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Problem 5 (500 pts): Consider the interconnected liquid-level system shown in Figure 3. $\bar{Q} + q$ Tank 1 Tank 2 $\bar{H}_1 + h_1$ $R_1$ $\bar{H}_2 + h_2$ $R_2$ $\bar{Q} + q_2$ $C_1$ $\bar{Q} + q_1$ $C_2$ $\bar{Q}$: Steady-state flow rate $\bar{H}_1$: Steady-state liquid level of tank 1 $\bar{H}_2$: Steady-state liquid level of tank 2 Figure 3: Liquid-level system with interaction The system's governing equations with an assumption of small variations of variables from the steady- state values are given by $\frac{h_1 - h_2}{R_1} = q_1$ $C_1 \frac{dh_1}{dt} = q - q_1$ $\frac{h_2}{R_2} = q_2$ $C_2 \frac{dh_2}{dt} = q_1 - q_2$ If q is considered as the input to the system: a) find the transfer function $T(s) = \frac{Q_1(s)}{Q(s)}$ b) find the transfer function $T(s) = \frac{Q_2(s)}{Q(s)}$

          Problem 5 (500 pts): Consider the interconnected liquid-level system shown in Figure 3.
$\bar{Q} + q$
Tank 1
Tank 2
$\bar{H}_1 + h_1$
$R_1$
$\bar{H}_2 + h_2$
$R_2$
$\bar{Q} + q_2$
$C_1$
$\bar{Q} + q_1$
$C_2$
$\bar{Q}$: Steady-state flow rate
$\bar{H}_1$: Steady-state liquid level of tank 1
$\bar{H}_2$: Steady-state liquid level of tank 2
Figure 3: Liquid-level system with interaction
The system's governing equations with an assumption of small variations of variables from the steady-
state values are given by
$\frac{h_1 - h_2}{R_1} = q_1$
$C_1 \frac{dh_1}{dt} = q - q_1$
$\frac{h_2}{R_2} = q_2$
$C_2 \frac{dh_2}{dt} = q_1 - q_2$
If q is considered as the input to the system:
a) find the transfer function $T(s) = \frac{Q_1(s)}{Q(s)}$
b) find the transfer function $T(s) = \frac{Q_2(s)}{Q(s)}$

problem 5 500 pts consider the interconnected liquid level system shown in figure 3 barq q tank 1 tank 2 barh1 h1 r1 barh2 h2 r2 barq q2 c1 barq q1 c2 barq steady state flow rate b 05226

Added by Manuel S.

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