## unsteady, compressible flow

## unsteady, compressible flow

(OP)

I am trying to work a problem to find flowrate, and a time to reach equilibrium. It sets up like this: I have a tank with a volume of 400 cubic feet full of compressed air at 50psi. The tank has an 8" schedule 40 carbon steel pipe coming off of it with a valve at the tank. The pipe rises 100' from the tank and 100' laterally before discharging to atmosphere. Assume temperature is 70 degrees F. When the valve is opened at the tank, what is the flowrate at the end of the 8" pipe, and how long does it take for the system to reach an equilibrium point?

## RE: unsteady, compressible flow

The way the question is stated, the answer is that it takes an infinite amount of time to reach equilibrium, since the approach is asymptotic.

## RE: unsteady, compressible flow

## RE: unsteady, compressible flow

The easy part of the problem is the equation for the time required to drain the tank. Simply re-arrange:

Q,in – Q,out = dPressure,tank * volume / (Pressure,atm * dtime)

The hard part is finding Q,out. This will change over time as the pressure drops. The equation you need to use changes depending on whether the flow is choked or not, which is dependent on the pressure at the end of the pipe (which is dependent on pressure in the tank and pressure drop across the pipe (which is dependent on velocity in the pipe (which is dependent on whether the flow is choked or not (which…you get my drift…))))).

Here are some resources to get you started:

http://www.cheresources.com/discharge.shtml - Very good resource

http://www.aft.com/documents/AFT-CE-Gasflow-Reprin... - Article on choked/non-choked flow.

http://www.eng-tips.com/viewthread.cfm?qid=89248 – thread with discussion on a similar problem.

http://www.lmnoeng.com/Gas/choke.php - pay to use calculator but has good information underneath.

Hopefully the flow is choked at the start and hopefully the initial flow is so large that you can conclude that the tank will drain “fast enough” without needing to integrate the change in Q,out over time. Heck, it’s an 8” line to atmosphere, it’s going to drain a 400 cf tank pretty darn fast! Or you could simply do a test.

## RE: unsteady, compressible flow

David Simpson, PE

MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.Galileo Galilei, Italian Physicist