Our porcelain gets a 23% acid recommended by a janitorial supply, but it ain't nuthin like that, only calcium build-up. Consider taking that picture to a janitor supply and asking their opinion.
Have you tried powedered cleaning powder like Comet, Ajax or any other brand? It might not come out in one go as those stains look pretty deep, but it should come out eventually.
A forum community dedicated to Do it yourself-ers and home improvement enthusiasts. Come join the discussion about tools, projects, builds, styles, scales, reviews, accessories, classifieds, and more! Helping You to Do It Yourself!