This paper presents a novel non-invasive monitoring method, based on a Liénard-type model (LTM) to diagnose single and sequential leaks in liquid pipelines. The LTM describes the fluid behavior in a pipeline and is given only in terms of the flow rate. Our method was conceived to be applied in pipelines mono-instrumented with flowmeters or in conjunction with pressure sensors that are temporarily unavailable. The approach conception starts with the discretization of the LTM spatial domain into a prescribed number of sections. Such discretization is performed to obtain a lumped model capable of providing a solution (an internal flow rate) for every section. From this lumped model, a set of algebraic equations (known as residuals) are deduced as the difference between the internal discrete flows and the nominal flow (the mean of the flow rate calculated before the leak). Once the residuals are calculated a principal component analysis (PCA) is carried out to detect a leak occurrence. In the presence of a leak, the residual closest to zero will indicate the section where a leak is occurring. Some simulation-based tests in PipelineStudio® and experimental tests in a lab-pipeline illustrating the suitability of our method are shown at the end of this article