This paper presents a novel method for diagnosing leaks in a pipeline. The method is based on a discrete-space version of a Lienard-type model, which describes the fluid behavior in a pipeline only in terms of the flow rate. This latter detail was very useful in designing our method, which was conceived to deal with pipelines solely equipped with flowmeters or in conjunction with pressure sensors, but which are temporarily out of service. The working principle of our methodology is the generation of a set of residuals (each one defined for a specific section of the pipeline) to estimate the position of a leak. The residual near zero will indicate the section where a leak is occurring. The main advantage of our approach is that it does not require pressure measurements, which occurs in most existing methodologies. Thus, to show its potential, we present the results of some tests carried out in simulation.