  We study Yang-Mills lattice theories with $Sp(N_c)$ gauge group, with
$N_c=2N$, for $N=1,\,\cdots,\,4$. We show that if we divide the renormalised
couplings appearing in the Wilson flow by the quadratic Casimir $C_2(F)$ of the
$Sp(N_c)$ group, then the resulting quantities display a good agreement among
all values of $N_c$ considered, over a finite interval in flow time. We use
this scaled version of the Wilson flow as a scale-setting procedure, compute
the topological susceptibility of the $Sp(N_c)$ theories, and extrapolate the
results to the continuum limit for each $N_c$.
