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