A device for conveying a liquid, in particular a cutting liquid from a machining operation containing production residues. The device includes a vertical pump having a pump housing (14), a pump impeller (13), a drive shaft (19) surrounded by a housing (18), an electric motor, and a shaft connection between the electric motor and the pump impeller (13). The pump housing (14) has an inlet opening (15) and a liquid delivery opening (16). When the pump is started, a negative pressure is generated in the housing (18) surrounding the drive shaft (19). The zone of negative pressure extends into the pump housing (14) through a gap (22) between the shaft (19) and the housing (18) and thus assures that fluid will be drawn into the pump even when the liquid level is extremely low.