A lumped-parameter model for vanadium redox flow batteries, which use metallic current collectors, is extended into a one-dimensional model using the plug flow reactor principle. Thus, the commonly used simplification of a perfectly mixed cell is no longer required. The resistances of the cell components are derived in the in-plane and through-plane directions. The copper current collector is the only component with a significant in-plane conductance, which allows for a simplified electrical network. The division of a full-scale flow cell into 10 layers in the direction of fluid flow represents a reasonable compromise between computational effort and accuracy. Due to the variations in the state of charge and thus the open circuit voltage of the electrolyte, the currents in the individual layers vary considerably. Hence, there are situations, in which the first layer, directly at the electrolyte input, carries a multiple of the last layer's current. The conventional model overestimates the cell performance. In the worst-case scenario, the more accurate 20-layer model yields a discharge capacity 9.4% smaller than that computed with the conventional model. The conductive current collector effectively eliminates the high over-potentials in the last layers of the plug flow reactor models that have been reported previously.