  The article is devoted to the asymptotic limit of the compressible
Navier-Stokes system with a pressure obeying a hard--sphere equation of state
on a domain expanding to the whole physical space $R^3$. Under the assumptions
that acoustic waves generated in the case of ill-prepared data do not reach the
boundary of the expanding domain in the given time interval and a certain
relation between the Reynolds and Mach numbers and the radius of the expanding
domain, we prove that the target system is the incompressible Euler system on
$R^3$. We also provide an estimate of the rate of convergence expressed in
terms of characteristic numbers and the radius of domains.
