It depends on the ambient humidity where you are. Have you ever noticed after heavy rain how in dry weather, the moisture will just get sucked away, even in deep shade or under car ports. But in soupy humidity, moisture will linger. So, in a dry region or a dry season, a day should do it. Otherwise, I'd give it a few days. I don't run water through briar pipes on any regular basis. Wiping the chamber with a dry towel will do the job and avoid the need to ream. However, cleaning up estate pipes, even meerschaums, running some water through them is a perfectly fine method. It horrifies some, but of course a water rinse is used in carving most pipes, though I think soaking might not be so good, in my opinion. I do soak the stems in dish detergent if they need sanitizing.