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.
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