I know its been asked a few times, with various different solutions for being able to create a digital Hydrometer for brewing beer.
After finding this page containing the basic idea that their float uses in an industrial product, it honestly doesnt seem that complex...so i am wondering if i am missing something.
I dont have a lot of experience with Hall sensors and how accurate they really are...http://www.gardco.com/pages/density/electric_hydrometer.cfm
The interesting part is this
The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides an single output voltage whose magnitude is a direct linear measure of the quantity to be measured.
Basically its just a tube that is inserted into the fluid vertically, and a sliding tube inside of it holding a magnet is pushed up towards or away from the hall sensor based on the fluids density which will change as the beer ferments to create alcohol.