This pump comprises a chamber and an annular pumping diaphragm secured to the said chamber and the inner edge of which is secured to a central drive part. This diaphragm has a convex domed profile so that its expulsion stroke results essentially in the energy-generating flexing of the intake stroke. The rigidity of the diaphragm is chosen so that the absolute pressure of the chamber lies within the following range: Patm&minus(&DgrPvalve&mdashin+&DgrP&Dgrh&mdashin+&DgrPpd)&gEP>Pvap where: Patm=atmospheric pressure, Pvap=vapour pressure of the pumped fluid, &DgrPvalve&mdashin=pressure difference between the upstream and downstream side of the inlet valve for opening it, &DgrP&Dgrh&mdashin=pressure difference in the upstream pipe between its distal end and the upstream side of the inlet valve as a result of the weight of the column of fluid, &DgrPpd=pressure drop in the upstream pipe for the desired flow rate.