An annular air flow passage for a turbine engine such as a turbojet or a turboprop, crossed by an instrumented rod that includes mechanism(s) for measuring characteristics of a flow potentially traveling along the passage, the rod extending between an outer annular wall and an inner annular wall of the passage. Outer connection(s) fasten(s) an outer end of the instrumented rod to the outer wall in a manner that is rigid in all directions, and inner connection(s) fasten(s) an inner end of the instrumented rod to the inner wall, in a manner that is rigid in the circumferential direction and that has at least one degree of freedom to move in a first direction extending between the inner and outer walls of the passage and having at least a radial component.