Abstract: An automatic flow rate control valve, includes a tubular body, defining a flow path between inlet apertures having a gradually variable cross-sectional area and a fluid outlet at one end; a flow control piston is axially movable within the tubular body, under opposite actions of the fluid pressure and a biasing spring, to choke the fluid inlet apertures, while maintaining a constant flow rate. The control piston is in the form of a first cup-shaped element sliding on a second cup-shaped element to define a hydraulic damping chamber, communicating with the flow path.