Partial blockages in water pipe networks may contribute to large energy dissipation throughout the system and reduce service effectiveness for customers. In this paper, a recently developed stochastic model using transients for detecting partial blockages in water pipelines is tested and numerical and experimental case studies are presented. The model is a stochastic successive linear estimator previously used in groundwater hydrology for detecting the heterogeneity pattern of the subsurface. The model estimates the distribution of diameters within a pipe with partial blockages and quantifies the uncertainty associated with these estimates. Results show that a first good estimate of the extent and size of the blockages can be obtained by a single test generated by the fast closure of a valve.