URGENT $($please solve it correctly $)$

Problem $2$: $(25$ points$)$

$5$

The following fluid system is given. There are three tanks. Tanks $1$ and $2$ are connected. The cross$-$sectional areas of the tanks $1,2,$ and $3$ are $A_1,A_2,$ and $A_3$; respectively. Ignore all fluid inertias. The input flow rate is $q.$ There are three valves with following flow losses, $R_1,R_2,$ and $R_3.$ The flow directions are shown in the picture. Find the following transfer function, $\frac{Q_3(s)}{Q(s)}.($Recall compliances $C_1,C_2,$ and $C_3$ are: $C_1=\frac{A_1}{g},C_2=\frac{A_2}{g},C_3=\frac{A_3}{g}).$

Solution: