Answer to what - Weld proximity between adjacent welds? This has been asked many times and ASME Codes/Standards provide no guidance for how close adjacent welds can be in piping or other pressure retaining components. This is left up to the designer, using good engineering practices.

The statement in UW-40 has no applicability to your question, rephrased as,"How close can two adjacent welds be?"  

As has been pointed out in other discussions Code rules make it possible to place a nozzle opening adjacent to or even in a welded joint.
I agree with both responses above.

could it be applied to two circumferential welds on a pipe run ?

ghkskn,
No
You have quoted from a pressure vessel code and then asked a question about a piping situation.
Oranges and Lemons,
Regards,
Kiwi

On any question that the Code is silent on, you should immediatly think:

a)  this item is of either a very small significance, or none at all.  ASME and API codes have hundreds of thousands of man-years of experience behind them.  On basic processes, like welding, you have not found something new.

b)  if you feel that this item must be addressed for your jobs, write a company specification that addresses the item, and see to it that your spec is included in all bid and contract documents.  [Anticipate a small increase in bid prices]

There are people here who feel that overlapping heat affected zones from welds is bad practice.  It may be bad practice- but it is bad practice that is practiced WIDELY, and which is permitted in pressure vessel construction.  So the minimum distance between circ welds on pipe IS, as Duwe6 correctly points out, an issue on which the piping codes are (usually) silent, and that silence tells you something in itself.  

In practical terms, the minimum distance between adjacent circ welds on piping is the distance that you need to separate them in order to correctly carry out the necessary non-destructive testing on each weld per code.