Flowmeter Normalisation

We have an Emerson 3051SFA DP annubar flowmeter configured for square root output. We don't normally use annubars so although vaguely aware of what is involved I've never written or commissioned software myself. The issue was with the correction factor to normalise the flowmeter output at different pressures and temps.

Some old software I was given (which supposedly worked OK but we've all heard that before...) gave normalised flow Qn as:

Qn = Qa x (273/tm) x (Pm/1.013)

where tm was measured abs temperature and Pm measured abs pressure (units bar and °C)

This gave rubbish results but seemed to be mathematically wrong (i.e. it's based on P1.V1/T1 = P2.V2/T2 right?) and was missing the datasheet pressure and temp conditions at flow so I wasn't surprised. I tried:

Qn = Qa x (tm/td) x (Pd/Pm)

where td and Pd were abs temps/pressures from the data sheet.

Results at least seemed sensible but the gas composition wasn't fixed and we had no other flow meter to compare with so no one seemed to know for sure. An instrumentation guy then told us we should be using:

Qn = Qa x sqrt[ (tm/td) x (Pd/Pm) ]

I couldn't work out why we needed to root the correction factor and he seemed to struggle to explain it. But then it's not unusual for a guy with years of experience to forget the first principles when he's away from his desk and an internet connection plus it was outside my experience anyway, so we gave it a go.

Our customer was happy enough due to the varying gas composition and this device was only really for indication but I'd like to know what the proper/practical way to do it is. Any ideas?

An internet search (including on this site) and discussions with the supplier have left me none the wiser, various often complex equations have been bandied about but no clarity. What have others used?

This can be as simple as the ratio of absolute temperatures and pressures or quite complex. Like the answer to all good questions, the answer to this one is "it depends".

First, of course, is establishing "normalized". For most of the EU that means 0 °C and 1 atmosphere (101.3 kPa). If the gas is air then the condition of 0% Relative Humidity is added.

If the transmitter is scaled to give a volumetric flow rate output the problem is quite simple - Boyle's Law and Charles' Law do it:

Q2 = Q1 x (p1/p2) x (T2/T1) where p is absolute pressure and T is absolute temperature.

Note that absolute pressure is relative to a vacuum and = gauge pressure plus barometric. Absolute temperature (°K) is relative to absolute zero and = measured °C + 273.16.

Also note that the square root goes into calculating the volumetric flow rate from the differential pressure and is not part of the correction to normalized flow.

On the other hand, sometimes the transmitter is scaled to output a normalized flow rate at an assumed line pressure and temperature. In that case the correction gets a little messier. Let us know if that is the case for you.

Sounds like that is the case we have. The transmitter was scaled 250 to 2000 Nm3/h at 7.55 barg and 50°C.

My initial correction, before the square root crept it, was using your equation for Q2 using the above data, i.e. p1=8.55 bara, T1=323 K and abs versions of my measured temperature and pressure.

That looks like the final equation we used which is good news. I understand the use of (P1.V1)/T1 = (P2.V2)/T2 to get the earlier correction factor you posted, but can't see why there is a square root in this equation. I don't suppose you can fill in how this equation was developed? Though the commissioning is done and dusted and customer has paid up, I feel I'm lacking some fundamental understanding here which always makes me uncomfortable...

Pride goeth before a fall

I noticed that I had inverted the temperature and pressure values in the density correction for the formula I posted earlier. Attached is the correct formula!

Rats.