A fluid container particularly useful in a centrifuge system for separating the various fractions in blood. The container comprises two circular sheets of flexible material, having central openings therein. The outer peripheral edges are sealed together, as well as annular-like portions extending outwardly from the central opening. Concentric-like inner and outer annular-like channels are thus formed at the outer peripheral portion of the assembly. Radial arcuate portions are sealed off, thereby providing interrupted annular-like channels. At a first end of the inner annular-like channels, an inlet tube is provided, extending outwardly from the central opening and communicating with the first end of the inner annular-like channel. At the outlet or second end of the inner annular-like channel, there is provided a radially extending inter-channel connector, which comprises a sealed off portion extending between the adjacent ends of the inner and outer annular-like channels. Also at this outlet end of the inner channel, a radially enlarged region is provided, acting as a first collecting chamber, into which an outlet tube is sealed, extending from the inner opening. A second collection chamber is provided at the outlet end of the outer annular-like channel. A plurality of outlet tubes extend radially outward from the center of the bag to open within the second collection chamber at different radial distances. Through these outlet tubes, selected separated portions of the fluid are withdrawn from the bag.