The tidal hydrodynamics and effluent distribution in estuaries involve a complicated range of solute transport phenomena modelled by partial differential equations. Therefore, the quantitative estimation of the risks of water and soil contamination of coastal areas as a result of polluted estuary flows, or effects of the effluent input on the chemical loads, involves the solution of these equations. Generally, the pollutants load in an estuary is determined by the nature of land use which by altering the watershed hydrology or chemical detention/release in the river banks affect the water quality of the estuaries. The present modelling work aims to investigate the solute transport behaviour in the Tay Estuary in Scotland. Based on this study, an attempt to devise an estuary specific discharge strategy for the Tay has been made. The numerical calculations are based on using 2D Galerkin finite element discretisation of the governing equations in an Eulerian co-ordinate system. The flexibility of the formulation allows it to be extended to moving boundary situations encountered in most tidal water systems.