Pressure Equalization -- speed and time of duration

[Aeronut]

I have two pressure vessels (volumes known) at different pressures (known) . There is a connecting tube between them of known diameter. I first want to calculate velocity during the equalization and should easily be able to determine the time to equalization. P1 V1 P2 V2 Cross section of interconnecting tube A1. Not an assignment. Just an old quandary. Thanks

 

[Chestermiller]

I have two pressure vessels (volumes known) at different pressures (known) . There is a connecting tube between them of known diameter. I first want to calculate velocity during the equalization and should easily be able to determine the time to equalization. P1 V1 P2 V2 Cross section of interconnecting tube A1. Not an assignment. Just an old quandary. Thanks

What are your thoughts so far on how to analyze this?

 

[Aeronut]

if Volume V1 > V2 and Atmospheric Pressure P1< P2 The higher pressure chamber V2 will transition to V1 until equalization is achieved. The cross sectional area of the line connecting them together is area Aa. This cross sectional area determines the speed and therefore the time to equalization. Ignoring temperature, the two cannot be set equal to each other and solved for the other.. This is where I am now.

 

[Chestermiller]

Suppose you had an equation for the molar flow rate of gas from chamber 1 to chamber 2 (through the connecting tube) as a function of the pressure difference between the two chambers. Would you know what to do then? Would you know how to calculate the final pressure of the system (assuming that the temperature remains constant)?

 

[Aeronut]

Absolutely. YES I would. That is fantastic. Thanks much

 

[cjl]

Unfortunately, this is far from a trivial problem. As long as the pressure ratio between the two is larger than approximately 2:1, finding the mass flow from the higher pressure one to the lower is relatively easy (it's just a problem in choked flow), but as soon as the ratio is less than that, the flow dynamics between the two will be quite complicated. Depending on the details, you might be able to make some simplifying assumptions, but you'd probably be left just running it in CFD.

(To be fair, it's been a couple years since my last fluid dynamics class... @boneh3ad might be able to add more, since he's probably dealt with this kind of problem more recently than I have)

 

[Chestermiller]

Unfortunately, this is far from a trivial problem. As long as the pressure ratio between the two is larger than approximately 2:1, finding the mass flow from the higher pressure one to the lower is relatively easy (it's just a problem in choked flow), but as soon as the ratio is less than that, the flow dynamics between the two will be quite complicated. Depending on the details, you might be able to make some simplifying assumptions, but you'd probably be left just running it in CFD.

(To be fair, it's been a couple years since my last fluid dynamics class... @boneh3ad might be able to add more, since he's probably dealt with this kind of problem more recently than I have)

If you're not sure, you shouldn't give an answer. This just confuses the OP. And your response is not correct.

@Aeronut: Basically, what you have is compressible flow in a tube of constant cross section from the higher pressure tank to the lower pressure tank. The mass flow rate through the tube will adjust itself to match the pressures at the two ends. Are you familiar with how to analyze compressible fluid flow in a pipeline? This is a standard approach for natural gas pipelines. Please tell me whether you have had enough fluid dynamics training to describe compressible or incompressible flow in a pipe, in terms of establishing the pressure drop/flow rate relationship. (Concepts involved here are Reynolds number, friction factor, and Darcy-Weissbach correlation).

Chet

 

[boneh3ad]

If you're not sure, you shouldn't give an answer. This just confuses the OP. And your response is not correct.

Depending on the assumptions used for the solution, his response could be correct (although the exact ratio of pressures for choked flow will be geometry-dependent). A very short tube between the tanks comes to mind. If the tube is longer, concepts like Fanno flow may also be important and more appropriate depending on the geometry.

 

[Chestermiller]

Depending on the assumptions used for the solution, his response could be correct (although the exact ratio of pressures for choked flow will be geometry-dependent). A very short tube between the tanks comes to mind. If the tube is longer, concepts like Fanno flow may also be important and more appropriate depending on the geometry.

We obviously need to hear more about the specific situation, particularly the tube dimensions. Tank volumes and pressures are also needed.

 

[cjl]

I was assuming a short tube, true. I hadn't considered the possibility of a longer pipeline, which would significantly change my answer.

 

[Aeronut]

OK, no problem. I am not trained in Flow Engineering. OK, here are the pressures and volumes of each vessel..
P1 = 13.41 PSIA P2= .0016424
V1 = 12759.5 Ft^3 14ft diameter x 80ft long V2 = 138.05 Ft^3 5ft diameter x 6ft long
The connecting tube: 2ft diameter x 6ft long

Thanks for all of your incite.

 

[Chestermiller]

OK, no problem. I am not trained in Flow Engineering. OK, here are the pressures and volumes of each vessel..
P1 = 13.41 PSIA P2= .0016424
V1 = 12759.5 Ft^3 14ft diameter x 80ft long V2 = 138.05 Ft^3 5ft diameter x 6ft long
The connecting tube: 2ft diameter x 6ft long

Thanks for all of your incite.

Would you be willing to settle for an upper bound estimate, so that the amount of time would be less than X?

 

[Aeronut]

Depends. How "upper bound estimate". Equalization time is less than 2-3 seconds. If the estimate is too WAG, the velocity would be inaccurate. Depends on time "x" assumption