Question $1$:

A completely mixed high$-$rate activated giludge plant with recycling treats $18,000\frac{m^3}{?}$ day of industrial wastewater. The influent to the activated sludge reactor has a $BO{D}_5$ of $980m\frac{g}{L}.$ It is desired to reduce the influent $BO{D}_5$ to $100m\frac{g}{L}$ prior to discharge to a municipal sewer. Pilot plant analysis gave the following results: mean cell residence time $=6d,$ MLSS concentration in reactor $=5000m\frac{g}{L},Y=0\mathrm{.}62k\frac{g}{k}g,k_d=0\mathrm{.}033d^{-1}.$ Determine the following:

a$.$ The hydraulic retention time and volume of the activated sludge reactor.

b$.$ The volumetric loading rate in kgBO$\frac{D_5}{m^3}-$day to the reactor.

c$.$ The $\frac{F}{M}$ ratio in the reactor.

d$.$ The mass and volume of solids wasted each day at an underflow solids concentration, $x_u=11,500m\frac{g}{L}.$

e$.$ The sludge recirculation ratio.