# Experiences with mathematical models used for water quality and quantity problems

Experiences with mathematical models used for water quality and quantity problems

Author Date1974-01-01

AbstractThe use of models for solving water quality and quantity problems is not restricted to mathematical modeIs, as other types also have their possibilities and drawbacks. Mathematical methods, however, have certain properties which make them particularly suitable for water management studies. The examples of mathematical models dealt with in this paper involve one or two spatial dimensions (in the horizontal plane) and time. Research on two-dimensional modeIs in the vertical plane and three-dimensional modeIs is not far advanced enough for them to be available for routine use. Quality parameters that do not affect the flow of water are the only ones considered in this paper. Methods of evaluating the effects of buoyancy and stratification are peing developed but are not yet operationaI. Situations which can be investigated by means of present-day mathematical models are: a. Flow of water and dispersion of heat or dissolved substances in canals or systems of canals (networks), either for steady or for unsteady flows, b. The same phenomena in shallow lakes, estuaries or seas characterized by twodimensional flow in the horizontal plane. One-dimensional flow models have been used to study water management in several networks of canals. The studies concern both design problems, such as the location and capacity of new pumping stations, and decision problems connected with the operation of a system of pumping stations and sluices. The one-dimensional technique has also been successfully applied to the Oosterschelde estuary, much of which consists of natural channels. Similar methods are being used to determine the distribution of flow in the major beds of river systems when designing dikes. In the latter type of computation the flow is assumed to be quasi-steady. Once the flow in channels or rivers is known, either from one-dimensional models as described above, or from other sources, the water quality can be studied by means of convection-dispersion equations for the transport of dissolved substances or heat. Examples are the cooling-water circuit of a power plant (steady flow), the quality of water in artificial or natural storage basins (unsteady flow, including tidal effects) and the distribution of waste water in estuaries (considering net-flow only; dispersion is taken to include tidal mixing). The coefficient of dispersion involved in these models depends very greatly on the schematization and is empirical.

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PublisherRijkswaterstaat

SourceRijkswaterstaat Communications 18

Part of collectionHydraulic Engineering Reports

Document typereport

Rights© 1974 Rijkswaterstaat