An ideal fluid of density 800 $\mathrm{kgm}^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers 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 $\frac{\sqrt{x}}{6} \mathrm{~ms}^{-1}$ for $\mathrm{x}=$ $\_\_\_\_$ (Given $\mathrm{g}=10 \mathrm{~m}^{-2}$ )
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