  Filamentary structures are ubiquitous in observations of real molecular
clouds, and also in simulations of turbulent, self-gravitating gas. However,
making comparisons between observations and simulations is complicated by the
difficulty of estimating volume-densities observationally. Here, we have
post-processed hydrodynamical simulations of a turbulent isothermal molecular
cloud, using a full time-dependent chemical network. We have then run radiative
transfer models to obtain synthetic line and continuum intensities that can be
compared directly with those observed. We find that filaments have a
characteristic width of $\,\sim\!0.1 \, {\rm pc}$, both on maps of their true
surface density, and on maps of their $850 \, {\rm \mu m}$ dust-continuum
emission, in agreement with previous work. On maps of line emission from CO
isotopologues, the apparent widths of filaments are typically several times
larger because the line intensities are poorly correlated with the surface
density. On maps of line emission from dense-gas tracers such as N$_2$H$^+$ and
HCN, the apparent widths of filaments are $\lesssim 0.1 \, {\rm pc}$. Thus,
current observations of molecular-line emission are compatible with the
universal $0.1 \, {\rm pc}$ filament width inferred from ${\it Herschel}$
observations, provided proper account is taken of abundance, optical-depth, and
excitation considerations. We find evidence for $\sim 0.4 \, {\rm km \,
s^{-1}}$ radial velocity differences across filaments. These radial velocity
differences might be a useful indicator of the mechanism by which a filament
has formed or is forming, for example the turbulent cloud scenario modelled
here, as against other mechanisms such as cloud-cloud collisions.
