$14\mathrm{.}23$ A waste$-$water stream of $Q=1\frac{m^3}{h}$ with substrate at $2000m\frac{g}{L}$ is treated in an upflow$-$packed bed containing

immobilized bacteria in form of biofilm on small ceramic particles. The effluent substrate level is desired to be

$30m\frac{g}{L}.$ The rate of substrate removal is given by the following equation:

$r_S=-\frac{r_{\text{m}\text{a}\text{x}}xS}{K_S+S}$

The particles are very small and the immobilized bacteria are of a very thin film and thus the effectiveness factor can

be considered to be $100\%.$ By using the following information, determine the required height of the column $(H)$ for

a bed diameter of $2m.$

$r_{\text{m}\text{a}\text{x}}=0\mathrm{.}5h^{-1},x=0\mathrm{.}1\frac{g}{m^2},K_S=200m\frac{g}{L},a=100\frac{m^2}{m^3}$