Dynamin is a ubiquitous GTPase that tubulates lipid bilayers and is implicated in many membrane severing processes in eukaryotic cells. Setting the grounds for a better understanding of this biological function, we develop a generalized hydrodynamics description of the conformational change of large dynamin-membrane tubes, taking into account GTP consumption as a free-energy source. On observable time scales, dissipation is dominated by an effective dynamin-membrane friction and the deformation field of the tube has a simple diffusive behavior, which could be tested experimentally. A more involved, semimicroscopic model yields complete predictions for the dynamics of the tube and possibly accounts for contradictory experimental results concerning its change of conformation as well as for plectonemic supercoiling.