  We consider a compressible Navier-Stokes system for a barotropic fluid with
density dependent viscosity in a three-dimensional time-space domain
$(0,T)\times \Omega_\varepsilon$ where $\Omega_\varepsilon =
(0,\varepsilon)^2\times (0,1)$. We show that the weak solutions of the 3D
system converges to the strong solution of the respective 1D system as
$\varepsilon\rightarrow0.$
