Gas Nozzle Size, Pressure, Flow Equation

1. Try one of these.
   Boyle's Law Example Problem - Gas Law Example Problem
   
2. Ideal Gas Law Equation Examples Tutorials and Help - Sophia

Q ≈ k (ΔP)^0.5 d^2.5 [Darcy-Weisbach]

Darcy-Weisbach applied to the flow of a fluid down a pipe not through a jet

Try this. The units are imperial but the conversions are easy.

Q=1658.5 x Cd x A x sqrt(p(in wg)/(SGx sqrt(jet pressure(absolute)/Atmospheric Pressure(absolute)) x sqrt(jet pressure(absolute)/Atmospheric Pressure(absolute)).

Cd is the coefficient of discharge of the gas jet and an reasonable estimate can be made based on standard literature.

If you want to double the flow through the same jet then you need 4 x the gas pressure.

The flow through your jet assuming Cd=0.9 would be 3.75m3/h

...or 2^0.4 x the original nozzle diameter.

Assuming the the burner associated with this jet is an atmospheric injected burner (Bunsen burner) then altering the jet size will adversely affect the flame picture leading to poor combustion. Not a good move.

Is this not overcomplicated? The OP mentions driving pressures of a few mbar and a 3mm nozzle. I cannot believe this approaches critical pressure conditions, and suggest that we are still in the range where the pneumatic equivalent of Ohm's law applies. Doubling the pressure will double the flow, though doubling the nozzle area cannot be guaranteed to halve the flow resistance.

Try this link: http://exploration.grc.nasa.gov/education/rocket/nozzle.html

The OP is talking Gas Engineering not rocket science. The maths describing a CD nozzle does not apply to a jet with only a few mb pressure drop across it. The formula outlined in my earlier post describes the flow through a jet of the type reered to by the OP.

You should investigate mass flow through truncated nozzles. The ratio of specific heats k=(Cp/Cv) = 1.31 for Natural Gas (Methane). There is a presentation that references this type of nozzle flow. You'll understand better by reading the paper to solve your problem. It's a small pdf file: http://www.e-ope.ee/_download/euni_repository/file/3286/EMH5020_OSA2_loeng2e.pdf

Hope this helps