- #1
samy4408
- 62
- 9
I found 2 formulas about surface tension -- which one is correct?
- Context: Undergrad
- Thread starter samy4408
- Start date
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Discussion Overview
The discussion revolves around two different formulas for calculating surface tension, with participants exploring their derivations and applications in specific scenarios involving solid objects floating in a fluid.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant requests context or references for the derivation of the two surface tension formulas.
- Another participant suggests that the choice of formula depends on the specific question being addressed, providing examples involving a solid disk and a thin ring.
- The formulas presented are ##\gamma_{\text{disk}}=\dfrac{W}{C}## for the disk and ##\gamma_{\text{ring}}=\dfrac{W}{2C}## for the ring, with an explanation of the reasoning behind the differences based on the geometry of the objects and the distribution of forces.
- The concept of surface tension being likened to a uniform distribution of tiny parallel springs is introduced, with ##\gamma## compared to a spring constant.
Areas of Agreement / Disagreement
Participants have not reached a consensus on which formula is correct, as the discussion highlights differing applications and interpretations of the formulas based on the context of the problem.
Contextual Notes
The discussion does not clarify the assumptions underlying the derivations of the formulas or the specific conditions under which each formula is applicable.
- #2
- 15,895
- 9,061
Can you provide the context or references of how these formulas were derived?
- #3
samy4408
- 62
- 9
I found the first one by typing surface tension formula on google , and the second :kuruman said:
- #4
- 15,895
- 9,061
Which you use depends on what question you wish to answer. Say you have a solid disk and a very thin ring both of circumference ##C## and weight ##W## floating in a fluid. In the case of the disk, ##\gamma_{\text{disk}}=\dfrac{W}{C}##; in the case of the ring, ##\gamma_{\text{ring}}=\dfrac{W}{2C}.##
You can imagine the surface tension force as the resultant of a uniform distribution of tiny parallel springs around the length of the interface of the object and the fluid with ##\gamma## playing the role of the spring constant. The ring has twice as long an interface (on the inside and outside) as the disk and therefore twice as many springs. Thus, half the spring constant is required to support the same weight.
You can imagine the surface tension force as the resultant of a uniform distribution of tiny parallel springs around the length of the interface of the object and the fluid with ##\gamma## playing the role of the spring constant. The ring has twice as long an interface (on the inside and outside) as the disk and therefore twice as many springs. Thus, half the spring constant is required to support the same weight.