I say forget about trying to prove some obscure quirk you think you have discovered and just simplify what you are thinking about.
Water is incompressible, so an easy way to imagine the inner working of a loop is to keep in mind that flow rate is constant through the whole loop, it doesn't vary in any part of the loop, the only thing that varies is velocity, ie less restriction=lower velocity, higher restriction=higher velocity, velocity increases in a restricted component to compensate for the restricted size of the path of flow to maintain the same total volume of flow, the volume of flow will be reduced in the whole loop with more restrictive components, not just in the restrictive component itself.
Saying that a varying velocity will change the accuracy of the flow rate measurement implies that velocity is constant and flow varies in your test loop, but that isn't the case unless you have a loop with no changes in restriction, ie basically impossible, volume flow rate is constant, and velocity varies, but, higher velocity implies a more restrictive loop, so actual flow rate will be lower than with a less restrictive loop, this is all you will prove by changing your tubing size, ie the largest tubing size has the least restriction so your flow rate will be higher than with the smallest tubing size, but as long as the flow rate is within the measurable range of the flow meter, the recorded result will be accurate, you are trying to skew the results by measuring outside its accurate range (I think, I can't really grasp what you are trying to prove, other than seemingly rigging an experiment to display the "result" that you want)
I still don't think you will achieve your desired result as the smallest end of the taper inside the rotameter or the inlet/outlet or the valve will be your highest restriction point regardless of whether you use larger or smaller tubing (Jak stated the ID of his rotameter on the smaller end of the taper is about 8mm, so that is smaller than the ID of any 1/2" barbs/compression fittings, so in a loop that contains nothing other than barbs, rotameter, tubing and pump, you can't escape the fact that the rotameter itself is the most restrictive component, and it isn't really restrictive at all. Varying tube size in order to "prove" that velocity will skew the results is pointless when the point of highest velocity in the loop should be in the small tapered end (or the inlet barb or the valve) of the rotameter itself.
I am curious though, you say you will maintain the same "flow rate" with all tubing sizes, now you are trying to prove that the rotameter is innaccurate with differing tubing size, so how are you maintaining the same flow rate? If you just run your pump at full speed your flow rates will vary across the tubing sizes due to differing restriction, but if you don't trust the rotameter to measure your flow rate accurately, that leads me to believe that you are relying on an inferior flow meter (Jak mentioned you had a koolance flow meter?) now these types of flow meters are innaccurate with different tubing/barb ID sizes as they do lose accuracy due to differing tubing/fitting sizes as velocity does change the way the impeller works (the calculation for rpm to flow rate is done by the conversion of impulses to a calculated flow rate. I have a Aquacomputer G1/4" high flow flow meter and it has been said that it's standard calculation of impulses/s is wrong for the larger tubing/fitting sizes that are typically in use these days, so I have to drop it from 169ips to about 158ips (based on martins testing) this is because aquacomputer favors smaller ID tubing and fittings than most people use these days, so yes in this case, velocity will change the accuracy of a flow meter if using impulses per second, however the king instrument rotameter doesn't work that way and as such is not influenced by velocity in the way that cheaper impeller based flow meters are, ie if you are testing all tubing sizes with the same flow rate the velocity inside the rotameter will not change regardless of the tubing size. So, if you are trying to maintain a set flow rate based on an impeller style flow meter, or even an uncalibrated MPS flow meter, then you have invalid results.
The only way for you to "prove" anything with this "test" of yours is to actually knowingly skew the results, ie trying to measure outside accurate ranges of equipment or purposefully varying the flow rate to show the results you want to show. I will say that I don't believe you will be able to take the rotameter outside of its accurate range just by varying the tubing size, this slightly reduces restriction which will increase or decrease the flow rate and varies the velocity through the tubing itself which will only increase or decrease the velocity in the tubing, any variation of flow or velocity inside the rotameter will simply be a function of the loops flow rate, which if you say you will maintain the same flow with all tubing sizes means there will be no change whatsoever as you are manipulating the loop to compensate for higher or lower restriction to maintain the desired flow rate. So you will in effect prove exactly what you are trying to disprove.
Edited by LiamG6 - 2/1/16 at 3:33pm