Premise plumbing systems are the final stage in water delivery for most water consumption and exposure. When contamination events occur, these systems must be flushed to ensure high quality water is available for subsequent use. Premise plumbing systems are made up of numerous small pipes that typically experience flowrates that result in transport associated with laminar to low turbulent flow regimes. Previous work highlighted the transport associated with laminar and highly turbulent flow using a two-dimensional random walk particle tracking approach. This past work omitted transitional and low turbulent flow cases from consideration, but these correspond to many use cases in premise plumbing systems. This presentation will explore modeling of the transitional to low turbulent flow regime cases that extends previous two-dimensional random walk particle tracking, specifically predicting how effective flushing of premise plumbing systems will be using different flow rates and within systems of different pipe diameters and lengths. The approach utilizes published two-dimensional flow profile data to fill the gap in predicting transport behavior for Reynolds numbers between laminar and highly turbulent flow regimes that was not previously explored.