I have read a number of resources, and heard a number of respected presenters explain that "water has 12 times the resistance of air". This statement is false. It will be true only under a very specific set of circumstances that would have to be carefully defined.
Resistance in water = coefficient of drag (an experimentally determined number based on how streamlined the object passing through the water is - i.e.: a cupped hand has a different C of D than a flat hand; a ball has a different C of D than a stick...lab testing will tell you what coefficient of drag is for any given object, hence all the flow studies for new car shapes).
No wonder it is so hard to quantify work in the water!
Work = Resistance (force) x ROM (distance)
This is not from a research paper. This is from university physics texts re: fluid dynamics. It's kind of like the laws of gravity.
Visit the downloads page of this website to see a picture by Line Marr of an aquatic dumbbell being weighted with a land weight of 5 lb to barely submerge it. Estimating work done when moving this buoyant object through the water does not account for the resistance factors mentioned above, including the speed of motion, which will dramatically increase resistance. Range of motion will determine work done.
Aquatic resistance is not easily quantified, and the figure "12X the resistance of air" is frankly, useless.