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If I were to set a propane torch's valve to a fixed open position, would it run out of gas faster lit or unlit? Does the flame produce any kind of pressure change that affects the flow rate through the nozzle? Are any other measurable phenomenon at work?

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the combustion process inside the flame holder in the torch nozzle occurs after the gas has left the valve outlet and mixed with air. as such, the burning of the flame is causally disconnected from the gas outflow through the valve.

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