Flow rate / remaining pressure

Assume a 6.6CF tank that receives an additional 59.4CF of air every one-second cycle. Within eight cycles the pressure would reach 1022psi and within sixteen cycles 2033psi. The tank is equipped with a safety valve set for 3,000psi. If I begin releasing air after the 16th cycle, how can I calculate the flow rate given that 1) I don’t want the pressure to go above that 3,000psi threshold and 2) the tank is constantly being refreshed at that rate of 59.4CF/sec.?

If you don’t want to keep increasing the tank pressure indefinitely, the outgoing flow rate obviously has to be the same as or greater than the incoming flow rate.

Do you want a constantly increasing outgoing flow rate to equalize with maximum pressure or a constant one that in a certain number of cycles won’t let the pressure breach 3,000 psi?

Constant output flow rate is what is needed. As this looks to allow the pressure in the tank to keep increasing, it may also work to add more exhaust hoses for additional output.

True, I am just having trouble comparing apples to oranges. For example, the 59.4CF of air coming in starts life at 14psi and is forced into the 6.6CF tank. The force pushing it along will be sufficient to do this job. The air in the tank is constantly increasing in pressure under this influx or decreasing as some is exhausted. I need a formula to figure out how this tank pressure will be simultaneously influenced by both of these processes.

I think you are reading more into your problem more than you need to. You could easily install a pressure switch to turn off your compressor at a specified setpoint.

At any rate, you want the mass flow at the inlet and exit to be the same. Mass flow is a function of density, velocity and the area at the inlet / exit.

Continuity equation:
rho1V1A1 = rho2V2A2

rho1 = density at inlet
V1 = velocity at inlet
A1 = area at inlet

rho2 = pressure at exit
V2 = velocity at exit
A2 = area at exit

Also, you probably want the ideal gas law to convert for density:

P = pressure
V = volume
N = moles
R = gas constant - 8.314 (kpam^3)/(kmolK)
T = temperature

There are a few websites that can explain the theory. Try www.engineeringtoolbox.com. If I were you I would worry more about the mechanical energy needed to maintain your assumed constant flow at high pressure.