Problem $1$

After coagulation$/$flocculation and sedimentation, a municipal water treatment plant uses a

$1-$foot deep homogeneous filter comprised of sand grains of $0\mathrm{.}5$ mm diameter. The porosity

of the clean filter is $0\mathrm{.}36.$ The sand has a specific gravity of $2\mathrm{.}6$ and a particle shape factor

of $7\mathrm{.}0.$ The hydraulic flow rate is $2gp\frac{m}{f}{t}^2$ at $20C.$ The influent stream contains discrete

particles of essentially uniform size $($approximately spherical shape; specific gravity of

$1\mathrm{.}05$ ; collision efficiency factor of $0\mathrm{.}8)$ at a concentration of $5m\frac{g}{l}.$

a$.$ Calculate the head loss through the filter at the onset of a filter run.

b$.$ For particle sizes of $0\mathrm{.}1,1\mathrm{.}0,$ and $10m$ diameter, calculate the single collector

efficiency and percent removal of the influent particles at the onset of a filter run.

c$.$ Comment on the relative contributions of the various transport mechanisms in the

filtration media for the different particle sizes. What comparisons can be made between

particle transport in the filtration process and particle transport in the flocculation

process?