Problem $1.$

A completely mixed high$-$rate activated sludge plant is to treat $15,000\frac{m^3}{d}$ of industrial wastewater. The primary effluent going to the activated sludge reactor has a BOD$5$ of $1100m\frac{g}{L}$ that must be reduced to $150m\frac{g}{L}$ prior to discharge to a municipal sewer. The flow diagram of the plant is given in the following Figure. Pilot plant analysis gave the following results: mean solid residence time $=5d,$ MLSS concentration in the area tank $=6000m\frac{g}{L}$ VSS$,Y=0\mathrm{.}7k\frac{g}{k}g,k_d=0\mathrm{.}03d^{-1}.$

Determine the following:

a$.$ The hydraulic retention time and volume of the activated sludge reactor. $(10$ points$)$

b$.$ The volumetric loading rate in kgBO$\frac{D_s}{m^3}-d$ to the reactor. $(10$ points$)$

c$.$ The $\frac{F}{M}$ ratio in the reactor. $(10$ points$)$

d$.$ The mass $(k\frac{g}{d})$ and volume $(\frac{m^3}{d})$ of solids wasted each day, at a waste solids concentration $x_w=12,000m\frac{g}{L}.(10$ points$)$

e$.$ The sludge recirculation ratio $(\frac{Q_r}{Q}).(10$ points