Twist on the 'classic' tank filling / emptying problem

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Ivan
Ivan 2012-12-3
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…

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回答（1 个）

Muthu Annamalai
Muthu Annamalai 2012-12-3
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.

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