Problem $6$:

Two liquid storage systems are shown in Fig. E$5\mathrm{.}9.$ Each tank has an area of $94\mathrm{.}24f{t}^2.$ For System I, the

valve acts as a linear resistance with the flow$-$head relation $q=8\mathrm{.}33h,$ where $q$ is in $f\frac{t^3}{m}in$ and $h$ is in

feet. For System II$,$ variations in liquid level $h$ do not affect exit flow rate q$.$ Suppose that each system is

initially at steady state with $\frac{?}{\text{b}\text{a}\text{r}}(h)=6ft$ and $\frac{?}{\text{b}\text{a}\text{r}}(q{)}_l=50ft\frac{3}{m}in$ and that at time $t=0$ the inlet flow rate

suddenly changes from $50$ to $70f\frac{t^3}{m}in.$ For each system, determine the following information:

$($a$)$ The transfer function $H^{\text{'}}\frac{s}{Q_i^{\text{'}}}(s)$ where the primes denote deviation variables.

$($b$)$ The transient response $h(t).$

$($c$)$ The new steady$-$state levels.

$($d$)$ If each tank is $8ft$ tall, which tank overflows first? When?

r ngure evos

$[1]$ Process Dynamics and Control, Seborg, Mellichamp $,$ Edgar & Doyle iii, $4$E

please tell me the step by step solution for each especially for a$)$ I dont understand how the transfer function is created, the answer has be solved before but they all have C in it which I dont understand. Can you please make it more understandable