Consider two non-interacting tanks-in-series as shown in figure. Water enters $TANK$ $1$ at $q$ $cm^{3}/s$ and drains down to $TANK$ $2$ by gravity at a rate $k\sqrt{h_{1}}\;\left ( cm^{3}/s \right )$. Similarly, water drains from $TANK$ $2$ by gravity at a rate of $k\sqrt{h_{1}}\;\left ( cm^{3}/s \right )$ where $h_{1}$ and $h_{2}$ represent levels of $TANK$ $1$ and $TANK$ $2$, respectively (see figure). Drain valve constant $k=4$ $cm^{2.5}/s$ and cross- sectional areas of the two tanks are $A_{1}=A_{2}=28 \:cm^{2}$.
At steady state operation, the water inlet flow rate is $q_{ss}=16\:cm3/s$. The transfer function relating the deviation variables $\tilde{h_{2}}\left ( cm \right )$ to flow rate $\tilde{q}\:\left ( cm^{3}/s \right )$ is ,
- $\frac{2}{\left ( 56s+1 \right )^{2}}$
- $\frac{2}{\left ( 62s+1 \right )^{2}}$
- $\frac{2}{\left ( 36s+1 \right )^{2}}$
- $\frac{2}{\left ( 49s+1 \right )^{2}}$