What is the relationship between water stream diameter and distance from faucet?

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SUMMARY

The discussion focuses on the relationship between the diameter of a laminar water stream and its distance from the faucet, specifically using Bernoulli's principle and the continuity equation to derive the diameter as a function of height (y). Participants emphasize the importance of understanding how water velocity, pressure, and flow rate change as the stream descends. The key takeaway is that the diameter decreases with distance due to conservation of mass and energy principles governing fluid dynamics.

PREREQUISITES
  • Understanding of Bernoulli's principle
  • Familiarity with the continuity equation in fluid dynamics
  • Basic knowledge of laminar flow characteristics
  • Ability to interpret energy diagrams in physics
NEXT STEPS
  • Study the derivation of the continuity equation in fluid mechanics
  • Explore applications of Bernoulli's principle in real-world scenarios
  • Learn about laminar versus turbulent flow and their implications
  • Investigate energy conservation in fluid systems through practical experiments
USEFUL FOR

Students studying physics, particularly those focusing on fluid dynamics, engineers working with hydraulic systems, and educators seeking to explain fluid behavior in practical contexts.

Corin511
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Homework Statement



Daphne goes to the kitchen for a glass of water. She turns on the faucet so the stream of water is laminar flow. She notes that the diameter of the water steam decreases with distance below the faucet assuming that the water exits the faucet of diameter D with speeds v0, find the diameter of the stream as a function of y.

2. Homework Equations

We have to create a step by stem reasoning for the solution of the problem.
So far we have come up with using:
Bernoulli's principle, continuity principle and and energy diagram.[/B]
Can anyone help break down this problem and actually explain what the principles actually do?

The Attempt at a Solution

 
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What do you expect in terms of the water velocity, pressure and the amount of water flowing through the cross-section per time?
 

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