In vanadium redox flow batteries, an accumulated imbalance of the states-of-charge between the two half-cell electrolytes caused by vanadium ion crossover and gassing side reactions can result in only one half-cell achieving 100% state-of-charge, which is referred to as capacity loss that needs to be corrected online. In order to implement rebalancing control, online states-of-charge have to be monitored. In this paper, the electrolyte viscosity and its use for online state-of-charge monitoring design are investigated. The study firstly measures the viscosities of both V2+/V3+ and VO2+/VO2+ redox couples in sulfuric acid as the negative and positive half-cell electrolytes at different states-of-charge and temperatures, followed by establishing an empirical neural network model that correlates the state-of-charge to viscosity and temperature. To overcome the limitation in online viscosity measurements, Darcy's law describing the flow of a fluid through a porous medium is further introduced to link the electrolyte viscosity to the pressure drop across a porous medium where the electrolyte solutions flow through. Together with the neural network model, the state-of-charge can be eventually represented as a function of pressure, temperature and flow rate that are readily measurable online, and accordingly an online state-of-charge monitoring design is developed, which could be readily integrated into the online battery control system for automated electrolyte rebalance. Experimental validation is performed on a 15 cell stack system and the results demonstrate the feasibility of the proposed method.