Water Flow from 17.0mm Faucet: When Does it Narrow to 10mm?

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To determine when the water stream from a 17.0 mm faucet narrows to 10 mm, the conservation of mass principle is essential. As the water exits the faucet at a speed of 2.20 m/s, it accelerates due to gravity, which causes the cross-sectional area to decrease. The required velocity for the smaller diameter can be calculated using the continuity equation. Kinematic equations can then be applied to find the distance at which this velocity is achieved. Understanding these principles allows for accurate calculations of fluid dynamics in vertical flows.
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Water flows out of a 17.0 mm-diameter sink faucet at 2.20 m/s.

At what distance below the faucet has the water stream narrowed to 10 mm diameter?

I am confused on how to approach this question as it is vertical and therefore using the bernoulli's eqn. for this makes no sense? or at least i think it doesnt? thanks for any help!
 
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Conservation of mass is required. The water will gain velocity as it leaves the faucet, and thus as the velocity increase due to gravity, the cross section must decrease. Find what velocity is required for the same flow to flow through the smaller cross section. Then use kinematics to find the distance it takes to reach that velocity.
 

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