I'm trying to calibrate a MiniVol air sampler pump with a minibuck flow calibrator.

Before I can do that, however, I have to check that I'm doing the calibration math correctly, and I'm having some trouble. While the spreadsheet I've prepared appears to produce numbers in the right range, the results differ from factory-provided calibration data sets. Can you help check my work?

### The MiniVol Calibration instructions

Appendix A: Calculating flow rate, on page 59 of the MiniVol Manual describes the calibration procedure.

The MiniVol has a rotameter for setting and checking pump flow in the field. Its readings are only nominal, and not the 5lpm (liters per minute) that are actually needed.

The rotameter needs to be set for a number that corresponds to an actual flow rate of 5lpm (liters per minute), not an indication of 5lpm To determine the actual flow rate, six measurements are taken with the flow calibration standard (in this case a MiniBuck) at six different flow rates from 4-6.5lpm as indicated on the rotameter.

In the following chart, the variables defining different variables are described as:

**m**slope of the least square line from the linear regression_{vol}**b**intercept of the least square line from the linear regression_{vol}**r**coefficient of determination from linear regression^{2}**Q**indicated flow rate on sampler's rotameter_{ind}**Q**actual flow rate as measured by the calibration standard_{act}**Q**calculated flow rate at standard conditions, from Equation 1_{@std}- standard pressure: 760mmHg, standard temp: 298°K)
- Equation 1: Q
_{@std}= m_{vol}x Q_{ind}+ b_{vol} **Q**calculated flow rate of sampler determined from the linear regression results_{calc}**Diff**the % difference between measured and calculated flow rates

This calibration chart came with the MiniVol:

### Recreating the calibration chart

I Attempted to re-create this chart in a LibreOffice spreadsheet (Download). I quickly noticed a few issues of clarity on the variables described above:

**m**slope of the least square line, intercept, & coeficient of determination from the linear regression_{vol}, b_{vol}, r^{2}*This is slightly unclear but I assume they mean of X,Y pairs (Q*_{ind}, Q_{act}) a least squares linear regression, which is a basic feature in LibreOffice.**Q**calculated flow rate of sampler determined from the linear regression results_{calc}*This statement is pretty unclear, and I therefore took it to be the equation described as: Q*_{act}, for use in calculating the actual flow rate under sampling conditions which appears to be different from Q_{act}for the purposes of the chart:- Q
_{act}= (m_{vol}Q_{ind}+ b_{vol}) x √((P_{std}/P_{act}) x (T_{act}/T_{std})) **Diff**the % difference between measured and calculated flow rates*This statement is also unclear, but I took it to be the difference between Q*_{act}(measured) and Q_{calc}(calculated).

and I got these results:

The spreadsheet appears to work pretty well-- I'm getting a decent correspondence between Q_{calc} and Q_{act}, BUT... the results don't match up with Airmetrics form AT ALL. None of the calculated values are the same, none of the Linear regression results match.

## Checking my results

I tried a few different checks.

The manual has an example calibration with different numbers:

Again, good correspondence within my sheet, and this time a closer correspondence to Airmetrics numbers.

#### Am I having a significant digits issue in my spreadsheet?

I tried to see if somehow I was using the wrong linear regression, so I replaced my calculated linear regression with Airmetrics results. That didn't bring me any closer to Airmetrics numbers though.

### Can you tell what's wrong? Is it my assumptions?

I'm not sure where my assumptions are going wrong, but I imagine the mistake is somewhere in these assumptions:

**m**slope of the least square line, intercept, & coeficient of determination from the linear regression_{vol}, b_{vol}, r^{2}*This is slightly unclear but I assume they mean of X,Y pairs (Q*_{ind}, Q_{act}) a least squares linear regression, which is a basic feature in LibreOffice.**Q**calculated flow rate of sampler determined from the linear regression results_{calc}*This statement is pretty unclear, and I therefore took it to be the equation described as: Q*_{act}, for use in calculating the actual flow rate under sampling conditions which appears to be different from Q_{act}for the purposes of the chart:- Q
_{act}= (m_{vol}Q_{ind}+ b_{vol}) x √((P_{std}/P_{act}) x (T_{act}/T_{std})) **Diff**the % difference between measured and calculated flow rates*This statement is also unclear, but I took it to be the difference between Q*_{act}(measured) and Q_{calc}(calculated).

Hi Mathew, There are three things that come to my mind: (1) To think more through Equation 1, I'm curious what P and T are. Pressure and Temp? (2) Rather than Qact, I actually think it should be Qcalc. Perhaps call the manual to see if there is an error? m and b are determined through a compilation of Qind and Qact, so cannot be equated like this, right? Also, Qact is an independent variable, so it wouldn't make sense as the "y" in "y=mx+b." What do you think? (3) Diff = (|Qcalc - Qact|)/Qact

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@gretchengehrke 1) yes, P and T are pressure and temp. There's Pstd and Pact (P standard and P actual) same for temperature. Those are the temperature at standard conditions and the temperature right now.

2) yes, it should be Qcalc, but there's no equation for Qcalc anywhere. I agree, since Qact is supposed to be an independent variable and a direct measurement, it makes no sense to have it be a calculated factor.

I think the manual suffers a clarity issue in that it explains how the calibration was conducted amidst explaining how to use the calibration. Under field conditions, the Qact equation is used to calculate the "actual" flow rate based on the indicated flow rate.

In the calibration procedure, the same formula (I'm assuming) is used to calculate Qcalc, while Qact is a direct measurement of flow, not a calculated number.

In the manual, a sample calibration chart,

to be used in the fieldis where the Qact equation is listed, while Qcalc is explained on the opposite page as a factor used only during calibration.here's how the pages look in the manual, for context:

3) I omitted the absolute value from the %Diff calculation because there were positive and negative percentages given in Airmetrics reference numbers. I'm not sure it makes much of a difference to display negative percentages.

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I contacted some folks at Airmetrics, and their initial reaction was that I appeared to be doing it correctly (but they didn't really dig in). The inconsistency between their numbers was a bit troubling and warranted looking into, but didn't seem to have any practical consequences:

The numbers I got were well within the +/- 2% range that the calibration is attempting to reach, we should be fine to use this calibration system, for now.

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Do we have contacts who've used these instruments that we could reach out to for input on these calculations?

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Airmetrics got to scratching their heads over this difference as well! It turns out there is an additional variable that isn't listed in the manual but used to calculate Qcalc: The pressure drop across the Laminar Flow Element calibrator that Airmetrics uses for their calibration.

They discovered this by contacting the former employee who wrote their calibration software, and are going to do some more digging to help explain the calibration process more completely. Stay tuned...

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I've been in touch with Airmetrics over the issue. they're been very helpful and responsive. (see below)

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