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.
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