Gary Coffman wrote:

Postulate a big air tank pressurized to 180 psi, with a long (long enough so
the air has time to cool to ambient) pipe to an ideal regulator which regulates
the pressure down to 90 psi. The regulator's output is a pipe of the same size
which is connected to a constant load. The cfm going into the regulator is
measured to be 10 cfm @ 180 psi. What cfm will come out of the regulator at
90 psi?


10 CFM of course. As you note, mass is conserved, or as Kirchhoff's laws
tell us, current is everywhere the same in a series mesh. There is nowhere
else for the air to go. If it has a certain mass flow into the valve, it has to
have exactly the same mass flow out of it.

This doesn't sound right to me. Let's think about the amount of air molecules
that go into the regulator during one minute. It's the number of molecules
in ten cubic feet at some temperature at 180 psi (which isn't an absolute
pressure to be sure). Now that many molecules have to come out the other side
in that minute, right? (Kirchoff and all that.) The gas law is PV = nRT. If
we call the input side 1 and the output side 2, then we can write P1V1 = nRT.
Since the number of molecules, n, is the same, and the temperature is the same,
and since R is a constant, then P2V2 = nRT. So once again I do not see why
P1V1 shouldn't equal P2V2.

I can (finally!) see why you can't plug in gage pressure into this equation.
The absolute pressure is (I believe) gage pressure plus 14.7 psi.

Therefore I predict the answer V2 = (180+14.7)*10/(90+14.7) = 18.6 cfm as
long as the temperature on both sides is equal.

Boy, I wish I had 2 flowmeters.

Grant Erwin