Peter was surprised to learn that, in addition to blood, there's another type of circulating body fluid that flows within separate vessels. what is the name of this circulating fluid that doesn't contain red blood cells?

The answer is tissue fluid. Tissue fluid holds far smaller quantity of protein molecules because they are too large to escape easily over the tiny holes in the capillary endothelium. Tissue fluid doesn't contain red blood cells because they are too large, but does comprise some white blood cells.