Two tanks are connected together in the following unusual way. The density of the incoming liquid, p$,$ is constant. The cross$-$sectional areas of the two tanks are A$1$ and A$2.$ w$2$ is positive for flow from Tank $1$ to Tank $2.$ The two valves are linear with resistance R$1$ and R$2.$ Two tanks are connected together in the following unusual way. The density of the incoming liquid, p$,$ is constant. The cros$-$sectional areas of the two tanks are Ai and A$2.$ is positive for flow from Tank $1$ to Tank $2.$ The two valves are linear with resistances R and R$2.($a$)$ Develop a model for this system that can be used to find hi$,,$ h$2,$ w$2,$ and wz as functions of time for any given variations in inputs $($b$)$ Perform a degrees of freedom analysis. Identify all input and $0$ output variables. Hint: the flow rate is determined by the pressure difference divided by the resistance.