  In this paper we employ the hydrodynamic formulation of time-dependent
density functional theory to obtain the van der Waal coefficients $C_{6}$ and
$C_{8}$ of alkali-metal clusters of various sizes including very large
clusters. Such calculation becomes computationally very demanding in the
orbital-based Kohn-Sham formalism, but quite simple in the hydrodynamic
approach. We show that for interactions between the clusters of same sizes,
$C_{6}$ and $C_{8}$ sale as the sixth and the eighth power of the cluster
radius rsepectively, and approach the respective classically predicted values
for the large size clusters.
