The pump consists of cylindrical rotor attached on a shaft. The rotor has a piston which runs along a static wall of a circular working chamber and which engages with a recess of a shut-off slide of similar diameter and thickness. The shut-off rotor is powered by rolling contact with the piston rotor and which is attached on a second parallel located shaft. The shafts of the piston slide and shut-off slide are interconnected by coupling gearwheels.