A tubular element (9) tubular element (9) provides an inner space forming a passage for conducting milk, with a first material portion (9a) which constitutes the main part of the tubular element (9) and an additional material portion (9b) which includes a vent passage (9b) adapted to supply air to the inner space of the tubular element (9). The first material portion (9a) and the additional material portion (9b) are fixedly connected to each other in a contact area (9d) such that the material portions (9a, b) form an integrated unit. A method of manufacturing the tubular element.
