Theory says ΔP is proportional to Q². I tried fitting this to your data, without luck. So now I'm stumped. But since you have actual data, doesn't it give you a usable curve?

it is showing almost linear curve because on gauge 0-10 LPM the readings are not linear.

for every change of 1 bar pressure there is 5 lpm. by which equation this can be proved.

See #1↑.

Isn't it wonderful to be at the leading edge of white-hot technological progress?

You can not rely on this type of flow gauge to give you accurate [only approximate] flow readings for argon or air because.

1/ It is a pressure gauge calibrated with a jetted outlet, ideally used with the appropriate gas , any other gas used must have a similar density.

2/ The volume delivery depends on the length of delivery lines and associated equipment due to resistance and back pressure. these vary considerably on different installations. So the question is has the gauge been calibrated originally to compensate for these applications or for delivery at the outlet ?

3/ Pressure Gauges calibrated for different maximum flows will not agree with each other very closely in the same situation.

4/ Only method of confirming flow rates is to use a bubble type flow gauge and compare with readings on pressure gauge type.