An explicit dynamic water quality modeling algorithm is developed for tracking dissolved substances in water distribution networks. The algorithm is based on a mass balance reaction within pipes that considers both advective transport and reaction kinetics. Complete mixing of material is assumed at pipe junctions and storage tanks. The algorithm automatically selects a pipe segmentation scheme and computational time step that satisfies conservation of mass and seeks to minimize numerical dispersion. In contrast to previous water quality models, there is no need to first find unique flow paths through the network. The resulting method is both robust and efficient, and can readily be applied to all types of network configurations and dynamic hydraulic conditions. The applicability of the method is demonstrated using an example pipe distribution network. Enhancement of distribution system water quality management is a principal benefit of the methodology.