Can a Pressure Vessel Control a Burning Bunsen Flame?

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Is it viable to construct a rig in which the pressure of the vessel can be controlled whilst a Bunsen flame is kept burning inside of it?
 
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In principle you could use a pressure transmitter and vessel pressure as the proportional signal for modulating the energy of the flame in a control loop.
 
A Bunsen uses the differential pressure of the gas and the ambient air to mix the gases before combustion. That should work at any reasonable pressure, so long as you have the correct pressure difference. That means you will have to control the gas pressure as well as the air pressure.

Of course you will need a continuous air flow through your pressure vessel, otherwise you will soon run out of oxygen!