Answer
Please see the work below.
Work Step by Step
From equation of continuity
$A.v=constant$
$\implies v_{\circ}\pi(\frac{d_{\circ}}{2})^2=v.\pi(\frac{d}{2})^2$
$d=d_{\circ}(\frac{v_{\circ}}{v})^\frac{1}{2}$
$\implies d=d_{\circ}(\frac{v_{\circ}}{(v_{\circ}^2+2gh)^{\frac{1}{2}}})^{\frac{1}{2}}$
$d=d_{\circ}(\frac{v_{\circ}^2}{v_{\circ}^2+2gh})^\frac{1}{4}$
