Liquid in a vertical pipe open at the lower end and closed at the top

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Discussion Overview

The discussion revolves around the behavior of liquid in a vertical pipe that is open at the lower end and closed at the top. Participants explore the conditions under which the liquid may fall out of the pipe, considering factors such as pipe diameter, surface tension, and the stability of the meniscus.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, Anders, questions whether the liquid will fall out of the pipe and seeks criteria for this behavior, suggesting that pipe diameter influences the formation of a stable meniscus.
  • Another participant proposes that the properties of the liquid, such as viscosity, may also play a role in determining whether the liquid falls out.
  • A later reply suggests that the stability of the meniscus is crucial, indicating that in larger pipes, surface tension may not be sufficient to maintain stability.
  • One participant claims to have found an answer, stating that long wavelength capillary waves can cause instability in larger diameter tubes, leading to the liquid falling out, referencing the Rayleigh-Taylor instability.
  • This participant also mentions a critical diameter of 8.5 mm for water in air, below which the liquid remains in the tube due to stable meniscus formation.
  • Theoretical support for these claims is provided by a textbook reference, indicating a connection to established physics concepts.

Areas of Agreement / Disagreement

Participants express varying views on the factors influencing whether the liquid will fall out, with some focusing on surface tension and meniscus stability, while others introduce the role of liquid properties. The discussion does not reach a consensus on the exact criteria or conditions.

Contextual Notes

Participants mention specific physical phenomena and critical dimensions without resolving the underlying assumptions or dependencies on definitions related to liquid properties and pipe dimensions.

anders_r_r
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Consider a vertical pipe partially filled with liquid. The pipe is open at the lower end and closed at the top. See the attached picture. Will the liquid fall out or not?

In a small diameter pipe a stable meniscus will form due to surface tension and prevent the water from falling out. In a larger diameter pipe the liquid will fall out of the pipe. What is the exact criterion that determines wether or not the water will fall out? Where/how do I find the answer? Can someone point me in the right direction?

/Anders
 

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I suppose it depends on what liquid. Perhaps its viscosity, but maybe also other properties it may have.
 
Thanks for your input, Dr Lots-o'watts.

I suppose that the answer is closely related to the stability of the meniscus. In a large pipe the surface tension may not be strong enough to create a stable meniscus.
 
After a few days of searching I found the answer :-)

In the large diameter tube long wavelength capillary waves on the interface between the gas and liquid causes the interface to be unstable and the liquid will fall out. This phenomena is called the Rayleigh-Taylor instability.

When the diameter of the tube is sufficiently small, the longest possible wavelength of the capillary waves is not long enough to cause instablity, thus the liquid will stay in the tube.

If the gas is air and the liquid is water, the critical diameter of the tube is 8.5 mm.

The theory is very well explained in the textbook: "Physics of continuous matter" by B. Lautrup.
 

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