Redox flow batteries (RFBs) are potential solutions for grid-scale energy storage, and deeper understanding of the effect of flow rate on RFB performance is needed to develop efficient, low-cost designs. In this study we highlight the importance of modeling tanks, which can limit the charge/discharge capacity of redox-active polymer (RAP) based RFBs. At low flow rates the losses due to tank mixing dominate over the polarization-induced capacity losses that arise due to resistive processes in the reactor. A porous electrode model is used to separate these effects by predicting the time variation of active species concentration in electrodes and tanks. A simple transient model based on species conservation laws developed in this study reveals that charge utilization and polarization are affected by two dimensionless numbers quantifying (1) flow rate relative to stoichiometric flow and (2) size of flow battery tanks relative to the reactor. The RFB’s utilization is shown to increase monotonically with flow rate, reaching 90% of the theoretical value only when flow rate exceeds twenty-fold of the stoichiometric value. We also identify polarization due to irreversibilities inherent to RFB architecture as a result of tank mixing and current distribution internal to the reactor, and this polarization dominates over that resulting from ohmic resistances particularly when cycling RFBs at low flow rates and currents. These findings are summarized in a map of utilization and polarization that can be used to select adequate flow rate for a given tank size.