Differential equation for a temperature-operated valve

[ClaudioPedrazzi]

Hi everybody,

I hope I can get some answers here, notwithstanding the fact that I am actually asking more than just a MathCAD question. I tried to put up a MathCAD-framework in order to explain my problem.

I wish to compute numerically the flow passing through a temperature-operated valve, of which I know (from supplier datasheet and measures on site),

1) the time constant tau (assuming that it is first order linear system)

2) the law giving the flow as a function of the temperature f(T) in quasi static behavior (dT/dt=0)

and I assume a certain transient of temperature, T=T(t)

A lot of time ago, when I was young and still remembered "Control Theory 1", I would have solved this problem imediatly (maybe!). Now I am a little out of training . Can someone point me to the answer, or eventually if not, to the right forum where to ask for help? Or even to some appropriate literature?

Sorry if I am out of subject, I looked for a MathCAD-forum on Control Theory but it does not seem to exist, so I just posted here.

Best regards

Claudio

[AlanStevens · Accepted solution]

Like the attached?

Alan

NB Odesolve doesn't like units so I've removed them. You should put them back after the ODE has been solved (though I haven't bothered in the attached).

[ClaudioPedrazzi]

Alan

I think you have got it! My personal background is more in the structural mechanics field, it was difficult for me...

I don't know how to thank you... you not only wrote the equation, you also provided me with the MathCAD numerical solution!!!

I'm going to play around a little with your solution, removing units and so.

Thanks a lot!

Claudio