An ideal fluid of density 800 kg m - 3 , flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to a 2 . The pressure difference between the wide and narrow sections of pipe is 4100 Pa . At wider section, the velocity of fluid is x 6 m s - 1 for x = _____ . (Given g = 10 m s - 2 )

Step-by-step solution

From equation of continuity, a v 1 = a 2 v 2 ⇒ v 2 = 2 v 1 From Bernoulli's theorem, P 1 + 1 2 ρ v 1 2 + ρ g h 1 = P 2 + 1 2 ρ v 2 2 + ρ g h 2 ⇒ P 1 - P 2 = ρ g h 2 - h 1 + 1 2 v 2 2 - v 1 2 ⇒ 4100 = 800 10 - 1 + 1 2 3 v 1 2 ⇒ 4100 800 + 10 = 3 2 v 1 2 ⇒ v 1 = 121 4 × 3 = 363 6   m   s - 1 Therefore, x = 363 .