Analyzing the behavior of hydraulic systems at resonant frequencies, both with and without leaks, is crucial for effective fault detection and localization. This approach leverages the uniform impact of pipeline components, which consistently induce changes across signal periods, thus making resonant frequencies particularly sensitive to alterations within the system. This sensitivity is pivotal for detecting discrepancies that signify faults. This study demonstrates that most changes in the hydraulic system affect resonant responses in the frequency domain, which are critical to understanding the system’s behavior. Through an analytical formulation of the frequency response of a standard tank pipe-valve system, the research provides a localized study of system behavior with leaks at normalized resonance harmonics and assesses the impact of various dimensionless quantities. Moreover, this work addresses gaps in existing fault detection methods by deriving two new analytical formulas: one for sizing and another for locating leaks in frictionless pipe flows.