An apparatus for extracorporeal treatment of fluid and a process of setting up a medical apparatus for the delivery or collection of fluids are disclosed. According to the apparatus and the process, a control unit (10) is configured calculate set values of two or more of the fluid flow rates by imposing that an emptying time of containers of fresh fluid (16, 20, 21, 26) and/or a filling time of a waste container is substantially same as, or multiple of, the emptying time of one or more of the other containers of fresh fluid.