Flow rate and pressure drops
Flow rate and pressure drops
(OP)
How do you calculate the time for a container (fixed volume) filled with air, to drop from 100psi to atmospheric 14.7psi? Say the container had a ball valve that was closed and then opened once it reached 100psi.
I assume that the larger the container, the longer it would take.
Case 1: 1000 gal container
Case 2: 5000 gal container
I understand that it has everything to do with flow rate, I just don't know how to get it. It must be a differential equation, because once the pressure lowers, so does the flow rate.
Josh
I assume that the larger the container, the longer it would take.
Case 1: 1000 gal container
Case 2: 5000 gal container
I understand that it has everything to do with flow rate, I just don't know how to get it. It must be a differential equation, because once the pressure lowers, so does the flow rate.
Josh





RE: Flow rate and pressure drops
P2, P2/P1, Mach Number, Velocity, mass flow, time (probably want to use 0.1 second intervals), mass loss (found by multiplying flow rate by your time column and subtracting from initial air mass in tank [initial mass = PV/RT]). P2 would change at every 0.1 second interval. You will have to calculate the new pressure in the tank using the new air mass at each interval and solving P = mRT/V. Just keep dragging and dropping the the parameters in Excel until your flow rate is zero and your pressure inside the tank is atmospheric.
One thing I see happening is choked flow occurring for a while depending on the throat area of the valve. You will have a constant flow rate out of the valve until the pressure inside the tank is small enough for flow to become subsonic.
If you graph the flow rate over time, I think you will see a flat line for a while and then a negative parabolic drop hitting an inflection point and leveling out.
-Mike
RE: Flow rate and pressure drops
You can get very close to the actual time required to get to critical this way (I once calculated it to within 10 seconds out of 90 minutes on a big pipeline blowdown). Then it gets REALLY hard. Determining non-choked flow rate depends on using an empirical equation, most are not very precise at the limits of their applicability. In the blowdown referenced above I said it would take 87.5 minutes to get to non-critical flow and 35 minutes to blow down to zero psig, I nailed the first part, but the second part actually took just over 3 hours. I've done this sort of thing a few dozen times (it is useful for scheduling the start of the blowdown so that work can begin at daylight) and never been very close on the last section.
David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com
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RE: Flow rate and pressure drops
-Mike