Yes, you need to eat during rides. The fact that you did a metric with only water amazes me. You either are superhuman or you're ignoring what your body is telling you. For your century, I would suggest eating 200-300 calories every hour from the first hour of the ride. There will be stops along the ride likely every 15-20 miles. Most of us carry some additional food in our jersey pockets, too, or in a seat or top tube bag. You should also be taking in some electrolytes, typically in the form of a sports drink of some kind. This is crucial, especially on warm days.

The fact that you have no experience with what your stomach can handle and with the amount or frequency of your food/drink intake gives me some pause in encouraging you to do a century. Bonking (depleting your energy stores) mid-ride is exceedingly unpleasant.