Something seems strange

[MarkBuckton]

Still playing around with tank filling. This time my inflow hydrograph starts with zero flow and ends with zero flow over a period of 120 min (first graph). Unless I have overlooked something the calculated depth in the tank should also start at zero (no inflow) and end at zero (tank depleted i.e. no out flow) but instead although the solve block ODE shows that the depth in the tank is trending downwards but it never gets to zero depth (second graph) or zero outflow (third graph). This appears to be physically incorrect as I think all would agree. But why is the solve block returning answers that don't go to zero when as you can see by the hydrograph the inflow is zero at 120 minutes. Something is wrong but I don't know what it is can someone explain.

Kind regards, Mark

[MarkBuckton]

I think I have worked it out i.e. the outflow orifice was too small. That said given enough time, in my view, the tank should still drain. However even if you increase the time period over which the solve block calculates you still don't see the tank fully emptying which to me is strange but this must be some deep math reason that I don't understand as yet. But if someone knows why I am still interested.

Kind regards, Mark

[Werner_E · Accepted solution]

Its no surprise to me that the tank isn't empty at t=120 min but only a bit later. In case of the values in your sheet the tank is empty after 157,083 minutes, then the water height in the tank gets negative(!).

Simply let the solve block to solve until t=160 minutes to see it.

I also deleted the solve block for V, it wasn't necesary at all as V is simply calculated directly. The values of V are imaginary but as they are used later only squared, they yield a negative real result. Not sure if thats what you intended, though, and you might want to check the formula for V.

Is also noticeable that the water height in the tank is negative for the first five minutes (see attached sheet) which clearly isn't realistic, so there seems to be still something wrong with the model.Maybe it has something to do with the negaitive V^2?

[MarkBuckton]

Werner;

What can I say. If only my brain could work like yours your mathematical intuition astounds me. If you don't mind me asking what is your academic background?

Kind regards, Mark

[Werner_E]

Have you already found the cause for the problem in your model?

Concerning my background - it includes a degree in math but not in civil engineer, so I can look at your calculations unbiaed and relaxed from the outside 😉

BTW, what area exactly denotes A(h)? It doesn't seem to be the top surface of the waterlevel in the tank (which has what geometrical form exactly? 1 m height cuboid and then trapezoidal? What dimensions?)

[MarkBuckton]

Werner;

Without mathematicians engineers, scientist and most other technical disciplines would be still in the dark ages.

Regards, Mark