  Recent models of molecular cloud formation and evolution suggest that such
clouds are dynamic and generally exhibit gravitational collapse. We present a
simple analytic model of global collapse onto a filament and compare this with
our numerical simulations of the flow-driven formation of an isolated molecular
cloud to illustrate the supersonic motions and infall ram pressures expected in
models of gravity-driven cloud evolution. We apply our results to observations
of the Pipe Nebula, an especially suitable object for our purposes as its low
star formation activity implies insignifcant perturbations from stellar
feedback. We show that our collapsing cloud model can explain the magnitude of
the velocity dispersions seen in the $^{13}$CO filamentary structure by Onishi
et al. and the ram pressures required by Lada et al. to confine the lower-mass
cores in the Pipe nebula. We further conjecture that higher-resolution
simulations will show small velocity dispersions in the densest core gas, as
observed, but which are infall motions and not supporting turbulence. Our
results point out the inevitability of ram pressures as boundary conditions for
molecular cloud filaments, and the possibility that especially lower-mass cores
still can be accreting mass at significant rates, as suggested by observations.
