A pump includes a pump casing that defines a pump chamber, the pump casing having an inlet and an outlet. An impeller is arranged with respect to the pump chamber to displace fluid from the inlet into the pump chamber. A vortex shaping mechanism is arranged in the pump chamber and is configured to constrain fluid within the pump chamber into a rotational flow pattern about a rotational axis. At least the casing and the vortex shaping mechanism are configured so that a portion of the fluid is encouraged to establish a solid body vortex, with an outer periphery of the solid body vortex being determined by the vortex shaping mechanism, and a portion of the fluid defining a diffusion zone in fluid communication with the outlet such that fluid can diffuse across a fluid interface between the solid body vortex and the diffusion zone to generate a pumping pressure at the outlet.