Water from a tap emerges vertically downwards with an initial speed of 1 . 0 m s - 1 . The cross-sectional area of the tap is 10 - 4 m 2 . If we assume that the pressure is constant throughout and that the flow is steady, then the cross-sectional area of the stream, 0 . 15 m below the tap, is n × 10 - 5 m 2 . What is the value of n ?

Step-by-step solution

From conservation of energy v 2 2 = v 1 2 + 2 gh ...(i) [can also be found by applying Bernouilli's theorem between 1 and 2] From continuity equation A 1 v 1 = A 2 v 2 v 2 = A 1 A 2 v 1 ...(ii) Substituting value of v 2 from Eq. (ii) in Eq. (i) A 1 2 A 2 2 · v 1 2 = v 1 2 + 2 gh or A 2 2 = A 1 2 v 1 2 v 1 2 + 2 gh ∴ A 2 = A 1 v 1 v 1 2 + 2 gh Substituting the given values A 2 = 1 0 - 4 m 2 1.0 m/s 1.0 m/s 2 + 2 1 0 0.15 A 2 = 5 × 1 0 - 5 m 2