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

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SUMMARY

The discussion centers on calculating the distance below a 17.0 mm faucet where the water stream narrows to a 10 mm diameter, given an initial velocity of 2.20 m/s. The principle of conservation of mass is crucial, as the water's velocity increases when transitioning to a smaller cross-section. Participants emphasize the need to determine the required velocity for the smaller diameter and apply kinematic equations to find the distance to reach that velocity. The use of Bernoulli's equation is deemed unnecessary for this vertical flow scenario.

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  • Understanding of fluid dynamics principles, specifically conservation of mass.
  • Familiarity with kinematic equations for vertical motion.
  • Knowledge of cross-sectional area calculations for cylindrical shapes.
  • Basic grasp of fluid velocity and its relationship with diameter changes.
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  • Study the application of the continuity equation in fluid dynamics.
  • Learn how to calculate flow rates through varying cross-sectional areas.
  • Explore kinematic equations in the context of fluid motion.
  • Investigate the implications of gravitational effects on fluid velocity.
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Students and professionals in physics, engineering, and fluid dynamics who are interested in understanding the behavior of fluid flow through varying diameters and the application of conservation laws in practical scenarios.

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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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