A Hooka rig uses a compressor on the surface that feeds a SCUBA second stage. As stated the depth is limited by the length of the hose, but also by the volume that the hose can deliver at its length and the depth you are at. The longer and/or deeper you go, the bigger the hose has to be to get the volume you need. Many of the old double hose regulators like the Aqua Master and Royal Aqua Master had Hooka ports to be supplied by a compressor.
The Brownie’s system is used a lot where long duration dives are done in shallow water. I have used them when I was much younger cleaning boat bottoms. We had the compressor in a dink and just swam from boat to boat when they were close together, never having to get out of the water. I have also seen them used for gold mining in shallow streams where an air lift is guided by divers around rocks in shallow creeks and streams.
But, what you describe sounds like using a regular air tool compressor to feed an open hose. The open hose system has been used for many years by the “Mermaids” at the underwater shows down in Florida. But without a good filter system is required or you will be breathing some oil which can really screw up your lungs and/or lead to death.
Finally, if you scale up the compressor, get surface support, add a Kirby Morgan Helmet or Band mask, mix in a lot of training, you will have a commercial surface supplied rig. This type of rig has almost no depth limit and are used with diving bells and such down to 1,000 feet and deeper.
