  We retrieve the H_2O expansion velocity in a number of comets, using the
18-cm line shapes of the OH radical observed with the Nan\c{c}ay radio
telescope. The H_2O velocity is derived from the large base of a trapezium
fitted to the observed spectra. This method, which was previously applied to 9
comets, is now extended to 30 further comets. This allows us to study the
evolution of their water molecule outflow velocity over a large range of
heliocentric distances and gas production rates. Our analysis confirms and
extends previous analyses. The retrieved expansion velocities increases with
increasing gas production rates and decreasing heliocentric distances.
Heuristic laws are proposed, which could be used for the interpretation of
observations of cometary molecules and as a touchstone for hydrodynamical
models. The expansion velocities retrieved from 18 cm line shapes are larger
than those obtained from millimetric observations of parent molecules with
smaller fields of view, which demonstrates the acceleration of the gas with
cometocentric distance. Our results are in reasonable quantitative agreement
with current hydrodynamical models of cometary atmospheres.
