The vortex flow of a superfluid liquid between concentric cylinders rotating with the same angular velocity is studied. A general expression is obtained for the free energy of a liquid with vortices ofarbitraryintensity. The possibility of emergence of vortices whose vorticity is opposite in sign to the angular velocity (negative vortices) is studied. It is shown that the formation of negative vortices in a liquid corresponds to larger values of free energy than for positive vortices. The friction force exerted by the normal component on a vortex dislodged from equilibrium position is derived, and the energy barrier overcome by a vortex in crossing from one wall to another is calculated. It is shown that in view of the presence of the energy barrier, the probability of vortex formation is significant only for angular velocities considerably exceeding the theoretical angular velocity. Parametric equations are obtained for the envelope of a family of lines expressing the free energy as a function of the angular velocity of a rotating vessel with different numbers of vortices. An approximate relation between the angular velocity of a rotating vessel and the number of vortices formed at this angular velocity is obtained. ©1997 American Institute of Physics.