$3.$Two separate liquid storage systems are given in the figures below. Each tank is $4$ ft wide in diameter. Valve for left system as q $=8\mathrm{.}33$h$.$It acts as a linear resistance according to the given equation. Where q $=$ gal $/$ min and h $=$ ft$.$ In the system on the right, liquid level changes, h$,$ are not affected by the outlet flow rate q$.$ Each system is initially at steady state and hs $=6$ ft$,$ qis $=50$ gal $/$ min. is known. At time t $=0$ the inlet flow rate increased with one step change from $50$ to $70$ gal $/$ min. Accordingly, for each system

determine the following

a$)$ H $($s$)/$ Qi $($s$)$ transfer function

b$)$ h $($t$)$ transition response equation

c$)$ New steady state values

d$)$ Which tank will overflow first if each tank is $8$ feet high?

Show it mathematically.