Consider the two$-$tank system shown in the figure. The cross$-$sectional

areas for both tanks are constant at $10$ m$2$

$.$ Assume that the tanks have

different valve resistances such as $0\mathrm{.}1$ min$/$m$2$

and $0\mathrm{.}3$ min$/$m$2$

$,$ respectively.

The system operates under steady$-$state conditions with a mass flowrate $($qi$)$

at $100$ m$3$

$/$min$.$ At time t $=0,$ an extra $5$ m$3$

of liquid is instantly added to the

first tank.

a$)$ Developed the transfer functions H$1/$Qi and H$2/$Qi in terms of

deviation variables.

b$)$ Classify the transfer functions $(1$st or $2$nd order, over$-$ or underdamped,

with or without numerator dynamics$)$

c$)$ Determine the maximum deviation of liquid height in both tanks, and

the time at which these maximum deviations occur.