A Leak Detection and Isolation (LDI) algorithm based on a State Estimation Observer is designed and tested in real-time to locate a water-leak on a plastic pipeline prototype. In order to tackle the problem of friction variations in such a pipeline, the explicit so-called Swamee-Jain equation is implanted for the friction, instead of a constant parameter as in other studies. The observer is then designed as an Extended Kalman filter on the basis of a discretized model both in time and in space. The space discretization is nonuniform depending on the unknown leak location, and the time variable is discretized with the Heun's method. The approach assumes only flow and pressure sensors at the ends of the duct, and experimental results with data obtained from the pipeline prototype are presented to assess the method efficiency.