On Sat, 10 Jan 2004 01:19:26 -0600, Richard J Kinch wrote:
jim rozen writes:

To reiterate what has been said a dozen times befo

Any energy not used remains in the reservoir, behind
the restriction.

Let me show the absurdity of this, one more time.

Please do. Show your absurdities.

Say we operate a compressed air system at some specific requirement of a
given mass flow and pressure (forget the "cfm" canard for now and just
specify it mass flow). The mass flow of air is the same everywhere in
the output circuit, starting with what leaves the compressor/reservoir,
which then goes into the regulator, and then out of the regulator. The
pressure drops across the regulator, the volume of a unit of gas mass
expands, but the mass flow is still the same everywhere. This is just
conservation of mass, aka Kirchoff's law.

Now *why* does the pressure drop on the downstream side of the
regulator? If you have the same size pipe on the downstream side,
and the same mass of gas flowing in both the upstream and downstream
pipes, where did the pressure go? (Assume infinitely long pipes in
each direction, and that the steady state has been reached, to
simplify your answer.)

Until you provide a place for the air to expand, P remains proportional
to n/V, so upstream and downstream pressures are equal in the two
equal size pipes. Same mass, same volume, equals same pressure.
The gas laws insist upon it. The only way pressure can be lower
downstream of the regulator is if the volume into which it can expand
is larger than the upstream volume.

In the steady state, that means a bleed to atmosphere somewhere
downstream of the regulator. Without that bleed, there is no pressure
drop downstream of the regulator. If the bleed is *beyond* the load,
as is usually the case, no energy is "dissipated" until the exhaust
volume is reached. *That's* where energy is dissipated, not in the
regulator.

Note that this is also where energy is dissipated *if there is no
regulator present*. The presence or absence of a regulator
doesn't affect *where* the energy is dissipated, only the amount
that is dissipated at any given instant (more without the regulator
than with it, because the regulator is what limits mass flow).

You say the reservoir can be kept at an excess pressure, then regulated
down, and the energy output from the reservoir is the same in either
case, the difference "not used remains in the reservoir".

But the *mass flow* at the reservoir is *equal* in either case, while
the reservoir output pressure is different.

The pressure in the reservior is only decreased in proportion to the
mass flow of air out of it. In other words, P is proportional to n/V and
the V of the tank is fixed. Until you draw down the reservior significantly,
ie lower n in the reservoir significantly, reservoir pressure doesn't change
significantly. So the reservoir output pressure at any given instant is
simply a function of the mass flow out of the reservoir.

(With a compressor pounding more air into the reservoir, the output
pressure is simply a function of the net change in air mass in the tank,
which might be upward or downward at any given instant, depending
on which flow is greater.)

Thus the energy flow out of
the reservoir is higher with the regulator, and lower without. The
difference is being wasted by the regulator. This difference does not
"stay in the reservoir", it has gone into the output.

Since the way a regulator works is to *limit* mass flow (n) so that the
ratio n/V (pressure) is a certain set amount smaller downstream than
upstream, the reservoir pressure remains higher *with* the regulator
than with just an open pipe.

Since the potential energy in the reservoir is a function of how tightly
the air "spring" in the tank is wound (for a fixed V, this potential energy
is a function of n), more of the energy remains in the tank at any given
instant when mass flow is limited than when the air is allowed to gush
out through a large unrestricted opening.

The whole purpose of a regulator is to be responsive to load demand.
It allows only enough mass flow to occur to satisfy the load's demand
at the set pressure. Since this mass flow is necessarily smaller than
the flow the reservoir could provide without the restriction, more air,
and hence more potential energy, remains in the reservoir when a
regulator is present than when one is absent.

So the energy not required to meet load demand at the set pressure
does indeed remain in the reservoir. It is not dissipated in the regulator.
It never *reaches* the regulator. It is still in the tank waiting to be allowed
to flow to the load, and ultimately to exhaust to atmosphere where any
remaining energy not usefully converted to work by the load *is* dissipated.

Gary