Alterations in the rates, yields and product selectivities of chemical reactions can be achieved through the microfluidic control of localised concentrations within the micro channel networks  of “Lab-on-a-Chip” micro reactor devices. Understanding the physical chemistry of reaction effects in micro reactors requires a detailed knowledge of reactant flows. In this paper, we describe a theoretical analysis to predict pressure and voltage driven liquid flow rates and electrical currents in the channel networks of micro reactors. The flow rate equations are set up in terms of a driving variable (pressure or voltage) and a corresponding resistance to either pressure driven or electroosmotic flow or electrical current. This unified formulation enables exploitation of the similarities in the network analysis of the liquid flows within a channel network with the analysis of voltage/current  relationships in coupled DC circuits. Extensive experimental measurements of pressure and voltage driven flow rates, electrical currents and resistances for three micro reactor channel networks of different geometries were used to validate the analysis within an uncertainty  of approximately 20 %. The method provides a useful quantitative tool which enables the design of channel network dimensions required to achieve a desired set of flow characteristics prior to fabrication.