  We further develop the model of molecular cloud fragmentation introduced in
Field, Blackman and Keto (2007; FBK). We show that external pressure acting on
fragments establishes a scale-dependent critical mass. Fragments with masses
less than the critical value are confined largely by pressure, while those with
masses greater than or equal to the critical value collapse under self
gravitation. Both types of fragments are commonly observed. Without specifying
the source of the external pressure, and without assuming any other scaling
relations, we predict the power - law index in the relation between the rms
velocity of supersonic motions and the size of fragments . We then investigate
the possibility that the external pressure is due to the kinetic energy of H
atoms released by photodissociation of hydrogen molecules in the fragment. This
can account approximately for the observed values of external pressure and two
additional observations: the value of the scaling coefficient in the power law
mentioned above, and the observation of outflowing atomic hydrogen around
molecular clouds. A further prediction is HI at fragment edges with column
densities of order 1E20 per sq. cm and velocities of a few km/s that should be
detectable with high resolution 21 cm observations. Finally, we predict the
magnitude of the coefficient of dissipation in the observed supersonic flows.
