Aims. We retrieve the H2O expansion velocity in a number of comets, using the 18-cm line shapes of the OH radical observed with the Nançay radio telescope. Methods. The H2O 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 more comets. This allows us to study the evolution of their water molecule outflow velocity over a wide range of heliocentric distances and gas production rates. Results. 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 interpreting observations of cometary molecules and as a touchstone for hydrodynamical models. The expansion velocities retrieved from 18 cm line shapes are higher 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.
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