Trying to understand hydrostatic pressure with different vessel widths

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SUMMARY

Hydrostatic pressure remains constant regardless of the diameter of a vessel, as demonstrated in the discussion comparing vessels with diameters of 1 meter and 1 centimeter. The pressure at a given depth is determined solely by the height of the liquid column above it, not the cross-sectional area. While the total weight of the liquid changes with vessel diameter, the pressure exerted at the bottom remains the same. At atomic scales, however, the principles of hydrostatic pressure may not apply uniformly due to variations in atomic structure.

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abrek
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TL;DR
hydraulic pressure at minimum pipe diameter
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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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