Water quality models for municipal pipe networks commonly use the plug flow assumption to calculate axial mass transfer for all flow regimes. Classical works on axial dispersion, conducted five decades ago (Taylor's theory), laid foundations that have been examined and applied to chemical and industrial processes for laminar and turbulent flows. However, these experimental findings have not been fully integrated into water quality models for pressurized water distribution systems. The plug flow assumption often leads to discrepancies when compared to experimental or field data in unsteady low flow (laminar and transitional) zones of municipal pipe networks. The present study examines the axial dispersion of a non-reactive tracer in a pipe under laminar and transitional flow conditions. Inlet concentration readings are used as upstream boundary conditions for Computational Fluid Dynamics (CFD) simulations and 1D Advection-Dispersion (AD) models. The resulting downstream concentrations are compared with analytical approximations to determine the reliability of each approach. The present work will improve our fundamental understanding of solute transport and enhance our ability to model and predict water quality in municipal distribution systems. Improved water quality models with accurate spatio-temporal axial dispersion patterns will be critical in optimizing water quality sensor placement, assessing models for early warning systems, and generating the exposure information needed for quantitative risk assessment.