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pressure to flow rate conversion

anyone know, or know where I can find out how to convert pressure to flowrate by time? I have a 3Litre cylinder of normal air, at 300psi, and I want to release the air at between 0.5CFM and 1CFM (at around 15-30psi, through an airbrush, the internal diameter of the escape wold be no more than a millimeter. how can I figure out how long it will take to reach equilibrium with the outside air? cheers naught

chase!!8 years ago
You can convert to velocity by using the Bernoulli equation: P_0=P+1/2*Rho*V2 (P_0 is stagnation pressure the 300 psi, P is pressure of the flowing fluid, rho is density, and v is velocity).

You also have flow rate Q=rho*A*V where rho is density again, A is the cross sectional area of the flow, and V is velocity again. Q will give you units of mass/time, so you'll have to convert using ideal gas equations from your volume/time units.

But here's where things get fun for you, that 300 psi won't be a constant, so you'll have to apply ideal gas laws inside the cylinder, it's a non-linear equation. You could solve this problem, but if you have the stuff, it's probably a lot easier just to time it. Let me know if you have questions about the forumulas I posted.
naught101 (author)  chase!!8 years ago
perhaps a better way of doing it would be a simple volume conversion?

how much space at 30psi (high end pressure) would 3L of air at 300 psi take?
3L*300psi=30psi*X ? is that a correct equation, or aren't the units comparable like that?

if I knew the volume the gas would take up 30psi, and considering it escapes the cylinder at 1CFM, then wouldn't it be easy to calculate how long that would take? (how many cubic feet at 30 psi is one liter at 300psi?)
You can do that to find the final volume of the gas outside the tank, but the pressure gradient is what drives the movement of the gas. So the gas won't be flowing the same velocity all the time.

I forgot to mention before, but under these conditions it's possible (but I haven't run the numbers) that the gas will reach Mach 1 in the nozzle and become choked. That *would* give you a constant flow velocity until the pressure gradient can no longer drive the flow like that.
naught101 (author)  chase!!8 years ago
I had some idea it might be this complex. you're right, I'll try just timing it, see how it goes... cheers naught