d
We have $v_{1}=\sqrt{2 g h(h / 2)}=\sqrt{g h} \ldots . .(i)$
and by using Bernoulli's theorem
$\rho g h+2 \rho g\left(\frac{h}{2}\right)=\frac{1}{2}(2 \rho) v_{2}^{2}$
$\Rightarrow v_{2}=\sqrt{2} g h \ldots . .(i i)$
From Eqs. $(i)$ and $(ii)$
$\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{2}}$