Weird Engineering Unit - The Slinch
Technical fields are full of units that most non-technical people have never heard of. It gets even weirder with customary U.S. units, given the history of how these units came about. The most obscure unit I've ever actually used for real practical applications is the slinch.
If you're not involved in a technical field, you may not be familiar with the idea of coherent or consistent units. Basically, it's the idea that you shouldn't need any fudge factors in an equation because of the units you're using. For example, power can be calculated as a force times a speed, or P=F*V. Using consistent U.S. units gives an answer in ft-lb/sec, while using metric units gives an answer in N-m/sec (also known as Watts). A non-consistent unit of power that most people are familiar with is horsepower. If you multiply force times speed, you then have to divide by a fudge factor of 550 to get your answer in horsepower, or HP=F*V/550. And the fudge factors only work if the inputs are the units you're expecting. If people wanted to use mph instead of ft/s for the velocity, then you'd need another fudge factor on top of that, HP=F*Vmph*(5280/3600)/550. Equations can get pretty messy if you're not using consistent units, having to multiply all those fudge factors together.
In the standard units used for engineering in the U.S., pounds are a measure of force, not mass (this is already a distinction some people are unfamiliar with, confusing weight and mass). The unit for mass, which most non-technical people would already consider an obscure unit, is the slug. But trust me, I use slugs on a nearly daily basis as an engineer. On Earth, a slug weighs approximately 32 lbs (i.e. F=mg). Or for you metric people, it's equivalent to about 14.6 kg (which measure mass, not weight).
But the engineers who do stress calculations don't always use the normal FPS (foot-pound-second) system, because everyone's used to seeing stresses reported in lbs/in², or psi. And if you were using the normal FPS system, your stresses would come out in lb/ft², and you'd have to do a conversion at the end of your calculations to put the results in the psi that most people are used to seeing*. That's not a huge deal for spreadsheets or hand calcs, but it does make it more difficult for certain finite element programs. So, the stress guys sometimes use a different set of units based on pounds and inches, with the mass unit being the slinch. A slinch is 1/12 of a slug (i.e. the ratio between feet and inches). On Earth, a slinch weighs approximately 32/12 lbs, or 2.7 lbs.
Of course, a lot of these weird units could be simplified if all the engineers in the U.S. started using the metric system like the rest of the world, but that's not the way it is right now, so I've got to use units that other U.S. engineers are familiar with. And if Wikipedia is to be trusted, the metric stress guys have their own weird mass unit of glugs in the centimeter-gram-second system.
* Speaking of weird stress units, I remember working with a foreign engineer one time who gave me her results in Pascals, which is the normal metric way to do it. When I asked her to convert her results to U.S. units, she gave them to me in N/ft².
Image Source: Wikimedia Commons, slightly Photoshopped to remove a dead fly
Note that this entry was adapted from a response I left on Quora.