A hydrostatic
rotary machine with radial pistons comprising: an internal element and an external element coaxial and mounted to rotate relative to each other about an axis of rotation, one of these elements being a rotor and the other a
stator; the internal element comprising a
cylinder block (10); the external element comprising a
cam track. The
machine includes a drainage circuit which includes, for at least one cylinder (11), an injection conduit (26) passing through the wall of the cylinder (11), the injection conduit (26) opening at one end into the cylinder (11) through a port (27), and opening at the other end, from the
cylinder block (10), into a drainage space supplied with
hydraulic fluid. Figure for the abbreviation: Fig. 2