The shape of the surface of a soap film

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Homework Help Overview

The discussion revolves around the shape of a soap film connecting two coaxial rings, focusing on deriving a differential equation for the radial distance as a function of the axial position. The problem involves concepts from fluid mechanics and surface tension, particularly how these relate to the stability and shape of the film under varying distances between the rings.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the mathematical formulation of the problem, including the use of cylindrical coordinates and the symmetry of the soap film. There are attempts to derive force balance equations and explore the implications of surface tension. Questions arise regarding the assumptions made about gravity and the uniformity of the film's thickness.

Discussion Status

The discussion is ongoing, with participants exploring different mathematical approaches and interpretations of the problem. Some have provided insights into the force balance and the conditions necessary for the film's stability, while others are seeking clarification on specific aspects of the derivation.

Contextual Notes

There are constraints regarding the assumptions made about the system, such as the uniformity of the film and the absence of gravity in the analysis. Additionally, the problem requires boundary conditions to be applied, which has led to further exploration of the implications of these conditions on the solution.

  • #31
I don't understand that.would you please do it for me?
 
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  • #32
no i can't help you do it but
##
\frac {10}{r_0} = cosh(L/2 r_0)\\
\frac{1}{ r_0} = x\\

10 x = cosh (Lx /2)
##
now you can think of it graphically what is necessary for x to have solution
 
  • #33
Hi. I was trying to solve the same problem you submitted. And I've read Chestermiller's solution to the problem. But I don't understand why in the post #13 there is a sqrt(1+(dr/dz)^2)) ? I would appreciate the help. Thank you.
 
  • #34
LordGfcd said:
Hi. I was trying to solve the same problem you submitted. And I've read Chestermiller's solution to the problem. But I don't understand why in the post #13 there is a sqrt(1+(dr/dz)^2)) ? I would appreciate the help. Thank you.
The square root factor is associated with getting the z-component of the surface tension force.
 
  • #35
LordGfcd said:
Hi. I was trying to solve the same problem you submitted. And I've read Chestermiller's solution to the problem. But I don't understand why in the post #13 there is a sqrt(1+(dr/dz)^2)) ? I would appreciate the help. Thank you.
Let's see your derivation of the force balance on the film.
 
  • #36
Ok thanks very much. It was the project of the tension on the z-axis.
My solution had the same idea as Raihan's - pressure equillibrium.
 

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