Z4DP V: The Hydrodynamic Nature of Mass - Vortex Rotation of Galaxies and the Derivation of the Tully-Fisher Relation

This paper presents a comprehensive redefinition of mass and gravity through the mechanics of an elastic superfluid continuum (Z4DP). Instead of the classical concept of mass as a source of attractive force acting at a distance, the Z4DP model redefines and fully utilizes mass as a hydrodynamic sink capacity. Using the example of bodies in free fall in a vacuum, we demonstrate that the equivalence principle is a natural consequence of convective advection in a medium. Subsequently, we derive cosmic velocities as hydrodynamic parameters of a stationary macro-vortex. In the main section of the paper, the model is applied to fundamental anomalies: nuclear mass defect, the origin of inertia, and galactic dynamics. By employing the explicit constitutive equation of the elastic continuum, we derive the flat rotation curves of galaxies from first principles. Finally, utilizing the Buckingham π-theorem, the Baryonic Tully-Fisher relation is analytically derived as a fundamental scaling law of a stable macro-vortex, thereby completely eliminating the need for dark matter or ad hoc modifications of dynamics.