A free energy functional arising from kinetic mean field models of interacting particles is considered. We study the variational limit, in the regime of long time and strong interaction. While the density of particles only features a weak limit in the phase space (say position and velocity), the projection of such a density on the spacial coordinates has a meaningful limit, which satisfies a hydrodynamic equation. We characterizes the tensors appearing in the hydrodynamic limit, in terms of the interaction and velocity field of the original model.