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If the rust is heavy and you're planning to replace the pipes anyway, electrolysis is worth considering - it's slower than chemical methods but gentler on weakened metal and you can set it up in your yard with a battery charger and some scrap steel. For pipes you want to keep, phosphoric acid (the stuff in rust converters) actually chemically bonds with rust rather than just dissolving it, so you get better long-term protection than vinegar alone if you follow up with a coat of oil or paint.
Don't use harsh wire brushes or sandblasting if the pipes are thin - you'll punch holes right through them. For light surface rust, soak the pipes in white vinegar for a few hours, then scrub with a softer brush or steel wool. For heavier buildup, phosphoric acid products (naval jelly type stuff) work better than vinegar and won't damage the metal as much. If the rust is really bad and the pipes are still in use, you might need to replace that section instead of fighting it.
I've had good luck with a paste of baking soda and a little water - spread it on, let it sit overnight, then scrub with a soft brush. The other methods work but this one's gentler on older metal and you probably have it in your kitchen already.
When I pulled up an old well pipe at home that had been sitting for years, the rust was thick enough that I was worried about damaging it, so I soaked sections in a vinegar bath for a day and then used one of those soft brass wire wheels on a drill - took longer but didn't eat through the metal like harsher methods would've.
Rust on old well pipes is a real pain - pulled some corroded sections out of a property years back that looked completely shot. The vinegar soak method works, but what saved mine was letting them sit in vinegar for a full day, then going at them with a cheap brass brush (softer than steel) and following up with a wire wheel on low speed if the metal seemed thick enough. The key is patience and checking as you go rather than aggressive scrubbing right away.
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