A pump (2) including a submersible motor (10) sealed within a motor chamber (11), an impeller (6) rotatably mounted in an impeller chamber (12), and motor and impeller shafts (72, 76) coupled to one another to interconnect the motor and impeller. The impeller pumps fluid from the impeller chamber into the motor chamber where the fluid flows around the motor to cool the motor and muffle the motor noise before being discharged from the pump. The impeller shaft (76) is rotatably mounted in a bearing (90) fixed to an impeller housing (4) and having grooves (106) facing the impeller shaft (76) and providing fluid communication between the impeller and motor chambers. Fluid flows into the grooves from the impeller or motor chamber depending on the pressure gradient across the bearing, which varies according to downstream pump conditions (e.g., pressure). As the impeller shaft continues to rotate, fluid from the grooves forms a thin lubricating film in a clearance space provided between the impeller shaft and bearing. With this construction, the need for conventional impeller shaft seals is eliminated.