Pressure Rise in Closed Tank with 2 Inputs

[robinhill510]

Supposing you had a cylindrical closed tank inside the body of a submarine; the top of the tank is at 200m depth. The tank has height 2.5m and internal volume 1.8m^3.

A section of pipework is connected between the top surface of the submersible (level with the top of the tank) and to the tank (assume inlet is at the bottom of the tank); an orifice plate will control the incoming flow rate.
A separate pipe connects to the side of the tank, through which air will be supplied at a constant pressure of 30 bar; with volumetric flow rate 5.7m^3/min (if required).

Assuming the initial pressure inside the closed tank is normal atmospheric (1 bar), how would you calculate the time for the pressure of the air bubble in the top of the tank to equalise with the pressure external to the top of the tank at 200m?
Ignore frictional losses in the pipeworks.

http://files.engineering.com/getfile.aspx?folder=b449412d-30d1-40a7-816a-a73f093262da&file=1.jpg

 

[BigInch]

That's a bit of a complex problem. You will have to solve an iterative calculation of flowrate through an orifice, given the upstream and downstream pressure. you will have to do that many many times. You will only know the pressures with 100% accuracy at timeStep 0. Assume a very small time step, 1 second or so and calculate the volume passing through the orifice. Calculate the resulting pressures. See if those pressures would give you the same flowrate and volume changes. If not, calculate the flowrate that they would produce. Use that flowrate and calculate the new pressures. If there is still too much error, reduce the timeStep by 1/2 or so, until the error is acceptable. Then proceed to the next timestep, using the new time step interval as appropriate and the flowrate and pressures from the previous timestep.

Independent events are seldomly independent.

 

[berkshire]

Are you building a submarine? or is this homework, and is this related to your other question about flow from a filled tank at 200 metres?
B.E.

You are judged not by what you know, but by what you can do.

 

[ewh]

Given all of the assumptions, these sure seem like homework questions to me.

“Know the rules well, so you can break them effectively.”
-Dalai Lama XIV