A tool comprising a cutting section, on which a multiplicity of blades or cutting edges and flutes are formed; a shank section, which forms a chucking section on a side which faces away from the cutting section, wherein a number of fluid channels which corresponds to the number of flutes is formed in the chucking section, which channels in each case have an axial discharge opening and lead along the shank to an associated flute of the cutting section. Also, a method for supplying the blades of such a tool with a pressurized fluid.