We describe a simple realization of Fizeau's "aether-drag" experiment. Using an inexpensive setup, we measure the phase shift induced by moving water in a laser interferometer and find good agreement with the relativistic prediction or, in the terms of 19th century physics, with Fresnel's partial-drag theory. This appealing experiment, particularly suited for an undergraduate laboratory project, not only allows a quantitative measurement of a relativistic effect on a macroscopic system but also constitutes a practical application of important concepts of optics, data acquisition and processing, and fluid mechanics.