  Blue straggler stars (BSS) are well studied in globular clusters but their
systematic study with secure membership determination is lacking in open
clusters. We use Gaia DR2 data to determine accurate stellar membership for
four intermediate-age open clusters, Melotte 66, NGC 2158, NGC 2506 and NGC
6819, and three old open clusters, Berkeley 39, NGC 188 and NGC 6791, to
subsequently study their BSS populations. The BSS radial distributions of five
clusters, Melotte 66, NGC 188, NGC 2158, NGC 2506, and NGC 6791, show bimodal
distributions, placing them with Family II globular clusters which are of
intermediate dynamical ages. The location of minima, $r_\mathrm{{min}}$, in the
bimodal BSS radial distributions, varies from 1.5$r_c$ to 4.0$r_c$, where $r_c$
is the core radius of the clusters. We find a positive correlation between
$r_\mathrm{{min}}$ and $N_{\mathrm{relax}}$, the ratio of cluster age to the
current central relaxation time of the cluster. We further report that this
correlation is consistent in its slope, within the errors, to the slope of the
globular cluster correlation between the same quantities, but with a slightly
higher intercept. This is the first example in open clusters that shows BSS
radial distributions as efficient probes of dynamical age. The BSS radial
distributions of the remaining two clusters, Berkeley 39 and NGC 6819, are
flat. The estimated $N_{\mathrm{relax}}$ values of these two clusters, however,
indicate that they are dynamically evolved. Berkeley 39 especially has its
entire BSS population completely segregated to the inner regions of the
cluster.
