A device for supplying a large number of consumer stations with a predetermined amount of a process medium, in particular a coating device for containers, has a supply line for the process medium and a connection at the consumer station. In order to make such a device simpler from the structural point of view and less expensive, a unit is used, which keeps a predetermined flow rate constant and which comprises a capillary path extending before each connection and dimensioned in accordance with the predetermined amount of process medium, and a unit which is associated with a plurality of connections and which is used for maintaining a defined flow velocity along the capillary path.