The Passaic River Basin, the third largest drainage basin in New Jersey, encompasses 950 mi2 (square miles) in the highly urbanized area outside New York City, with a population of 2 million. Water quality in the basin is affected by many natural and anthropogenic factors. Nutrient loading to the Wanaque Reservoir in the northern part of the basin is of particular concern and is caused partly by the diversion of water at two downstream intakes that is transferred back upstream to refill the reservoir. The larger of these diversions, Wanaque South intake, is on the lower Pompton River near Two Bridges, New Jersey. To support the development of a Total Maximum Daily Load (TMDL) for nutrients in the nontidal part of the basin (805 mi2), a water-quality transport model was needed. The U.S. Geological Survey, in cooperation with the New Jersey Department of Environmental Protection and New Jersey EcoComplex, developed a flow-routing model to provide the hydraulic inputs to the water-quality model. The Diffusion Analogy Flow model (DAFLOW) described herein was designed for integration with the Water Quality Analysis Simulation Program (WASP) watershed water-quality model. The flow routing model was used to simulate flow in 108 miles of the Passaic River and major tributaries. Flow data from U.S. Geological Survey streamflow-gaging stations represent most of the model's upstream boundaries. Other model inputs include estimated flows for ungaged tributaries and unchanneled drainage along the mainstem, and reported flows for major point-source discharges and diversions. The former flows were calibrated using the drainage-area ratio method. The simulation extended over a 4+ year period representing a range in flow conditions. Simulated channel cross-sectional geometry in the DAFLOW model was calibrated using several different approaches by adjusting area and top width parameters. The model also was calibrated to observed flows for water year 2001 (low flow) at five mainstem gaging stations and one station at which flow was estimated. The model's target range was medium to low flows--the range of typical intake operations. Simulated flow mass balance, hydrographs (flood-wave speed, attenuation, and spread), flow-duration curves, and velocity and depth values were compared to observed counterparts. Mass balance and hydrograph fit were evaluated quantitatively. Simulation results generally were within the accuracy of the flow data at the measurement stations. The model was validated to observed flows for water years 2000 (average flow), 2002 (extreme low flow), and 2003 (high flow). Results for 19 of 20 comparisons indicate average mass-balance and model-fit errors of 6.6 and 15.7 percent, respectively, indicating that the model reasonably represents the time variation of streamflow in the nontidal Passaic River Basin. An algorithm (subroutine) also was developed for DAFLOW to simulate the hydraulic mixing that occurs near the Wanaque South intake upstream from the confluence of the Pompton and Passaic Rivers. The intake draws water from multiple sources, including effluent from a nearby wastewater-treatment plant, all of which have different phosphorus loads. The algorithm determines the proportion of flow from each source and operates within a narrow flow range. The equations used in the algorithm are based on the theory of diffusion and lateral mixing in rivers. Parameters used in the equations were estimated from limited available local flow and water-quality data. As expected, simulation results for water years 2000, 2001, and 2003 indicate that most of the water drawn to the intake comes from the Pompton River; however, during many short periods of low flow and high diversion, particularly in water year 2002, entrainment of the other flow sources compensated for the insufficient flow in the Pompton River. As additional verification of the flow model used in the water-quality model, a Branched Lagrangian Transport Model (B