Problem $1.(40$ pts$)$ Consider the two storage tanks in Figure $1.$ For each system, develop the transfer

functions between the liquid levels and the inlet streams. Assume that the flowrates of the effluent streams

are nonlinear functions of the corresponding liquid levels:

$F_2=0\mathrm{.}5[\frac{f{t}^3}{f{t}^{\frac{1}{2}}*min}]**\sqrt[\phantom{2}]{h}[f{t}^{\frac{1}{2}}]$

Note: The flowrates values in Figure $1$ are their steady$-$state values.

$($b$)$

Figure $1$