An ideal fluid flows through a pipe of circular cross-section with diameters 5 cm and 10 cm as shown in the figure. The ratio of velocities of fluid at A and B is

Question

An ideal fluid flows through a pipe of circular cross-section with diameters 5 cm and 10 cm as shown in the figure. The ratio of velocities of fluid at A and B is, 4 : 1, 1 : 4, 2 : 1, 1 : 2

MARKS App · Accepted Answer

From continuity equation, a 1 v 1 = a 2 v 2 v 1 v 2 = a 2 a 1 a 1 = π d 1 2 2 ⇒ a 2 = π d 2 2 2 Where d 1 a n d d 2 are the diameters of the openings. ⇒ v 1 v 2 = π d 2 2 4 π d 1 2 4 = d 2 2 d 1 2 = 10 c m 5 c m 2 = 10 × 10 5 × 5 = 4 1 o r 4 : 1

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