Water emerges from a tap vertically downwards with an initial speed of 1.0 m / s . The cross-sectional area of the tap is 10 – 4 m 2 . Assume that the pressure is constant throughout and that the flow is steady, the cross-sectional area of the stream 0.15 m below the tap is

Step-by-step solution

From conservation of energy v 2 2 = v 1 2 + 2 g h ... (1) [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 (2) Substituting value of v 2 from Eq. (2) in Eq. (1) A 1 2 A 2 2 . v 1 2 = v 1 2 + 2 g h or A 2 2 = A 1 2 v 1 2 v 1 2 + 2 g h A 2 = A 1 v 1 v 1 2 + 2 g h Substituting the given values A 2 = 1 0 - 4 m 2 1.0 m / s 1.0 m / s 2 + 2 10 m/s 2 0.15 m A 2 = 5.0 × 10 - 5 m 2