The development of hydrodynamics metamaterials and transformation hydrodynamics has enriched the methods of fluid flow control. In the proposed study, coupling flow rotation and amplification functions, hydrodynamic rotating concentrators with tensorized viscosity are designed based on transformation hydrodynamics. Through numerical simulations, we have demonstrated that the rotating concentrators can simultaneously magnify and rotate the velocity in creeping flows. In the central area of the rotating concentrators, the fluid velocity is amplified, exhibiting the venturi effect; in the external area of the rotating concentrators, the flow state is not interfered with due to the presence of the rotating concentrators, maintaining the original flow state. Additionally, we discover and explain the mechanisms of the rotational hysteresis phenomena that are caused by the nonreciprocity of spatial coordinate transformations. The proposed studies 1) extend and optimize the traditional flow concentrators, 2) raise new approaches for applications related to Venturi effects, and 3) shed light on the design of nonreciprocal coordinate transformations for metamaterials.