The effective structural health monitoring (eSHM) system fully exploits the flexibility offered by the 3D printing process for analysis of the structural integrity of additive manufactured parts by integrating a smart technology inside the component. The eSHM system relies on the propagation of pressure waves through capillaries/small ducts embedded in 3D printed metallic components and allows the detection and localization of fatigue cracks. However, the nature and propagation of these waves seem to be determinant for the accuracy of the crack localization system. To achieve a better physical understanding of the propagating waves through the capillaries, computational fluid dynamics simulations are performed and compared with experimental results, obtained by Schlieren flow visualization and high-speed imaging techniques. The presence of propagating shock waves and contact discontinuities is observed in the simulations, as well as a complex reflection mechanism around the leak location. The Schlieren experiments exhibit the same wave shape behavior and complex reflection mechanism around the crack location for the contact discontinuity, and the shock tube analogy is confirmed.