what would be a good python code for it$?$ Develop a generic python code to determine the dynamic heights $\backslash ($ h$\_\{1\}($t$)\backslash )$ and $\backslash ($ h$\_\{2\}($t$)\backslash )$ of two connected tanks as a function of time. The first tank has a time varying input $\backslash ($ Q$($t$)\backslash )$ entering the tank and a pipe of length $\backslash ($ l$\_\{1\}\backslash )$ and cross$-$sectional area $\backslash ($ s$\_\{1\}\backslash )$ at a height $\backslash ($ H $\backslash )$ that connects it with tank $2.$ The liquid in tank $2$ drains via gravity through another pipe with length $\backslash ($ l$\_\{2\}\backslash )$ and cross$-$sectional area $\backslash ($ s$\_\{2\}\backslash ).$

Prove that your code works as intended by choosing a set of realistic values $($initial heights, pipe lengths and sizes, tank dimensions, time$-$varying flow input, etc...$)$ and plot the height of each tank as a function of time. You are expected to modify the base problem to make it more interesting AND$/$OR do a sensitivity analysis on one of the variables to see how this affects the results. Your project will be judged using the following criteria: model, narrative$/$discussion$,$ reader's interest, depth, and originality of study. Note that "reader interest" does not mean you should fabricate a creative story, it means that it is written in a professional manner that easy and interesting to read. Interesting because of the material and original study you've generated, which should be unique to you and you alone. Also note that this problem can be made quite simple or extremely complicated. You should do your best to add enough complexity to the problem that you are able to solve it in the allotted time. It is recommended that you start simple and incrementally add more details. For example, you could explore the effect of a unique time$-$varying function $\backslash ($ Q$($t$)\backslash ),$ or look at the effect of friction on the bridging pipe, or the effect what happens when the liquid level dips below the bridging pipe. There are many, many interesting things you could explore. I would recommend you focus on one or two of these aspects and learn what you can above the base case. What to turn in:

$-$ Your python file for a fully functioning $2-$tank system.

$-$ A $2$ page technical memo. At the minimum include the problem, your model$/$assumptions$,$ the code, the transient behavior, and your model's limitations$.$