  In this contribution, we report on our study of the properties of the Wilson
flow and on the calculation of the topological susceptibility of $Sp(N_c)$
gauge theories for $N_c=2,\,4,\,6,\,8$. The Wilson flow is shown to scale
according to the quadratic Casimir operator of the gauge group, as was already
observed for $SU(N_c)$, and the commonly used scales $t_0$ and $w_0$ are
obtained for a large interval of the inverse coupling for each probed value of
$N_c$. The continuum limit of the topological susceptibility is computed and we
conjecture that it scales with the dimension of the group. The lattice
measurements performed in the $SU(N_c)$ Yang-Mills theories by several
independent collaborations allow us to test this conjecture and to obtain a
universal large-$N_c$ limit of the rescaled topological susceptibility.
