There are several methods, most involving a mandrel of appropriate size. The first point is whether it is seamless or seamed. Seamed being the easiest/simplist. Back in the dark ages BC (before computers), even before electricity, gun barrels were wrapped in a spiral around a mandrel and beat by the smith to 'weld' the seam. The mandrel forming the bore. . .
At work (before retirement), we used a seamless stainless tubing for instrument work. Nominally for treated water or for dried air. Occasionally for other 'fluids'. The OD was within a thou tolerance, the ID was not that important, it might vary a couple of thou here or there. The OD of 1/4 inch, .250 with an ID of 3/16, .1875 would pass a BB shot of .177 with consistancy. It was produced from semi-molten (called plastic) metal being forced out of a 'collet' with a hardened mandrel inside to adjust ID. The metal was quick chilled (solidified) shortly after exit. Soft copper tubing is made by a similar process. Hard copper (pipe) is seamed. It is smooth but under stress the seam will reveal itself. Iron/steel pipe is the same. They are both rolled from flat stock until rounded. Then welded, either electrically or with pressure.
At the "Pipe Shop" (foundry), ductile iron pipe was cast. Early on with pouring vertically, later by the DeLaVaud 'spin casting" process. At USSteel's pipe mill, drill casing is made by piercing a solid billet with the 'piercing mandrel' then spun up in a semisolid state. In both cases, the result was six or eight inches diameter and larger, and certainly not to your specifications.
Modern day gun barrels (small bore) are drill lengthwise, then reamed and rifled. Larger guns like coastal guns and ship guns are cast and then milled to exact size. Of the many processes, part will be "proprietary". Either in the process or the metalurgical makeup of the tooling.
You could start by looking for "instrument" tubing. For the short lengths desired, it might be better to do the 'finish' work yourself. Turn a piece of tubing to the appropriate OD, chuck in a collet, and ream to the desired ID. For the small diameters you mentioned, the cost of "DIY" would be a small fraction of the cost of instrument tubing. Years back, I had need of the 1/4 inch tubing. The supply house quoted for (minimum) 20 foot lengths in 100 ft bundles. I ended up "misallocating" what I needed, far less than ten feet. The price from 25 years back would be irrelevant today, but was atrocious.
Depending on the application, there is also glass and plastic tubing, such as found at chemistry supply houses. They could neet your tolerences but would not do good for mechanival motion.
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