  We consider linear arrays of cells of volume $V_\mathrm{c}$ populated by
monodisperse rods of size $\sigma V_\mathrm{c}$, $\sigma=1,2,\ldots$, subject
to hardcore exclusion interaction. Each rod experiences a position-dependent
external potential. In one application we also examine effects of contact
forces between rods. We employ two distinct methods of exact analysis with
complementary strengths and different limits of spatial resolution to calculate
profiles of pressure and density on mesoscopic and microscopic length scales at
thermal equilibrium. One method uses density functionals and the other
statistically interacting vacancy particles. The applications worked out
include gravity, power-law traps, and hard walls. We identify oscillations in
the profiles on a microscopic length scale and show how they are systematically
averaged out on a well-defined mesoscopic length scale to establish full
consistency between the two approaches. The continuum limit, realized as
$V_\mathrm{c}\to0$, $\sigma\to\infty$ at nonzero and finite $\sigma
V_\mathrm{c}$, connects our highest-resolution results with known exact results
for monodisperse rods in a continuum. We also compare the pressure profiles
obtained from density functionals with the average microscopic pressure
profiles derived from the pair distribution function.
