A rotary pressure filter apparatus comprising: a housing capable of withstanding an internal pressure above ambient; a rotary drum having at least one generally round cross-section and configured to rotate inside the housing around an axis, a length of the axis defining a longitudinal direction; the rotary drum being spaced from the housing to define a generally annular plenum therebetween; at least one sealing member configured to contact the rotary drum, each sealing member separating the annular plenum between the housing and the rotary drum into zones, the sealing members adapted to pressure seal each zone from the other zones, the sealing member extending in a generally tangential direction and in the longitudinal direction; at least one material passageway adapted to allow passage of material between the annular plenum in each zone and a location outside the housing; a plurality of compartments on an outer surface of the rotary drum and configured such that material can flow between the plenum and the compartments, the compartments positioned so as to rotate sequentially through each of the zones as the rotary drum rotates, each compartment having at least one filter member; at least one filtrate outlet in fluid communication with the at least one filter member; and characterized in that the sealing member has at least one cutout portion (240, 242, 250, 260) such that the size of the at least one cutout portion (240, 242, 250, 260) in the generally tangential direction is variable along at least one portion of the longitudinal direction, the cutout portion (240, 242, 250, 260) allowing a gradual opening of the compartments to the pressure in an upstream zone on entering a new zone as the rotary drum rotates. a housing capable of withstanding an internal pressure above ambient; a rotary drum having at least one generally round cross-section and configured to rotate inside the housing around an axis, a length of the axis defining a longitudinal direction; the rotary drum being spaced from the housing to define a generally annular plenum therebetween; at least one sealing member configured to contact the rotary drum, each sealing member separating the annular plenum between the housing and the rotary drum into zones, the sealing members adapted to pressure seal each zone from the other zones, the sealing member extending in a generally tangential direction and in the longitudinal direction; at least one material passageway adapted to allow passage of material between the annular plenum in each zone and a location outside the housing; a plurality of compartments on an outer surface of the rotary drum and configured such that material can flow between the plenum and the compartments, the compartments positioned so as to rotate sequentially through each of the zones as the rotary drum rotates, each compartment having at least one filter member; at least one filtrate outlet in fluid communication with the at least one filter member; and characterized in that the sealing member has at least one cutout portion (240, 242, 250, 260) such that the size of the at least one cutout portion (240, 242, 250, 260) in the generally tangential direction is variable along at least one portion of the longitudinal direction, the cutout portion (240, 242, 250, 260) allowing a gradual opening of the compartments to the pressure in an upstream zone on entering a new zone as the rotary drum rotates.