  The influence of confinement on the drag force $F$ on a static cylinder in a
viscous flow inside a rectangular slit of aperture $h_0$ has been investigated
from experimental measurements and numerical simulations. At low enough
Reynolds numbers, $F$ varies linearly with the mean velocity and the viscosity,
allowing for the precise determination of drag coefficients $\lambda_{||}$ and
$\lambda_{\bot}$ corresponding respectively to a mean flow parallel and
perpendicular to the cylinder length $L$. In the parallel configuration, the
variation of $\lambda_{||}$ with the normalized diameter $\beta = d/h_0$ of the
cylinder is close to that for a 2D flow invariant in the direction of the
cylinder axis and does not diverge when $\beta = 1$. The variation of
$\lambda_{||}$ with the distance from the midplane of the model reflects the
parabolic Poiseuille profile between the plates for $\beta \ll 1$ while it
remains almost constant for $\beta \sim 1$. In the perpendicular configuration,
the value of $\lambda_{\bot}$ is close to that corresponding to a 2D system
only if $\beta \ll 1$ and/or if the clearance between the ends of the cylinder
and the side walls is very small: in that latter case, $\lambda_{\bot}$
diverges as $\beta \to 1$ due to the blockage of the flow. In other cases, the
side flow between the ends of the cylinder and the side walls plays an
important part to reduce $\lambda_{\bot}$: a full 3D description of the flow is
needed to account for these effects.
