Richard J Kinch wrote:
Gary Coffman writes:

It isn't the regulator which is wasteful. The energy loss is in the
compressor you're asking to pump to a higher tank pressure. And no
surprise, it is the compressor which gets hot as it does so. *That's*
where the energy loss in your scenario occurs, not in the regulator.

No. The compressor can be assumed perfect.

THE MAXIMUM ATTAINABLE WORK DOWNSTREAM OF A RESTRICTION IS NECESSARILY
LESS THAN UPSTREAM OF THAT RESTRICTION.

The operating principle of a conventional regulator is a restriction.
It is just a valve with a feedback arrangement on the handle
Restrictions are lossy. Otherwise we'd be using the thinnest possible
air hoses instead of paying for big ones.

The regulator itself has nearly zero loss, as my example of drawing
down a filled tank to supply a load shows.

I've lost track of who is exhibiting what. But this waving of hands
with Boyle's law and energy being P*V is flawed analysis. It
shouldn't even take analysis. It should be obvious, anything that
impedes the flow of compressed air has got to be robbing power.

The velocity and turbulence downstream of the orifice is essentially wasted.
That's a lot of kinetic energy that is doing no useful work. However, all
this discussion of where the heat/energy is lost has little to do with using
air to do mechanical work. Compressor inefficiency is also not really the
issue. If we set Pressure*Volume equal to some constant, it takes more work,
even with an ideal compressor, as P goes up and V goes down. A system that
reverses that downstream wastes all of that extra work. I'm saying work
because even an ideal compressor piston will have to exert a greater force
when filling a tank that is at a higher pressure. That is not waste heat or
bypassed air, just an unavoidable fact.