An ideal fluid of density \( 800 \mathrm{~kg} / \mathrm{m}^{3} \), flows smoothly through a bent...

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An ideal fluid of density \( 800 \mathrm{~kg} / \mathrm{m}^{3} \), 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 \( 4100 \mathrm{~Pa} \). At wider section, the velocity of fluid is \( \frac{\sqrt{x}}{6} \mathrm{~ms}^{-1} \) for \( x= \)
(Given \( g=10 \mathrm{~m}^{-2} \) )
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