The organ shown below is controlled by a proportional controller. A liquid carries a drug into an organ of volume $Vcm$ at a rate $q_{1}c\frac{m^3}{m}in$ and also water added at a rate of $1c\frac{m^3}{m}in$ and leaves at a rate $1c\frac{m^3}{m}in.($Assume; outlet flow$=$inlet flow$)$ The concentration of drug in the solution leaving the organ is controlled by adding a concentrated drug through a control valve.

The following data apply:

Concentration of concentrated drug solution $C_1=25g$ drug $\frac{?}{c{m}^3}$ solution.

Controlled concentration $C=0\mathrm{.}1$gdru$\frac{g}{c}{m}^3$ solution.

Control valve: The flow through the control valve varies from $0\mathrm{.}002$ to $0\mathrm{.}0006f\frac{t^3}{m}in$ with a change of valve$-$top pressure from $3$ to $15.$ This relationship is linear.

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

Neglect lags in the valve.

contral valse