- #1
samy4408
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I I found 2 formulas about surface tension -- which one is correct?
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The discussion centers on two formulas for calculating surface tension, specifically for a solid disk and a thin ring. The formula for the disk is given as γ_disk = W/C, while for the ring it is γ_ring = W/2C, highlighting the difference in interface lengths. The reasoning behind this difference is explained through the analogy of surface tension as a distribution of tiny parallel springs, where the ring has a longer interface, necessitating a lower spring constant to support the same weight. The choice of formula depends on the specific scenario being analyzed. Understanding these derivations is crucial for applying the correct formula in practical situations.
- #2
- 15,859
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Can you provide the context or references of how these formulas were derived?
- #3
samy4408
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I found the first one by typing surface tension formula on google , and the second :kuruman said:
- #4
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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.
I already posted a similar thread a while ago, but this time I want to focus exclusively on one single point that is still not clear to me.
I just came across this problem again in Modern Classical Mechanics by Helliwell and Sahakian. Their setup is exactly identical to the one that Taylor uses in Classical Mechanics: a rocket has mass m and velocity v at time t. At time ##t+\Delta t## it has (according to the textbooks) velocity ##v + \Delta v## and mass ##m+\Delta m##. Why not ##m -...