Capillary Action Homework: ΔP, γ, R1, R2

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Homework Help Overview

The discussion revolves around the topic of capillary action within the context of fluid mechanics, specifically focusing on the Young-Laplace equation and the behavior of different liquids, such as water and mercury, in relation to meniscus formation between plates.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to explain the behavior of water and mercury in terms of adhesion and cohesion, questioning the implications of the Young-Laplace equation in the context of plates and radii of curvature. Other participants inquire about the next steps in solving the problem and express uncertainty about rearranging the equation for pressure calculations.

Discussion Status

The discussion is ongoing, with participants exploring their understanding of the concepts involved and seeking clarification on how to proceed with the problem. Some guidance has been offered regarding the nature of meniscus formation, but no consensus has been reached on the next steps for the calculations.

Contextual Notes

Participants are navigating the complexities of applying the Young-Laplace equation to a scenario involving plates, with some uncertainty about the definitions and assumptions related to radii of curvature in this context.

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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