How to design an automated system to measure flow rate of a gas
(bubble ) ..and thus able to calliberate the mass flow controller.
Well, the normal engineering approach to solving this problem with minimal human intervention (in our humble opinion) would be to install an electronic flowrate sensor in line with the gas flow. The output of these sensors can be fed into a computer, or a PID controller, in order to provide flowrate regulation through an automated valve. Problem solved.
A simpler, less-expensive solution that would require minimal human intervention would be to install a rotameter-type flowmeter. These devices are a simple, robust, non-electrical, and reliable means for measuring the flowrate of a gas (provided the flowrate is within the range of the rotameter). Humans would be required to read the flowrate from the device as there is no electronic readout.
Good luck with your project.