ACFM to SCFM conversion problem 1

[sirkingsley]

I am having trouble determining the proper equation to convert from actual air flow (acfm) to standard (scfm). The way that most sources say to make this conversion is a manipulation of the ideal gas law that looks like:
scfm=acfm*(Pact/Pstd)*(Tstd/Tact)
It makes sense to me, but on the literature for a certain flow meter we use, this conversion has the pressure and temperature ratios under a square root sign:
scfm=acfm*sqrt((Pact/Pstd)*(Tstd/Tact))
The rep from this company told me that it is derived from the Ideal Gas Law AND Bernoulli's Equation, and that Bernoulli is required since the air is in motion. I don't understand where Bernoulli would factor into this, since air is compressible. Any help anyone could offer would be appreciated.

 

[psafety]

The first equation, I use.

SCFM = ACFM*(T2a/T1a)*(P1a/P2a)

T1 = actual, deg R
T2 = standard, deg R
P1 = actual (psia)
P2 = standard (psia)

 

[crjones]

The first equation is what is regularly used. The flow meter equation comes into play because that is flow within a pipe.

 

[zdas04]

pcvallin,
The rep was blowing smoke up your pant legs and you were enjoying it. Bernoulli has nothing to do with this conversion, but not because air is compressible. The Bernoulli equation is used to determine lift of AIRPLANES, which fly in AIR for goodness sake. The Bernoulli Equation is irrelevant for the same reason the Coulomb's Law is irrelevant--neither has anything to do with what you are trying to do.

The square root of the quantity pressure over temp is a very common term in many inferential measurement devices (like square edged orifice measurement which infers a flow rate from a dP at a pressure and temperature), but that term is multiplied times a meter-specific constant that embodies orifice size, pipe size, unit conversions, and various fluid-specific coefficients.

In the conversion of actual flow rate of a specific fluid at a given pressure and temperature to volume flow rate at at "standard" temperature and pressure there is no square root. I put "standard" in quotes because STP is anything but standard, it is a contractual/regulatory set of values that must be selected for each operation.

The only problem I see with your basic equation is that if your actual pressure is much over 44 psig (305 kPag) then you have to include compressibility (it goes with the temp term, i.e., T(a) should be [T(a)Z(a)]). Below about 3 bar(g) it doesn't make enough of a difference to matter except in custody transfer.

Psafety,
Your designators are about as confusing as any that I've ever seen and I've been doing this a long time. There really isn't any reason to make this particular problem any more complex than it started with. In fact, if I've puzzled it out properly, then your equation is wrong. The correct equation is (the time is immaterial, you would use the same equation for SCFM or MCF/day):

SCF = ACF [(Pact*Tstd*Zstd)/(Pstd*Tact*Zact)]

The way I'm interpreting your subscripts it looks like you have reversed the actual and standard (I just looked for the 8th time and your equation looks correct this time, but dang it was a challenge--I guess I was confused by temp being first and everything haveing an "a", now I'm assuming that the "a" in your equation means "absolute" not "actual").

David

 

[Latexman]

The combined Boyle's and Charles's Law from high school chemistry (or was it Physical Science in the 7th grade) is the most simple explanation:

P[sub]1[/sub]V[sub]1[/sub]/T[sub]1[/sub] = P[sub]2[/sub]V[sub]2[/sub]/T[sub]2[/sub]

It rearranges to:

V[sub]2[/sub] = V[sub]1[/sub](P[sub]1[/sub]/P[sub]2[/sub])(T[sub]2[/sub]/T[sub]1[/sub])

Remember to use absolute temperatures ([sup]o[/sup]K or [sup]o[/sup]R) and pressures (psia).


Good luck,
Latexman

 

[zdas04]

I learned that equation as the "Ideal Gas Law" which has helped me keep it in perspective for real gases since the 60's. For a real gas you need a compressibility term.

David

 

[Latexman]

One and the same. I've also seen it called the "Combined Gas Law". A rose by any other name . . .

Good luck,
Latexman

 

[zdas04]

Yeah, but my point was that the word "Ideal" reminds me to use compressibility.

David

 

[vzeos]

pcvallin:

I have come across this before with respect to turbine meters. The ideal gas treatment is correct for displacement meters. However, turbine meters are inferential meters and the square root expression is correct. I used to have a Rockwell turbine meter handbook that gave a pretty good explanation of this. Essentially, what you are doing is making a correction on a flow rate rather than on displacement volume.

 

[Latexman]

You know, I think you are mistaken, the "Ideal Gas Las" is PV = nRT. I don't see why we're talking about compressibility. I don't think the OP gave any indication that complexity was needed. Nope, he didn't.

