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 $\frac{\mathrm{a}}{2}$ . The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $\frac{\sqrt{\mathrm{x}}}{6}{\mathrm{ms}}^{-1}$ for x = ...............(Given g = 10 ms^–2)