There is a mixing tank as shown in the figure below, assuming complete and uniform mixing. The solute concentrations

of the two feed streams are $C_1$ and $c_2[\frac{kg}{m^3}],$ the volume flow rate is $f[\frac{m^3}{m}in],$ the flow rate of the outlet stream

is $f,$ and the concentration is $C.$ Assuming that the volume of liquid in the tank is constant, please use the

discharge concentration $c$ as the output variable to derive the following four transfer functions

$\frac{(\frac{?}{\text{b}\text{a}\text{r}}(C))(s)}{\frac{?}{\text{b}\text{a}\text{r}}(C{)}_1(s)},\frac{(\frac{?}{\text{b}\text{a}\text{r}}(C))(s)}{\frac{?}{\text{b}\text{a}\text{r}}(C{)}_2(s)},\frac{(\frac{?}{\text{b}\text{a}\text{r}}(C))(s)}{\frac{?}{\text{b}\text{a}\text{r}}(F{)}_1(s)},\frac{(\frac{?}{\text{b}\text{a}\text{r}}(C))(s)}{\frac{?}{\text{b}\text{a}\text{r}}(F{)}_2(s)}$