Brutally, fasting is like Jesus in the desert: no food or water for 40 days. Supernatural. He may have found water to drink; I wasn't there.
However, a fast is definitely one that contains NO SOLID FOOD. Therefore, OJ and broth could conceivably count as two days of fasting or certainly pre-lim.
I have encountered my share of anal-retentive, bossy, elitist, "Rules rule!" type of zealots all over these forums and so what I tell people to do is PRAY ABOUT IT. Listen to YOU. Listen to YOUR body. Trust yourself to do what is best for YOU.