Exercise $6.-$ We have a system of two cylindrical liquid tanks in series with the same base area A$.$ The first tank

has an input flow rate $F_A,$ a level $h_1$ and an output flow rate $F_1={}_1{h}_1.$ The second tank has an input flow $F_1,$ a

level $h_2$ and an output flow $F_B={}_2{h}_2.$ The equation that relates the input and output flows of a tank to its

height is the following:

$A\frac{dh}{dt}=F_{in}-F_{\text{o}\text{u}\text{t}}$

a$)$ Make a sketch of the overall setup.

b$)$ Write down the equations that govern the whole system of two tanks.

c$)$ Assuming that the system is initially at rest, calculate the transfer function from the input flow $F_A$ to the

level of the second tank $h_2.$