I fired an M1917 with cloth belts. It was water jacketed, several inches of water around the barrel. Or, if you will, the barrel went through the middle of a cylindrical tank of water. There was no flow-through, but there was a vent and an overflow.
Water will keep the barrel surface below 212 F even if it’s not flowing.
We were trying to hit dynamite taped to snow fence slats.
That sounds like fun.
Most pictures I can remember of the water cooled 30 had it connected to a tank.