  Filamentary structures identified in far-infrared observations of molecular
clouds are typically found to have full-widths at half-maximum $\sim\!0.1$ pc.
However, the physical explanation for this phenomenon is currently uncertain.
We use hydrodynamic simulations of cylindrically-symmetric converging flows to
show that the full-width at half-maximum of the resulting filament's surface
density profile, FWHM$_{\Sigma}$, is closely related to the location of the
accretion shock, where the inflow meets the boundary of the filament. For
inflow Mach Number, ${\cal M}$, between 1 and 5, filament FWHM$_{\Sigma}$s fall
in the range $0.03$ pc $\lesssim$ FWHM$_{\Sigma} \lesssim 0.3$ pc, with higher
${\cal M}$ resulting in narrower filaments. A large sample of filaments, seen
at different evolutionary stages and with different values of ${\cal M}$,
naturally results in a peaked distribution of FWHM$_{\Sigma}$s similar in shape
to that obtained from far-infrared observations of molecular clouds. However,
unless the converging flows are limited to ${\cal M} \lesssim 3$, the peak of
the distribution of FWHM$_{\Sigma}$s is below the observed $\sim 0.1$ pc.
