Hydrostatic pressure on a teapot spout

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SUMMARY

The discussion centers on the "teapot effect," which describes how water flows along the outside of a teapot spout due to pressure differences between the water and the atmosphere. Key points include that points A and D are at atmospheric pressure, while point B experiences higher pressure due to Pascal's Law. Point C is determined to be at lower pressure than D, attributed to gravitational effects and energy conservation principles. The analysis emphasizes the relationship between fluid velocity and pressure, confirming that faster-moving fluids exhibit lower pressure.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly Bernoulli's principle.
  • Familiarity with Pascal's Law and its implications in fluid mechanics.
  • Basic knowledge of pressure concepts in physics.
  • Ability to analyze pressure differences in fluid systems.
NEXT STEPS
  • Study Bernoulli's equation and its applications in fluid flow.
  • Explore Pascal's Law in greater detail, particularly in hydraulic systems.
  • Investigate the relationship between fluid velocity and pressure in various contexts.
  • Examine case studies of the teapot effect in practical applications.
USEFUL FOR

Students studying fluid dynamics, physics enthusiasts, and engineers interested in fluid mechanics and pressure analysis will benefit from this discussion.

ShizukaSm
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Homework Statement



First of all I apologize, the question is originally in my mother language, so I will do my best to translate it. I apologize if I commit any mistakes, and feel free to tell me if something is unclear.

The phenomenom where water flows on the outside side of a teapot spout is named "The teapot effect", and occurs due to a difference in pressure between water and the atmosphere. Consider the image of a teapot spout and order in an ascending order the pressures of points A, B, C and D.
Teapot.PNG

("Bico" means "Spout", and "Água" means "Water")


The Attempt at a Solution


I've been kind of lost in this question due to different theories, so I'm going to arrange them into statements to make it more organized:

1)(This doesn't alter the answer, but I wanted to know if it's correct)The whole stream of water has a lower pressure (if compared to atmospheric) because it has a certain velocity, and fluids with velocity have lower pressure;

2)A and D must be atmospheric pressure, since they're both in direct contact with air;

3)B must be higher than both because of Pascal's Law;

4)C must be lower than D, but I don't have a clue why this is true. I'm assuming that because it must be the pressure difference that supports water against gravity (considering that I'm right about D being atm pressure), but that is kind of "doing the problem in reverse", what would the real reason be?
 
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Well, maybe this is a naive solution to the problem, but let me try: a is at atmospheric pressure, due contact to air, b is higher to Pascal's law. C and d are at lower positions, so they must have less potential due to gravity, and by energy conservation, have higher velocities. So, must have lower pressures, but, d must be greater than c because both Pascal's law and atmosphere contact.
 

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