How Long Does It Take for Connected Water Tanks to Equalize Pressure?

[zax]

Hey, I have a problem in which there are two water tanks with different pressure. If they are connected together, how to calculate the time it takes to arrive to the steady state(same pressure)?
Thank you.

 

[revgrad]

Hydrodynamics

Have you tried Poiseuille's law? Does this sound familiar - the total volume of liquid which flows across the entire cross-section of a cylindrical tube in time? See link http://en.wikipedia.org/wiki/Poiseuille's_law

 

[zax]

Thank you for the reply.
The detail of the problem is that two tanks have pressure 87psi and 40 psi respectively. The 40psi tank connects to the water main. The 87psi tank has a expansion tank connected. When they are connected together, is it possible to know how pressure in the 87psi tank change with time?
Thanks for any help.

 

[Q_Goest]

hi zax,
The flow of water is restricted by the various pipe lengths, fittings and valves you have installed between the tanks. The change in pressure is also a function of the thermodynamics of the air in the tank and heat transfer.

Look through this post https://www.physicsforums.com/showthread.php?t=221054"to get a general idea of some of the concepts and what you might do to calculate things. In your case you might want to simplify the heat transfer and thermodynamics a bit. If you need help understanding flow restrictions, check the attached. Generally in industry, we use the Darcey Weisbach equation as indicated on the attached.

 

[tletterm]

hi zax,
The flow of water is restricted by the various pipe lengths, fittings and valves you have installed between the tanks. The change in pressure is also a function of the thermodynamics of the air in the tank and heat transfer.

Look through this post here to get a general idea of some of the concepts and what you might do to calculate things. In your case you might want to simplify the heat transfer and thermodynamics a bit. If you need help understanding flow restrictions, check the attached. Generally in industry, we use the Darcey Weisbach equation as indicated on the attached.

What if there was no heat transfer just 2 cold water tanks at atmospheric pressure and both tanks were say a head pressure of 30psi? What would be the best claculation method to ensure both tanks draw water at the same time and not have one tank draw down before the other one starts its draw down?

 

[Q_Goest]

What if there was no heat transfer just 2 cold water tanks at atmospheric pressure and both tanks were say a head pressure of 30psi? What would be the best claculation method to ensure both tanks draw water at the same time and not have one tank draw down before the other one starts its draw down?

All you should need to do is to ensure the irreversible pressure drop in the pipe from each tank to the point where the two lines connect is relatively small. The best way to do this is to use lines large enough so that given your highest expected flow through those pipes, the flow restriction is small. In the case of a 30 psi head tank, you might for example try to minimize the irreversible pressure drop between the tank and T to a few psi or less. The smaller you make this pressure loss, the closer the tanks will come to emptying equally.

Once you get to the T in the line that connects the 2 tanks, it no longer matters how much restriction you put in the line downstream of that T.

Note that this assumes the tanks are at the same elevation. If that isn't true, you may have to actively control tank level.

 

[tletterm]

Awsome so bascially ballancing the pressures at were the Two lines connect. Does the cross sectional venting associated with the Tank have to be at least 1-1/2 the cross sectional diameter of the discharge piping configeration in order to flow correctly should this be calculated as well or does it matter. One more thing if a pump is attached to this configeration does accelerated suction velocities need to be accounted for to ensure the ballanced pressure at the connection point of the lines connecting the two tanks?

Thank You for the reply it is great information

 

[Q_Goest]

Does the cross sectional venting associated with the Tank have to be at least 1-1/2 the cross sectional diameter of the discharge piping configeration in order to flow correctly should this be calculated as well or does it matter.

Not sure what you mean by the "cross sectional venting". Are your tanks enclosed such that they need a vent? Or are you referring to the liquid discharge lines? In any case, I'd suggest performing a flow analysis on every line so there are no surprises.

One more thing if a pump is attached to this configeration does accelerated suction velocities need to be accounted for to ensure the ballanced pressure at the connection point of the lines connecting the two tanks?

I would always do a flow analysis including any acceleration losses to ensure adequate NPSH to the pump. Basically, add the irreversible flow losses into the equation for head and acceleration losses as shown by equation 16 of the manual I posted above.

 

[tletterm]

Not sure what you mean by the "cross sectional venting". Are your tanks enclosed such that they need a vent? Or are you referring to the liquid discharge lines? In any case, I'd suggest performing a flow analysis on every line so there are no surprises.


I would always do a flow analysis including any acceleration losses to ensure adequate NPSH to the pump. Basically, add the irreversible flow losses into the equation for head and acceleration losses as shown by equation 16 of the manual I posted above.

Thank You for the information

 

[tletterm]

Thank you for the information