We developed a one-dimensional, time-independent, hydrodynamic model for dusty gas flows in cometary atmospheres that accounts for a broad size distribution and fragmentation of dust. In this model, water vapor is the only constituent of the gas and the grains do not evaporate. The initial gas Mach numbers were obtained as a function of radius of nonfragmenting dust particles of a single size in the range (10^{-6}) to (10^{+1} \mathrm{~cm}), assuming a mass ratio of dust-to-gas release rates (\boldsymbol{\chi}=1). It was found that particles larger than about (1 \mathrm{~mm}) decelerate the initial gas flow very little. The velocities of particles with radii of (10^{-6}) to (1 \mathrm{~cm}) were also calculated as a function of distance from the nucleus in order to find the acceleration regions for particles of different sizes when a dust size distribution is considered. The continuous dust size distribution was approximated by 21 discrete sizes with a logarithmic scale from (10^{-4}) to (1 \mathrm{~cm}) in particle radius. The fragmentation model was applied to study the deviation of intensity profiles from the simple (1 / z) relationship for dust jets in Comet Halley observed by the Giotto spacecraft, (z) being the radial distance from the surface of the nucleus. We found that the observed increase of (I \cdot z) by a factor of 10 , where (I) is the dust intensity, implied that a parent particle must fragment into (10^{12}) daughter particles within tens of seconds of release from the nucleus to counteract the strong effect of acceleration on the profile. If dust particles fragment in such a short time scale, only micrometer-sized grains are likely to have been measured by Giotto; however, millimeter-sized grains were detected beyond (600 \mathrm{~km}) from the nucleus of Comet Halley. Therefore, fragmentation is not the only physical mechanism for explaining the deviation of the dust intensity profiles. Additional factors such as divergent flows from different parts of an extended surface source region, each part emitting dust into overlapping cones with nearly the same opening angle, are needed to interpret the intensity deviation. 1993 Academic Press, Inc.