In this work, a two-dimensional mathematical model is developed to study the flow patterns and volumetric flow penetrations in a segment of flow channel over porous electrode layered system in vanadium flow battery with flow field design. The flow distributions at the interface between the flow channel and porous electrode are examined. It is found that the non-linear pressure distributions can distinguish the interface flow distributions under the ideal plug flow and ideal parabolic flow inlet boundary conditions. Nevertheless, the volumetric flow penetration within the porous electrode beneath the flow channel through the integration of interface flow velocity reveals that this value is identical under both ideal plug flow and ideal parabolic flow inlet boundary conditions. The volumetric flow penetrations under the advection effects by both flow channel and landing/rib are estimated. The maximum current density achieved in a flow battery with a flow field architecture can be predicted based on the 100% amount of electrolyte flow reactant consumption through the porous electrode beneath flow channel and landing/rib. The corresponding theoretical maximum current densities achieved in vanadium flow battery with one and three layers of SGL 10AA carbon paper electrode have reasonable agreement with experimental results under a proper permeability.