For the fluid system below

a$.$ Give the dynamic systems model for $h_1,h_2,$ and $h_3$ in state variable matrix form.

b$.$ Determine the height of the water in each tank in steady state, assuming that $A_1=2,$

$A_2=3,A_3=1,R_1=R_2=R_3=1,q_{mi}=5k\frac{g}{s},g=10\frac{m^2}{s},=0\mathrm{.}1k\frac{g}{m^3}.$

For the fluid system below:

a$.$ Give a dynamic systems model for $h_1$ and $h_2$ in state$-$variable matrix form.

b$.$ Suppose that $q_{mi}=30k\frac{g}{s},A=20m^2,A_2=50m^2,=1k\frac{g}{m^3},R_1=R_2=R_3=\frac{2}{?}$

$m*s.$ At a given moment, suppose that $h_1=5m,h_2=10m.$ Is $h_1$ increasing or

decreasing? Is $h_2$ increasing or decreasing?

c$.$ Under these conditions, which tank has a total greater force on the bottom of the tank

due to the water?