Fault tolerance and security in drinking water distribution operations are important issues that have received increased attention in the last few years. In this work the problem of leakage detection is formulated within a systems engineering framework, and a solution methodology to detect leakages in a class of distribution systems is proposed. Specifically, the case where water utilities use standard flow sensors to monitor the water inflow in a District Metered Area (DMA) is considered. The goal is to design algorithms which analyze the discrete inflow signal and determine as early as possible whether a leakage has occurred in the system. The inflow signal is normalized to remove yearly seasonal effects, and a leakage fault detection algorithm is presented, which is based on learning the unknown, time-varying, weekly periodic DMA inflow dynamics using an adaptive approximation methodology for updating the coefficients of a Fourier series; for detection logic the Cumulative Sum (CUSUM) algorithm is utilized. For reference and comparison, a second solution methodology based on night-flow analysis using the normalized inflow signal is presented. To illustrate the solution methodology, results are presented based on randomized simulated leakages and real hydraulic data measured at a DMA in Limassol, Cyprus.