A flowrate control device for a fluid, includes a cartridge body defining a path for the fluid and having an upstream portion for the entry of the fluid, and a downstream portion provided with an outlet opening for the fluid. A shutter element is arranged in the cartridge body for sliding movement between an upstream end of the cartridge body corresponding to a minimum throttling position for the fluid and a downstream end of the cartridge body corresponding to a maximum throttling position for the fluid. The shutter element is provided with a throttling wall arranged downstream for throttling the outlet opening in a controlled manner and an upstream wall cooperating with the upstream portion of the cartridge body for bounding an inlet section for the fluid. A counter spring element exerts a contrasting force on the shutter element suitable for displacing the shutter element towards the upstream end. A section-varying assembly increases or decreases the area of the inlet section according to the variation of the contrasting force due to the movement of the shutter element along the longitudinal axis. The section-varying assembly, in addition to taking account the variable force of the counter spring element in order to ensure a constant flowrate, also minimizes the operating minimum pressure difference and controls the relation between the flowrate and the operating minimum pressure difference.