# Two tank system modeling

1. Mar 3, 2014

### KybKyb

Hello!

I'm currently working on a project where i am supposed to model a two tank system. The only information the project gave me, was that i have to control the fluid level in tank 2 (what kind of fluid
is up to me). I have tried to put the problem in a practical contex, where i have imagined a simplified water treatment process.

Water flows into tank 1, which i control. I'm assuming tank1 is bigger than tank 2. And there is a valve on the "connection" between tank 1 and tank 2 that i control. The flow out of tank 2 is constant and i do not control it.

The problem:
1) I want to find the water flow in, that allowes for the fluid level in tank 2 to be constant, even with constant flow out.
2) Also, as a second problem, i want to simulate som disturbances in the water flow in, so that i am forced to use the water in tank 1 as a buffer (the goal is still to maintain a constant level in tank 2, while constant flow out)

Could someone help me/help get me started? Kinda new to this way of thinking, and im finding it somewhat difficult.

EDIT: fixed attached picture

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Last edited: Mar 3, 2014
2. Mar 3, 2014

### HallsofIvy

Am I missing something? To keep the level in tank 2 constant, set the flow in from tank 1 equal to the flow out of tank 2.

3. Mar 4, 2014

### KybKyb

I may have done a poor job of formulating my problem , sorry about that. I'm gonna sit down and think this through, i see your point, its actually pretty simple :P

4. Mar 4, 2014

### Travis_King

Here's a couple things to ponder:

1) As the water level lowers, the differential pressure will decrease between the water's surface (atmospheric) and the point just before discharge (if the valve were closed), causing a lower volumetric flow rate, thus filling the second tank slower than it would with a full tank.

2) If you want to maintain a constant flow rate, then in industry you would use a control valve which was programmed to open and close based on pressure (or volumetric flow) feedback from the system. Valves have what are called Cv curves, which tell you basically how much pressure loss you'll see for a given flow (the actual Cv, flow coefficient, value tells you how many gallons per minute of water will result in a 1 psi pressure drop through the valve at a given % open or setting)

As the flow rate increases, the fluid will see greater losses across the valve, decreasing the differential pressure and thus reducing the maximum theoretical flowrate (if you just used the simplified Bernoulli equation).

Additionally, the higher velocity of the fluid when the tank is full will cause more losses in the transfer piping and any other fittings (elbows, flowmeters, additional valves, etc) and further reduce the theoretical max. flow rate.

Basically, in designing a gravity system with constant flow rate, you'd have to consider all losses and the effect that all variables (i.e. fluid height, valve opening) will have on the system performance.

5. Mar 10, 2014

### KybKyb

Thanks for the replies, and sorry for not answering, have been quite busy with the project. I have coupled the tanks a bit different, and the result was a second order system. Im struggling with findint the damping, and the gain of the system, based on the following equations:

dH1/dt=(1/(PA1)*(f_in-R1(H1-H2)

dH2/dt=(1/(PA2)*(R1(H1-H2)-(R2*H2)

R1, R2, 1/PA1 and 1/PA2 are just constants. f_in flows into the top of tank 1.

I'm not sure if i've bit of more than i can chew, i've found a approximation of the time constant simply by looking at the graph, but any help with the damping and gain would be appreciated :)

EDIT: fixed attachments

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