how many miles to pass emissions after water cooling repair?

Not entirely sure I understand your question but if you are asking how many miles you have to drive after having work done on your engine to pass emissions test...0. It should pass immediately unless there is another problem. And what is 'water cooling repair'? exactly?

Thanks for saying all that, David- I think the problem here is something else than a "cooling repair"- the real problem is that it's an old Audi- good luck with those emissions tests