Capillary Action Homework: ΔP, γ, R1, R2

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SUMMARY

The discussion centers on the application of the Young-Laplace equation, ΔP = γ(1/R1 + 1/R2), in the context of capillary action involving water and mercury. Participants confirm that water exhibits a concave meniscus due to adhesion, while mercury forms a convex meniscus due to stronger cohesive forces. The question arises regarding the interpretation of radii of curvature when dealing with parallel plates, leading to confusion about calculating pressures above and below the meniscus. The need for clarity on rearranging the Young-Laplace equation for specific scenarios is emphasized.

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  • Understanding of fluid mechanics principles
  • Familiarity with the Young-Laplace equation
  • Knowledge of surface tension and capillary action
  • Basic concepts of meniscus formation in liquids
NEXT STEPS
  • Study the derivation and applications of the Young-Laplace equation in fluid mechanics
  • Explore the effects of surface tension on different liquids, particularly water and mercury
  • Learn about the mathematical modeling of capillary action in various geometries
  • Investigate the relationship between meniscus shape and liquid properties
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Students and professionals in fluid mechanics, physics enthusiasts, and anyone studying the behavior of liquids in confined spaces will benefit from this discussion.

MFAHH
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Homework Statement



Kindly view the attached.

Homework Equations



ΔP = γ(1/R1 + 1/R2)

The Attempt at a Solution


[/B]
I've began the topic of fluid mechanics, capillary pressure, surface tension and such and was given this question to try. Now from my limited knowledge it seems to me that in the case of the liquid being water, a concave meniscus will be formed due to the water's adhesion to the inner plate walls (due to the water's polarity) and this will result in upwards capillary action. As for the case in which the liquid is mercury, the greater cohesive force between the mercury and the walls will cause the height of the mercury between the plates to drop lower than the surface of the mercury outside, and the mercury will form a convex meniscus. Is this correct?

For the second part of the question, the young-laplace equation as given is in terms of two radii of curvature, but since we are dealing with plates, would I be right in thinking that it only has a single radius of curvature (the distance between the plates) and the other would be undefined (due to their being no definite end to plates in the direction parallel to them)? How this comes into play, and how to calculate the pressure above and below the meniscus, I'm not too sure on though. Can anyone please give some help?

Much appreciated.
 

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Anyone?
 
MFAHH said:

The Attempt at a Solution


[/B]
As for the case in which the liquid is mercury, the greater cohesive force between the mercury and the walls will cause the height of the mercury between the plates to drop lower than the surface of the mercury outside, and the mercury will form a convex meniscus. Is this correct?

http://en.wikipedia.org/wiki/Meniscus
 
SteamKing said:
http://en.wikipedia.org/wiki/Meniscus

Awesome, so from what I read there I'm more or less on the right track. As for the next part of the question, how is it that I am meant to proceed? Is it just that I rearrange the young Laplace equation for the pressures above and below? But then that answer won't be in terms of what I know from the question.
 
:oldconfused:
 
Anybody? :)
 

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