which engineering area?

aquifers and  water table,  raising damp, soil stability, self cleaning glass, surface treatment to achieve wetting/ non-wetting, mineral separation, etc

probably, from an engineering point of you, the interest is not so much for measuring it as probably more for its related effects. In hydraulic or geothecnical engineering there are some applications where it could play a key role. Carlos mentioned among the others the spilling from aquifers, In addition I cound mention the evaluation of weir's discharge (for low head to crest height ratios, Rehbock corrected the discharge coefficient to take into account capillarity effects). Probably, teaching the surface tension (either for measuring or controlling it) makes more sense in other branches of enfineering (there are so many applications in mechanical and chemical engineering).

http://www.hach.ulg.ac.be/cms/system/files/Kandaswamy_1957.pdf

Thank you Carlos and Giacomo,

As you said plus teaching the how to measure surface tension will broaden the engineering student mind. 

I take a different angle looking at the question you have posed. We observe a rapid growth of application of mist technologies, firefighting (I do that), burners and fuel supply systems (also for biofuels and waste oils). When you look at the surface phenomenon in a fairly dynamic two-phase flow, everything we have learned in fluid mechanics coursework litterally goes up into the Sky. Very little is known about the surface phenomenon when impulses coming from different sources excite the intephase, moreover, any two-phase flow just before it undergoes atomization becomes chaotic, but non-turbulent; shear layers deform and intermingle badly, therefore most loss predictions, based on the experience-to-date fail miserably. Essentially, two-phase flows is the new area of the fluid dynamic research. So far, mathematical prediction fail, because Newton (Navier-Stokes) shear is only important in terms the influence in creating the flow initially. Soon after, surface tension intervenes and a cascade of events follows. It is surely worth teaching students about the surface phenomenon, a lot of further research is also desperately needed.