The system shown below is controlled by a proportional controller. The concentration of salt in the solution leaving the tank is controlled by adding a concentrated solution through a control value.

The following data apply

Concentration of concentrated salt solution C$\_(1)=25$ lb salt$/$ft$3$ solution.

Controlled concentration C$=0\mathrm{.}1$ lb salt$/$ft$3$ solution

Control valve: The flow through the control valve varies from $0\mathrm{.}002$ to $0\mathrm{.}0006$ ft$3/$min with a change of valve$-$top pressure from $3$ to $15$ psi. This relationship is linear.

Distance velocity lag: It takes $1$ min for the solution leaving the task to reach the concentration measuring element at the ead of the pipe.

Neglect lags in the valve. Place in each block the appropriate transfer function Calculate all the constants and give the units.

Please show all the steps clearly.