Good luck,
Latexman

 

[zdas04]

vzeos,
You couldn't be more wrong. Every commercial flow meter is inferential. A turbine meter infers a volume from the speed of the rotor (which includes some optimistic assumptions about the displacement per pulse). A Vortex meter infers a volume from inferring a number of Von Karmen streets from pressure variations. An Ultrasonic meter infer es a volume from a shift in sound frequency. Coriolis meters infer a volume from the movement of a pipe. It goes on and on. Counting molecules in the field is beyond us.

Several of the commercial meters will give you an ACF value and the coversion to SCF is the equation above. All sorts of fancy arithmetic is required to create the ACF number, but to go on to the SCF is a pretty simple ratio. But the bottom line is that any time you have an ACF value from any source, you can convert it an SCF (at whatever standard you want to use) with that equation. No square roots required.

Latexman,
I brought up compressibility because the error in the conversion from ACF to SCF gets pretty significant very quickly above 3 barg. The OP is talking about air which is really close to an ideal gas so it isn't terribly important to him, but others will read this thread and might be looking at something like Natural Gas that is distinctly non-ideal.

Boyle's Law, Charles' Law, and the Ideal Gas Law were all developed for a single chunk of gas at a measured set of conditions. If you take the Ideal Gas Law for one temperature and pressure and divide it by the Ideal Gas Law for another temperature and/or pressure (with the same number of gas molecules) then you get the equation that you put above. Is it still the Ideal Gas Law? I don't know or care. I call that equation a useful version of the Ideal Gas Law.

David

 

[Latexman]

"I call that equation a useful version of the Ideal Gas Law."

I don't.

Good luck,
Latexman

 

[vzeos]

You couldn't be more wrong.

I'm very impressed!!

 

[BigInch]

If I could add... Bernoulli is valid for any fluid, be it gas or liquid. Both gas and liquids are compressible, although liquids much less than gas. The use of Bernoulli implies a differential measurement between two points is being taken.

Compressibility factors for gases and (its inverse, the bulk modulus for liquids) become increasingly significant as either pressure OR temperature deviate farther away from the specific fluid's reduced pressure and temperature, as you can see in the following chart,

The ideal gas equation of state is modified to account for nonideal behavior by the introduction of the compressibility factor z as follows,
P1 * V1 / z1 / T1 = P2 * V2 / z2 / T2

where z1 and z2 are values at Pn and Tn, respectively.

https://www.e-education.psu.edu/png520/m8_p2.html

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[zdas04]

BigInch,
I don't know why I can't help being a pedantic jerk in this thread, but apparently I can't help myself. Bernoullis equation applies to any Newtonian[/b} fluid (i.e., stress varies lineraly with strain). Fluids such as paint and toothpaste do not behave like the equation predicts.

David

 

[BigInch]

The Bernoulli equation parameter for headloss (should you desire to include flow effects) between the two points is simply Hl. Bernoulli did not define how to calculate that. The Bernoulli equation does not therefore care in itself how you chose to model Hl. If the effects of friction factor for flow for compressible gas, a nearly incompressible liquid, or a Bingham plastic, or any other variant of a nonlinear shear stress vs shear rate function is to be modeled using some different equation for Hl, how that is to be done is left up entirely to you. Otherwise you can simply substitute some variant of the Darcy equation, Panhandle, Churchill or any other more common equation used to calculate the friction factor and arrive at something to substitute in place of Bernoulli's general Hl parameter.

Wasn't that a stroke of genius on the part of Mssr. Bernoulli?

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[sirkingsley]

Thanks everyone, I believe this discussion answers my question; for the relatively low pressures we'll be dealing with, it seems that the ideal gas ratios should suffice.

 

[vzeos]

pcvallin:

What kind of meter were you talking about?

 

[sirkingsley]

The meter in question is a variable-area flow meter.

 

[vzeos]

pcvallin:
This is interesting, the square root equation you posted is very similar to the turbine meter minimum capacity equation for elevated pressure P[sub]g[/sub]:

Q[sub]min[/sub] @ P[sub]g[/sub] = Q[sub] min [/sub] @ 0.25 psig * [√]((P[sub]g[/sub] + P[sub]a[/sub])/ P[sub]b[/sub])) [√](0.60/G) [√]S
where P[sub]g[/sub] = gauge press., P[sub]a[/sub] = atmos. press., P[sub]b[/sub]= base press., G = Gas Specific Gravity, S = Compressibility Ratio.)

Is it possible that the square root equation your vendor gave you is the means of calculating minimum flow capacity of variable-area flow meters and not a means of converting acfm to scfm?