A fluid metering device including a metering valve capable of sliding in a bushing under fluid feed pressure in order to enable a fluid to be admitted and then ejected. The valve can have, at a first end, an opening opening out into a longitudinal fluid admission bore, and at a second end forming an end wall, a valve head provided with fluid metering slots opening out into the longitudinal bore and defining varying flow sections. The valve head can further include at least one substantially transverse orifice disposed downstream from the metering slots in the fluid flow direction, the orifice communicating with the longitudinal bore and defining at least one fixed flow section.