$($a$)$ Determine the depth of low$-$rate trickling filter that has a diameter of $50m.$ The hydraulic loading is $0\mathrm{.}17\frac{m^3}{s}$ and the influent and effluent $BO{D}_5$ are $270m\frac{g}{l}$ and $45m\frac{g}{\text{I}}$ respectively. The unit operates at $27C.$ Assume that the empirical constants $m=n=1$ and $K_{25}=0\mathrm{.}2\frac{m}{d}.$ The packing media are rocks that have a porosity of $0\mathrm{.}7$ and Sa sphericity of $0\mathrm{.}9.$ The geometric mean size of the rocks is $85mm.$

$($b$)$ For the depth of the trickling bed obtained above if the temperature of operation is changed to $30C$ and all other conditions remaining the same, what will be effluent $BO{D}_5$ that will be coming out.

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