A nozzle is adapted to direct a jet of oil under pressure on an internal combustion engine. It has a variable outlet section, and it is provided with mechanical arrangement adapted to control its outlet section on the basis of the pressure of a fluid under pressure provided to this mechanical arrangement, independently of the oil going through the outlet of the nozzle. In the lubrication system an auxiliary line is provided with first proportional means controlling oil flow toward a nozzle. A control line connects a main line or the auxiliary line, upstream of the first proportional means, to a mechanical arrangement adapted to control the outlet section of the nozzle. The control line is provided with a second proportional arrangement controlling the pressure of oil delivered to the mechanical arrangement. The nozzle can be used as a piston cooling nozzle to direct oil toward a piston of an internal combustion engine.