Using modifed Velz equation determine A plastic media biotower has vertical flow packing with $n=0\mathrm{.}5$ and $k_{20}$ of $0\mathrm{.}045mi{n}^{-1}.$ The tower is cylindrical with a diameter of $10m.$ Depth of packing medium is $6m.$ Primary effluent flow rate is $2500\frac{m^3}{d}$ with a soluble $BO{D}_5$ of $250m\frac{g}{L}.$ The average wastewater temperature is $16C.$ Direct recirculation is practiced at $1$:$1$ ratio. Calculate the following:

a$.$ Organic loading rate of the biotower

b$.$ Hydraulic loading rate of the biotower

c$.$ Recirculation ratio

d$.$ Effluent soluble $BO{D}_5$ concentration