Water from a tap emerges vertically downwards with an initial velocity V 0 . Assuming pressure is constant throughout the stream of water and the flow is steady, find the distance from the tap at which cross-sectional area of the stream is

Question

Water from a tap emerges vertically downwards with an initial velocity V 0 . Assuming pressure is constant throughout the stream of water and the flow is steady, find the distance from the tap at which cross-sectional area of the stream is half of the cross-sectional area of the stream at the tap.

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Correct answer: B. 3 V 0 2 2 g

Using the 3rd equation of motion V 2 = u 2 + 2 g h V 2 = V 0 2 + 2 g h Using the equation of continuity A 1 V 1 = A 2 V 2 we get A 2 A 1 = V 0 V 0 2 + 2 g h Required condition A 1 A 2 = 1 2 = V 0 V 0 2 + 2 g h &#8658; 4 V 0 2 = V 0 2 + 2 g h h = 3 V 0 2 2 g

Water from a tap emerges vertically downwards with an initial velocity V 0 . Assuming pressure is constant throughout the stream of water and the flow is steady, find the distance from the tap at which cross-sectional area of the stream is half of the cross-sectional area of the stream at the tap.

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