from finite-volume codes. Finally the 2D model was coupled to a simple 1D model extension simulating the flow in axisymmetric elastic vessel (tube). Some of the coupling principles and implementation issues are discussed in detail.