Don't care about the equations, their good I'm sure. There is a third tank of water which is here to fill the first tank and to take the water from the second tank. So it's like your representation. It's independant.
For the next, in your representation, you could change the number of q1 with a bar. q1 represents the enter flux in the first tank. I just want the same thing but not only on the first tank, but on the second too. That mean tree bar like yours. The first exactly like q1, the second to increase or decrease the flux between the first tank and the second and the third to increase or decrease the flux to empty the second tank. The flux is representing by valves like on my representation, if you open more the valve, the flux increase and if you shut more the valve, the flux decrease.
I'm sorry if it was not clear before. I hope that is better now.