Water from a tap emerges vertically downwards with initial velocity 4 ~ms ⁻¹ . The cross-sectional area of the tap is A . The flow is steady and pressure is constant throughout the stream of water. The distance h vertically below the tap, w

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Water from a tap emerges vertically downwards with initial velocity 4 ~ms ⁻¹ . The cross-sectional area of the tap is A . The flow is steady and pressure is constant throughout the stream of water. The distance h vertically below the tap, where the cross-sectional area of the stream becomes ( 2 3 ) A , is (g=10 ~m / s ^2 )

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Correct answer: B. 1 ~m

The equation of continuity A₁ v₁=A₂ v₂A 4= 2 3 A v₂v₂=6 ~ms ⁻¹ From Bernoulli's theorem p+ g h₁+ 1 2 v₁^2=p+ g h₂+ 1 2 v₂^2g (h₁-h₂ )= 1 2 (v₂^2-v₁^2 )g h= 1 2 [(6)^2-(4)^2 ] [ h₁-h₂=h ]10 h= 1 2 [36-16]h= 20 20 =1 ~m

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