• meat I'm braising is threatening to dry out
• the salad dressing I've just made is too thick
• whatever I'm whirring in the blender needs liquid to make it blend properly
• the bottom of the pan has a lot of tasty carmelized brown bits that will release and boost the flavor of whatever I'm cooking with the addition of a little liquid and some spatula scraping, or
• dozens of other uses,

I turn to carrot juice more than anything else.

Use carrot juice as you would a stock. What would you do with a stock? You'd cook risotto with it, use it in soups, use it to thin vegetable or herb purees, add it to mashed potatoes, use it in pasta sauces, reduce it for a glaze used for fish or chicken,and even make ice cream with it. I usually cook my rice in carrot juice (my favorite proportion seems to be 2/3 water, 1/3 carrot juice).