A geared fuel pump (4′) operates to supply a determined flow but at low or zero pressure rise. It is planned to add gland packing (46) between support bearings (19) of the pinions (11), or between some of them, to provide hydrodynamic lift for these bearings, by delimiting a closed cavity (47) to provide lift by a fluid with better viscosity properties instead of using the fluid itself that is pumped. Possible application to fuel pumps for aircraft engines, in which the pump (4′) is a high pressure pump associated with a low pressure pump.