A one-dimensional model of hydrodynamic escape is used to study the loss of hydrogen from a hot, water-rich atmosphere of the Venus type. A range of EUV heating rates corresponding to the present solar cycle fluctuations of the EUV flux and different possible heating efficiencies are considered. The present model takes into account the transition to the collisionless state at the exobase through a modified Jeans' approach. For the fluid inner planetary corona, the conservation equations are solved from the base of the expanding flow (z≈200 km) up to the exobase, generally located at an altitude of ≈1 planetary radius. Solutions are found, for which the flux in the collisional region is equal to the Jeans escape flux at the exobase. The ionization state of the planetary wind is calculated, and the position of the obstacle is determined by equilibrating the solar wind ram pressure and the pressure of the expanding plasma. It is shown that ≈2/3 of the escape energy is supplied by energetic neutrals formed by charge exchange between escaping H atoms and solar protons in the heliosphere, a fraction of which intercepts the exobase and heats by collision the upper layers of the fluid planetary corona. Any planetary magnetic field pushing away the obstacle up to an altitude larger than ≈3 planetary radii would inhibit this effect. The combination of (1) the geometric amplification of solar EUV absorption at z>≈2000 km due to the increase with altitude of the cross-sectional area of the planetary corona and (2) the substantial inward flux of energy at the exobase through heating by energetic neutrals results in the formation of a stable hot region below the exobase, allowing substantial escape. A detailed energetic budget of the escape process is established. An upper limit of ≈3¿1011 cm-2 s-1 on the escape flux is found. The ratio of the EUV flux to the solar wind strength is shown to be of prime importance, since the solar wind regulates the escape flux from outside, through the action of energetic neutrals, and the EUV flux acts from inside, by supplying atoms with the energy required to lift them up to the exobase. ¿ American Geophysical Union 1996