  Motivated by many recent experimental studies of non-classical rotational
inertia (NCRI) in superfluid and supersolid samples, we present a study of the
hydrodynamics of a superfluid confined in the two-dimensional region
(equivalent to a long cylinder) between two concentric arcs of radii $b$ and
$a$ ($b<a$) subtending an angle $\beta$, with $0 \le \beta \le 2\pi$. The case
$\beta= 2 \pi$ corresponds to a blocked ring. We discuss the methodology to
compute the NCRI effects, and calculate these effects both for small angular
velocities, when no vortices are present, and in the presence of a vortex. We
find that, for a blocked ring, the NCRI effect is small, and that therefore
there will be a large discontinuity in the moment of inertia associated with
blocking or unblocking circular paths. For blocked wedges ($b=0$) with $\beta >
\pi$, we find an unexpected divergence of the velocity at the origin, which
implies the presence of either a region of normal fluid or a vortex for {\it
any} nonzero value of the angular velocity. Implications of our results for
experiments on "supersolid" behavior in solid $^4{\rm He}$ are discussed. A
number of mathematical issues are pointed out and resolved.
