My next project is building an in the wall 3 shelf bookcase to accommodate my printer, my modem and router, and hopefully an aquarium. I want to use 3/4" birch veneer plywood with dados for the unit including the shelves. The aquarium will weigh 175-180lbs when loaded. The shelves will be 27.5 " wide because the unit is going in an area that was built around a stove pipe and the studs are 27.5 " apart. Will this shelf support the weight ? If I added a stud inside each of the existing studs to bring the width down to 24.5", would this support the weight if the 27.5" span will not work?
Using the Sagulator, you're borderline for a noticeable sag... It will also depend on how deep your shelves are, and how wide the aquarium is (I assumed 16 inches deep shelves). Since you're using plywood you're going to be facing the shelves with something, right? I would just double up that shelf (two layers of plywood glued together) and you should be fine.
Also, you can run a strip of the plywood along the bottom back edge of the shelf which, combined with the front facing, should support all the weight you can throw at it.