The distribution of constituents from discharges in estuaries can be determined only to the detail with which the time-varying velocity field is known. Deep estuaries can exhibit complex vertical and horizontal circulation structures depending on tides, freshwater inflows, density stratification, and geometry. A numerical, time-varying, three-dimensional hydrodynamic and transport model is applied to the Gastineau Channel, a deep estuary in Alaska, to determine the dilution of material discharged from a submerged outfall into the Channel. The ability of the model to produce realistic flow fields is first confirmed by comparing computed velocities to measured velocities for stratified and unstratified conditions. Methods are then shown for determining the flushing rate of the estuary and the distribution of dilution throughout the estuary for these same conditions.