The present invention refers to a conduit arrangement (10) of a fluid distributing device (12), the conduit arrangement (10) comprises: a source fluid inlet (42) connected to a source fluid conduit (43) for guiding a source fluid entering through the source fluid inlet (42) to an outlet (46), a container fluid inlet (44) connected to a container fluid conduit (45) for guiding a container fluid entering through the container inlet (44) to an outlet (46) which is preferably detachably connected or detachably connectable to at least one hand piece (16) of the fluid distributing device (12), a plurality of valves (32, 34, 36) each having a first and a second state, and wherein each valve (32, 34, 36) is associated with at least one of the conduits (43, 45), and a controller (18) configured to switch each of the valves (32, 34, 36) from the first state to the second state and vice versa for allowing or preventing respectively the container fluid or the source fluid to enter the corresponding conduit (43, 45) and refers to a method for cleaning a conduit arrangement (10).