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In view of great importance of magneto-rotational instability (MRI) as a fundamental mechanism for angular momentum transfer in magnetized stellar accretion disks, several research centers are involved in experimental study of MRI under laboratory conditions. The idea of the experiment is to investigate the rotation dynamics of well conducting liquid (liquid metal) between two cylinders in axial magnetic field. In this Letter, an experimental scheme with immovable cylinders and fluid rotation driven by radial current is considered. The analytical solution of a stationary flow was found taking into account the external current. Results of axially symmetric numerical simulations of current driven fluid dynamics in experimental setup geometry are presented. The analytical solution and numerical simulations show that the current driven fluid rotation in axial magnetic field provides the axially homogeneous velocity profile suitable for MRI study in classical statement.