The water-cooled Brownings I do not know about but I am quite familiar with the water-cooled Maxims, which went into series production 26 years previously and continued in production until after the end of the Second World War.
Ammunition was packed in 250-round belts for the Maxim heavy guns and for the Vickers (simply a product-improved Maxim) and in 100-round belts for guns such as the German 1908/15, 1908/16 (extremely rare; only 1 known to exist) and the 1908/18 air-cooled heavy-barrel gun used by the infantry near the end of the Great War. Aircraft guns, especially, had metallic disintegrating belts. Water-cooled guns (except for Zeppelin guns) were fitted with a gland near the rear end of the jacket. To this gland normally was connected a fitting with a double hose. The free end of the hose COULD be just dumped into a convenient bucket of water (and often was) but the intent was to use it with a sealed container of cold water.
The barrel heated from the firing of the ammunition and heated the water. After 2 belts (500 rounds: 1 minute at rapid fire, perhaps 3 or 4 minutes at slow fire) the water in the jacket had heated to boiling. Following this, every 2 belts additional would boil away a pint of water. The jacket of the Maxim held 10 pints of water, the jacket of the lighter Vickers held only 8 pints. A sliding valve inside the water-jacket controlled the steam somewhat, directing it into the steam hose, which then delivered the steam to the pressure container. The steam hose then pressurised the water container, forcing cold water up the second hose and into the jacket to replace water which had been boiled out.
The system worked very well indeed.
The Vickers sometimes was given fresh water following its daily tear-down for maintenance and then "tested" with 2 belts. According to my Grandfather, this testing often coincided rather closely with tea-time. Fritz knew very well when tea-time was and wisely kept his pickelhaub down while the sandbags along his parapet were being shot to doll-rags.
BTW, either the Maxim OR the Vickers can be torn-down completely for service, including a barrel change if necessary, reassembled and returned to action in under 3 minutes by an experienced crew. Both Maxim and Vickers were of MODULAR CONSTRUCTION (the first instance of this practice on any industrial product; the concept was Maxim's) and parts were not changed-out: entire ASSEMBLIES were. This made keeping either gun in action very quick and easy. Break something in the feed mechanism, you changed the entire FEED BLOCK (took no more than 6 seconds). Anything not working in the recoil mechanism, you change that: no more than 6 seconds. Something not working in the firing mechanism, you changed out the entire Lock and the gun was back in service in 6 seconds. Barrel life on either gun was approximately 10,000 rounds and a burnt-out barrel could be changed-out and replaced in as little as ONE minute.
In the Second War, the German MG-42 used a barrel which was shorter than the 28-1/4 inches of the Maxim, and also heavier. Being that a hot barrel could be changed-out on the '42 in as little as 3 seconds (although 5 was more usual), the gun was issued with 3 spare, fitted, serialled barrels per gun. Barrels would be changed following the firing of one box (250 rounds) of ammunition, regardless of the actual heat of the barrel at time of change. That this practice was a success is attested by the condition of guns captured by our forces: burnt-out barrels were extremely rare.
Hope this helps.