Mike,
The diameter of the vessel is totally irrelevant.
I presume we are talking ASME IX.
For a 2'' nozzle they would do a welder qual on any diameter less than 2 7/8'and that qualifies for 1'' and greater to unlimited diameter.
Test coupon on 2 7/8'and over qualifies for that diameter and greater.
Hope this helps,
Regards,
Shane