In an apparatus for extracorporeal blood treatment, an extracorporeal circuit (6) is connected to a blood chamber (3) of a membrane device (2). A pump (10) displaces a priming fluid from a source of a priming fluid (9) to a drainage (11) for discharging the priming fluid. A control unit (13) is provided with a processor which controls the pump at a preset first flow rate value, and receives from a pressure sensor (12) a first pressure value, compares the first pressure value with a reference pressure value and, on the basis of this comparison, determines whether or not the extracorporeal circuit is of a pediatric type or of an adult type. The invention is particularly useful during a stage of readying a dialysis apparatus.