Undergrad I found 2 formulas about surface tension -- which one is correct?

[samy4408]

 

[kuruman]

Can you provide the context or references of how these formulas were derived?

 

[samy4408]

Can you provide the context or references of how these formulas were derived?

I found the first one by typing surface tension formula on google , and the second :

 

[kuruman]

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.