AbstractA model is described for the relation between water quantity and water quality in the aquifer with the diffuse substance input by the gravitation water being taken into account. The model is based on a partial differential equation of the second order for a flow pipe. For constant transport parameters, a sink of the kinetics of the first order and a time‐dependent source term an exact analytical solution is presented and explained by a model. At a diffuse substance input, the dispersion has only a slight influence on the transport of substances contained in water. Potential applications of these solutions to different problems are mentione