An ideal fluid of density  $800kg{m}^{-3}$,flows smoothly through a bent pipe (as shown in figure) that tappers in cross-sectional area from $a$ to  $\frac{a}{2}$.The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $\frac{\sqrt{x}}{6}m{s}^{-1}$ for $x=\_\_\_\_\_$.(Given $g=10m{s}^{-2}$)