We study the Sobolev imbedding inequality in a curved rod or pipe
with a smooth central curve $\gamma$. Using the variational approach
and the two-scale convergence for thin domains we find the limit of
the Sobolev imbedding constant W$^{1,r}\hookrightarrow L^{q}$ as
$\epsilon$, the ratio between cross section diameter and the lenght
of the rod, tends to 0.
