This work develops a formal hydrodynamic analogy, offering its self-consistent extension for describing the magnetic moments of elementary particles. Based on the analysis of experimental data on the electric charge distribution and magnetic moments of nucleons, a model of their internal structure as a system of coaxial toroidal vortices is constructed. The model demonstrates quantitative agreement with key experimental parameters, offering an intuitive picture for understanding microphysical processes. Concrete proposals for the experimental verification of the model are developed. It is emphasized that the approach does not claim to be fundamental but possesses significant potential for educational applications.