Discussion
Consider a liquid jet of diameter 'd'. Let 'p' be the pressure intensity inside the liquid jet above the outside pressure and '\(\sigma\)' be the surface tension of the liquid. What will be the correct mathematical expression to determine the surface tension on the liquid jet (\(\sigma\))?
Answer: A
Cut the jet along a diameter and consider a length L. The pressure force on the half jet is \(p \times d \times L\), acting over the projected area. It is balanced by the surface tension acting on the two edges of the cut, \(2\sigma L\):
\[ p\,d\,L = 2\sigma L \Rightarrow \sigma = \frac{pd}{2} \]The factors pd/4, pd/6 and pd/8 are not given by this balance. For a spherical droplet the relation is \(p = 4\sigma/d\), so \(\sigma = pd/4\) belongs to a droplet, not a jet, and pd/8 is the relation for a soap bubble with its two surfaces.
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