$1.$ Explain briefly the relations among total solids, total suspended solids, total dissolved solids, volatile suspended solids, fixed suspended solids, volatile dissolved solids, and fixed dissolved solids with respect to measurement methods. $(20$ points$)$

$2.$

Derive the following equation based on the particle mass balance over $z,$ unit thickness of filter bed in depth filtration. Assume that all particles of filter media are spherical, porosity $($n$)$ and grain dimesion are constant with time, and filtration occurs at first order removal with depth when filtration coefficient is $.$ Here, $L$ is thickness of filter bed, $a$ is attachment efficiency determined based on the coagulant dosage, $$ is transport efficiency and $d_c$ is the collctor particle diameter. You may use other assumptions and parameters, if necessary. $($Hint: Derive the mass flow approaching a single collector in the first place$)(30$ points$)$

:$.\frac{C_{\text{o}\text{u}\text{t}}}{C_{in}}=$exp$(-\frac{3(1-n)}{2d_c}L)$

$3.$

Explain about mechanism of coagulation. $(15$ points$)$

$4.$

Two rectangular clarifiers, each $27m$ long, $5\mathrm{.}0m$ wide, and $3\mathrm{.}8m$ deep, settle $6,000\frac{m^3}{d}.$ Total effluent weir length is $50m.$ Calculate the detention time and overflow rate. $(15$ points$)$