I haven't used muriatic acid but I have used phosphoric acid often. As well as removing rust, it puts a phosphate (I think) coating on the parts which prevents rusting for a period of time, even when you wash the acid off with water, as long as you dry them. If the rust is heavy it's fastest to sand the item then treat it with acid - you may need more than one application; the part will come up looking galvanised - works well where it's not practical to sandblast.
Phosphoric acid will eat away at the rust (& concrete floors) for as long as it is wet on the item, but won't damage clean steel.Once dry it becomes in-active unless moistened again.