A centrifugal blood pump without a mechanical bearing, comprising: - a pump casing with a central axis, a blood flow inlet disposed on the central axis and a blood flow outlet disposed on a circumference of the pump casing, - an impeller arranged in the pump casing so as to be rotatable about said central axis and freely moveable axially and radially within a limited axial clearance and limited radial clearance, the impeller being provided with permanent magnets or permanently magnetized magnetic regions (N/S) and further with radially extending blades defining passages therebetween for radial blood flow, and - an electromagnetic drive adapted to cooperate with the magnets or magnetic regions (N/S) of the impeller so as to set the impeller rotating about said central axis, wherein said radial clearance is 100 μm or less so as to form a hydrodynamic radial bearing for the impeller, characterized in that the radial clearance is defined by an outer circumference (17, 18, 22) of the impeller and an inner surface of (a) a wall that is arranged in a circle about said central axis within the pump casing and has a plurality of circumferentially spaced through openings for blood to flow from the impeller towards the blood flow outlet, or (b) a plurality of axially extending, spaced apart wall sections arranged in a circle about said central axis within the pump casing and providing through openings between the wall sections for blood to flow from the impeller towards the blood flow outlet, or (c) a plurality of wall sections comprising an upper circular wall section and a lower circular wall section, the upper and lower circular wall sections being axially spaced apart so as to form one continuous circumferential through opening for blood to flow from the impeller towards the blood flow outlet. - a pump casing with a central axis, a blood flow inlet disposed on the central axis and a blood flow outlet disposed on a circumference of the pump casing, - an impeller arranged in the pump casing so as to be rotatable about said central axis and freely moveable axially and radially within a limited axial clearance and limited radial clearance, the impeller being provided with permanent magnets or permanently magnetized magnetic regions (N/S) and further with radially extending blades defining passages therebetween for radial blood flow, and - an electromagnetic drive adapted to cooperate with the magnets or magnetic regions (N/S) of the impeller so as to set the impeller rotating about said central axis, (a) a wall that is arranged in a circle about said central axis within the pump casing and has a plurality of circumferentially spaced through openings for blood to flow from the impeller towards the blood flow outlet, or (b) a plurality of axially extending, spaced apart wall sections arranged in a circle about said central axis within the pump casing and providing through openings between the wall sections for blood to flow from the impeller towards the blood flow outlet, or (c) a plurality of wall sections comprising an upper circular wall section and a lower circular wall section, the upper and lower circular wall sections being axially spaced apart so as to form one continuous circumferential through opening for blood to flow from the impeller towards the blood flow outlet.