Singly ionized helium, a minor species in the polar ionosphere, is being propelled out along open magnetic field lines by an outward polarization electric field. In the present study we compare the kinetic and hydrodynamic descriptions of this transonic outflow treating the singly ionized helium as a test particle population in a static background of singly ionized oxygen and electrons. We find that the resultant He+ particle fluxes are equal in both the eight-moment hydrodynamic description and in the kinetic description based on the Fokker-Planck equation. A five-moment hydrodynamic description gives a flux that is some 40% lower. The increase of the He+ energy flux with altitude is also equal in the eight-moment hydrodynamic and in the kinetic descriptions. ¿ American Geophysical Union 1996