(Solved): Determine the transfer function H(s)/Q(s) for the liquid-level system shown below. You may assume ...

Determine the transfer function $H(s)/Q(s)$ for the liquid-level system shown below. You may assume that: 1. Resistances $R_t$ and $R_2$ are linear. 2. The flow rate from tank 3 is maintained constant at a value $b$ by a pump, meaning that the flow from tank 3 is independent of head $\mathbf{h}$. 3. The tanks are non-interacting. Please show all work for credit including: - Derivation of mass balance equation for each tank (30\%) - Derivation of deviation variables for each tank (15\%) - Derivation of transfer function for each tank including the Laplace transform. $(20\%)$ - Define time constants for tanks 1 and 2 (10\%) - Directly derive (must show calculation) the resulting transfer function $H(s)/Q(s)$ based on the above steps only. $(25\%)$