Emerson Exchange 365

I would not normally recommend re-spanning a transmitter that normally is operating in the middle third of its current span.
You would gain (slightly) if you re-spanned the transmitter. Generally you want to avoid the bottom third of the calibrated range. Often, you need to avoid the top third of the range as well, since small changes in flow can result in over-range. it would only take an increase of 10% in flow to overage a DP transmitter operating at 80% (all other parameters being equal, no critical flow).
The reason that you want to avoid measuring at low ranges on any transmitter (not just DP) is that there is always a zero drift. As this uncertainty at zero becomes large compared to the reading, your uncertainty increases. There may also be a precision limit based upon the digital resolution of the circuits.
This effect is so important that I include it as one of my four rules of measurement in the form of "You can't Measure zero!" There will always be some positive signal that you cannot distinguish from zero with your equipment. Re-spanning a transmitter just lowers where this occurs, but there will be a limit as to how low you can go before even re-spanning will not result in an improvement. This practical limit depends upon the transmitter.

Are you talking about re-ranging analog output? That might boost your accuracy, if your flow is so stable that you are actually running into quantization error, but that's pretty rare. If you are considering re-ranging the differential pressure cell, you may be able to get useful boost to your accuracy, but only if you are very sure about your maximum possible flow you will need to measure.

I've often heard that your expected measurement should be 75% of full scale on a pressure transducer, as good calibration can minimize nonlinear (3rd order) effects, but that rule of thumb may be bad if your actual measurement range is significantly variable. How sure are you of that "40-60 %"?

When the flow rate changes, the orifice dP changes as the square of the relative change in flow. In other words, if your flow rate is only 50% of the maximum flow used to set the maximum range of the PT, the dP is actually 25% of the pressure drop that would need to be read if its maximum were set for 100% flow. Likewise, if you re-calibrated the dP at 50% of the maximum, you just doubled your resolution and could actually continue to measure flow rates up to 70.7% of the original. Maybe that would work, but if your actual measured flow might go to 75% of your current maximum, re-ranging the dP to half would cause it to go over-range.

I'm not sure that I would say that flow meters are "incorrect" at low ranges, but they can be "inaccurate." The accuracy at low flow measurements is impacted by this dP-squared effect. At 10% of max flow, your dP will only be 1% of max pressure, so you can imagine pressure fluctuation, electronic noise, etc. have greater impact, and anything you could do to mitigate those issues would help improve accuracy. Another impact on low flow measurements is the fact that measurement systems employ a square-root function and may switch to a less accurate linear calculation near zero to reduce noise effects and prevent the the calculation from taking the square-root of a negative number. (PLCs and HART modules are not typically happy to handle imaginary numbers.)

So, the complex answer to a seemingly simple question is that you really need to clearly define: What are your highest and lowest required measurement values? And: What is the required accuracy at both of those conditions?

Putting this in perspective: I have a test system with a very large required dynamic range and so we implemented dual dPs on dual orifices in order to give us the necessary accuracy over the large range of flow.