The invention relates to a hydrodynamic bearing arrangement, particularly for a spindle motor to drive the platters of a hard disk drive, the bearing arrangement having a shaft and a bearing bush, which, supported by a lubricant circulating between their bearing surfaces, are rotatable with respect to each other, a covering cap being provided that covers an end face and regions of the outside diameter of the bearing bush adjoining this end face. A free space is provided between the bearing bush and the covering cap, the free space being connected to the bearing gap and at least partially filled with lubricant. According to the invention, a channel running substantially in the longitudinal direction of the bearing bush is provided on the outside diameter of the bearing bush, one end of the channel leading into the free space and allowing the filling level of the lubricant in the free space to be measured.