I'm sure he's drinking water during a fast like that. But in fasting lingo, you would say that was a "water only" fast,
if you are only drinking water and not eating food (rather than call that a "food only fast").
In general, one should drink lots of water when one fasts (I'm talking about fasting for health reasons--Fast Sunday is different because there we fast as an act of devotion). We get something like 40% of our daily water intake from the food we eat, so if you aren't eating food, you need to drink extra water. That's especially true for longer fasts.