  New rotation laws have been recently found for general-relativistic
self-gravitating stationary fluids. It was not clear whether they apply to
systems rotating with a constant linear velocity. In this paper we fill this
gap. The answer is positive. That means, in particular, that these systems
should exhibit the recently discovered general-relativistic weak-field effects
within rotating tori: the dynamic anti-dragging and the deviation from the
Keplerian motion induced by the fluid selfgravity.
