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/2. The…

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