How do you setup your primary and secondary regulators/hoses for recreational?

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the formula is r=d*w/v where R is the reynolds number, d is diameter, w is average speed, and v is viscosity. You then have to add up a pressure drop caused by friction turbulence and things like hose fittings, elbows/swivels, etc all get added into that.

That's not an explanation. It's just quoting the name of some formula.

I believe there is no increased friction in a longer hose because the air is not traveling any faster nor farther per breath. Because the hose is pressurized, the air in it IS the source for the 2nd stage. It's completely different than if the air in the hose were at ambient pressure.

The only thing that matters to the 2nd stage is the pressure of the air at the valve. With a larger supply of pressurized air, the pressure at this point should drop less given the same demand. It's not that complicated.

I did a little experiment; not very scientific. I put my inline adjusting tool with an IP gauge on a 2nd stage, and tried purging it attached to the same 1st stage, same port, once with a 7ft hose and once with a 22" hose. I couldn't see any appreciable difference in the IP drop. It looked like a bit more drop with the short hose, but this is a very basic gauge and all I was doing was pressing the purge a few times. And don't forget, that's full purge which means the air is moving way faster than it would while breathing. That should, if anything, increase the influence of friction in the hose.
 
That's not an explanation. It's just quoting the name of some formula.

I believe there is no increased friction in a longer hose because the air is not traveling any faster nor farther per breath. Because the hose is pressurized, the air in it IS the source for the 2nd stage. It's completely different than if the air in the hose were at ambient pressure.

The only thing that matters to the 2nd stage is the pressure of the air at the valve. With a larger supply of pressurized air, the pressure at this point should drop less given the same demand. It's not that complicated.

I did a little experiment; not very scientific. I put my inline adjusting tool with an IP gauge on a 2nd stage, and tried purging it attached to the same 1st stage, same port, once with a 7ft hose and once with a 22" hose. I couldn't see any appreciable difference in the IP drop. It looked like a bit more drop with the short hose, but this is a very basic gauge and all I was doing was pressing the purge a few times. And don't forget, that's full purge which means the air is moving way faster than it would while breathing. That should, if anything, increase the influence of friction in the hose.

the air is absolutely travelling a different distance per breath because air is compressible. When you breathe air out of a hose, the whole "ambient chamber" is involved and air is moving from all of the LP hoses because the pressure is going down. It's not like a car moving down a highway where it doesn't matter how long the highway is, the car is still moving 10 miles. That is more in line with how non-compressible fluids work. With non-compressible fluids, the pressure can build without any more fluid taking up the space. With air, the more pressure, the more air that occupies that volume. When you draw a breath, the volume stays the same but the pressure drops, so the air across the whole system is moving to accommodate the pressure drop.

You will not see any difference in an IP gauge that you have. The difference is small enough that no gauges any of us have are going to be anywhere near accurate enough. You would need a gauge that is accurate to 0.1psi or better to see any appreciable difference.

The easier explanation of this is to go take a shop air compressor and check the pressure gauge at the start of the hose, then put a 50' hose on and you can see the pressure drop if you put a gauge on the other end of the hose. Larger diameter hose, less pressure drop, but longer hose of the same diameter always equals pressure drop. Electricity actually does the same thing with voltage drop over distance. The difference with this, is the difference between a 2' and a 7' hose at this pressure, with this flow rate, is small enough that it isn't relevant, but that doesn't mean it isn't there.
 
the air is absolutely travelling a different distance per breath because air is compressible. When you breathe air out of a hose, the whole "ambient chamber" is involved and air is moving from all of the LP hoses because the pressure is going down.....When you draw a breath, the volume stays the same but the pressure drops, so the air across the whole system is moving to accommodate the pressure drop.

Yes, of course I understand that air is moving throughout the whole IP chamber (not an 'ambient' chamber), in fact that's part of my point. But because the overall volume of the pressurized air is larger, taking an equal amount of air from that chamber absolutely must result in less of a pressure drop. It's exactly the same as taking a single breath from either a 40 or a 80 CFt tank. With equal breaths, the larger tank will have a smaller pressure drop. The linear distance between the 1st and 2nd stage doesn't matter except for friction. This friction would only increase in a longer hose if the air were moving faster or further during a single breath, and it does not do that. It doesn't do that because the amount of air movement is a direct result of the amount of pressure drop. Less pressure drop, less air movement.

Another way to demonstrate this is to put a reg on a tank, pressurize, then turn off the valve. Start breathing off a long hose, see how many breathes it takes to empty the LP hose. It's going to be several breaths. Then do the same with a short hose. It will be fewer breaths. (I don't know how much difference, but some) This means without any doubt that the pressure drop in the IP chamber per breath is less with a long hose, because it takes more breaths to take the hose from !P to ambient.
 
Head loss due to friction occurs,
 

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