The cleaning of milk transporting conduit structure involves introducing fluid and an amount of gas into the milk transporting conduit structure, which causes a slug of fluid to be formed in and forwarded through the milk transporting conduit structure. A sensor arrangement measures at least one parameter related to the slug, and repeatedly forwards updatings of the at least one measured parameter to the data processor. Based thereon, the data processor produces an indicator of at least one quality of the cleaning process. The indicator reflects a cross-sectional profile of the slug at at least one position in the milk transporting conduit structure.
