Twist on the 'classic' tank filling / emptying problem

Folks

Help needed!

I’m working on problem in SIMULINK that has me stuck because it has been a long time since I last solved differential equations and I’m very rusty! It is a twist on the classic tank filling/emptying problem.

There is a liquid volume flow into the tank (F1 m3/s). Dissolved in F1 is a non-reactive compound of concentration C1 (kg/m3). Both F1 and C1 and not constant but are a function of time.

The volume out flow from the tank (F2 m3/s) is not constant and is a function of time.

Since F1 and F2 are not equal, the volume of liquid tank volume (V) is not constant but will be a function of time. Well mixed conditions in the tank can be assumed

How do I solve the mass-volume balance equations in SIMULINK so that the concentration of the compound leaving the tank (C2 kg/m3) can be calculated as a function of time?

Any assistance will be much appreciated…

Answer 1

[Muthu Annamalai]

You can see the standard ODE solutions in Simulink, described among other places, on Mathworks blogs http://blogs.mathworks.com/seth/2008/05/23/how-to-draw-odes-in-simulink/

To solve,

     d[x]/dt = F[x,t,x']

essentially you need to model the function, F[x,t,x'], as a Simulink block, with inputs to the integrator.

Once you have appropriate initial conditions for all the variables of interest, getting your solution is a breeze.

Goodluck.