Consider the following figure of an activated sludge process (ASP), depicting the flow $(\mathbf{Q})$, substrate $(\mathbf{S})$, and microorganism concentration $(\mathbf{X})$ at various points in the system, where subscripts "$\mathbf{0}$ ", " $\mathbf{r}$ ", " $\mathbf{w}$ ", "$\mathbf{e}$", and " $\mathbf{i}$ " indicate influent, recycle line, wastage, effluent, and flow from aeration tank to settling tank, respectively. Note that influent to the ASP has microbes too. $\mathbf{V}$ is volume of aeration tank.
Choose the correct option for net rate of formation of microorganisms in the system at steady state, from the following
- $\frac{\left(Q-Q_{W}\right) X_{e}+Q_{W} X_{r}-Q X_{0}}{V}$
- $\frac{\left(Q-Q_{W}\right) X_{e}+Q_{W} X_{r}}{V}$
- $\frac{\left(Q-Q_{W}\right) X_{e}+Q_{W} X_{r}}{V X}$
- $\frac{\left(\mathrm{Q}+\mathrm{Q}_{\mathrm{r}}\right) \mathrm{X}_{\mathrm{i}}+\mathrm{Q}_{\mathrm{W}} \mathrm{X}_{\mathrm{r}}}{\mathrm{VX}}$
