Trying to understand hydrostatic pressure with different vessel widths

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Discussion Overview

The discussion centers on the concept of hydrostatic pressure in vessels of varying diameters, specifically comparing vessels with diameters of 1 meter and 1 centimeter, and exploring the implications of even smaller diameters down to atomic scales. The scope includes theoretical considerations and conceptual clarifications regarding hydrostatic pressure principles.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether hydrostatic pressure will be the same in vessels of different diameters, including extreme cases down to atomic scales.
  • Another participant asserts that hydrostatic pressure will be the same regardless of pipe diameter, explaining that the weight of the liquid column is what determines pressure, and changes in cross-sectional area do not affect pressure at a given depth.
  • A different participant cautions that at atomic scales, the conventional rules of hydrostatic pressure may not apply, indicating that the answer could vary based on specific conditions, such as the type of atoms involved.
  • A later reply reiterates that while the total weight of water in the vessels will differ, the pressure distributions remain the same across different diameters, as previously stated by another participant.

Areas of Agreement / Disagreement

Participants generally agree that hydrostatic pressure is the same for different vessel diameters at macroscopic scales, but there is disagreement regarding the applicability of this principle at atomic scales, where the discussion remains unresolved.

Contextual Notes

The discussion highlights limitations related to the assumptions made about the behavior of fluids at different scales, particularly the transition from macroscopic to atomic levels where classical fluid dynamics may not hold.

abrek
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TL;DR
hydraulic pressure at minimum pipe diameter
2024_08_24_0xi_Kleki.png


will the hydrostatic pressure be the same on the vessels shown with a different diameter of 1 meter and 1 centimeter? and will it be the same in both vessels if the first pipe has a diameter even less than 1 millimeter, 1 thousandth of a millimeter, 1 atom?
 
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Yes. Same pressure. PSI = pounds per square inch. Regardless of the pipe diameter, you can think of the weight of a thin vertical column of liquid. If you double the cross sectional area of that column, you also double the weight, so the change cancels out.
 
When you get down to atomic distance scales these rules are likely to break down. But the answer will depend on a lot of specific things, like which sort of atoms, etc. There's no simple answer in the nanoscale cases.
 
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abrek said:
will the hydrostatic pressure be the same on the vessels shown with a different diameter of 1 meter and 1 centimeter?
As already covered by @DaveE the answer is yes. The weights of the two water pipes will be different (more water total means a heavier pipe+water combination), but the pressure distributions will be the same.
 

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