A method and apparatus for separating cell suspension into centrate and concentrate includes a solid wall rotatable centrifuge bowl (82). A single use rotatable core (88) is positioned in the bowl and bounds a cavity (90) which serves as a separation chamber. The bowl rotates about an axis (84). An inlet tube (92) and an outlet tube (102) extend along the axis in the bowl cavity. The centripetal pump (98) in the cavity is in connection with the outlet tube. The centrate discharge pump (120) is in connection with the outlet tube. A pressure damping reservoir (122) is fluidly connected between the outlet tube and the discharge pump. At least one control circuit (142) is operative to control the apparatus to maintain a positive pressure above atmospheric pressure within the cavity, so as to maintain the cell suspension away from at least one seal (106) that bounds the interior of the cavity.