If your tube is, (as you said), "thick and black", it's ABS sewer drain pipe, not PVC water pipe. ABS is actually a softer plastic than PVC and will take sanding and painting a little bit differently.
My rod tubes are white-PVC, so I don't bother painting them. But,my roof top 'Toon rack, I made from the ABS pipe and DID paint it.
I used fairly "soft" sandpaper, to roughen it, about 120grit. Then, two coats of gray, "sandable" primer. (sanding between, primer coats with 400grit and after the final coat before applying paint).
I then used Krylon's spray paint made for plastic. Then, as also mentioned, finished off with two coats of clear acrylic spray. It's held up, remarkably well now for 3 years!
Because the pipe is black, most paints, if you don't primer it are not going to show the same final results, (color wise), as they would if the pipe were white to begin with.
Plus, rattle can paints, plastic, and/or, regular just adhere better to a primed surface.