The arrangement comprises a fluid bearing comprising a first fluid bearing element located in a bearing housing and a piston located in a pump housing. The bearing housing comprises a bearing housing opening. The pump housing comprises a pump housing opening. The first fluid bearing element is connected to the piston by means of a connection means extending from the first fluid bearing element through the bearing housing opening to the piston through the pump housing opening. The piston is arranged to reciprocate in the pump housing. The pump housing is connected to a fluid reservoir by means of a first inlet. The bearing housing comprises a first outlet for allowing fluid to exit the bearing housing. The arrangement further comprises a fluid transport means fluidly connecting the pump housing and the bearing housing.