This paper presents a model for describing the flow of a mixture of water and glycerol in pressurized horizontal pipelines. The model is constituted by mass and momentum conservation equations together with experimental formulas for computing both the density and dynamic viscosity of the mixture. The model was programmed in MATLAB to be numerically solved, as well as to simulate flow with different fractions of water and glycerol in leaking pipelines, which could allow to conceive algorithms for diagnosing leaks during the transport of flows with high viscosity. To show the agreement between the model prediction and the actual flow behavior of the mixture, the numerical model solution, for certain boundary conditions, is compared with some data acquired during an experimental test in a laboratory pipeline.