For the following fluid system, let $A_1=5m^2,A_2=10m^2,R_1=\frac{1}{m}s,R_2=\frac{5}{m}s,D_1=1m,q_{mi}=$

$100k\frac{g}{s},=2k\frac{g}{m^3},g=10\frac{m^2}{s}$

a$.$ Give a dynamic systems model for $h_1$ and $h_2($does not need to be in state$-$variable

matrix form$).$ The input is $q_{mi}.$ Assume that $h_2>D_1.$

b$.$ Give MATLAB commands to specify the state$-$variable model $($i$.$e$.,$ use the ss

command$)$ where $h_1$ and $h_2$ are the output variables. You may consider $D_1$ as an input.