Complete the problem below:

Example: Designing a Flocculator: A water treatment plant is being designed to process $50,000\frac{m^3}{d}$ of water. Jar

testing and pilot$-$plant analysis indicate that an alum dosage of $40m\frac{g}{L}$ with flocculation at a Gt value of $4\mathrm{.}0{10}^4$

produces optimal results at the expected water temperatures of $15C.$ Assume the average $G$ value is $30s^{-1}.$

Determine:

$(1)$ The monthly alum requirement in $k\frac{g}{?}$ month

$(2)$ The flocculation basin dimensions if three cro$55-$flow horizontal paddles are to yoed The flocculator

should be a maximum of $12m$ wide and $5m$ deep in order to connect appropriately with the settling basin.

$(3)$ The power requirement.

$(4)$ The paddle configuration.

Monthly alum requirement:

$40m\frac{g}{L}Qx$ time $=$

$k\frac{g}{?}$ month

Basin dimension:

$($a$)$ Calculate detention time

Then $Gt=4{10}^4$

$t=4\frac{{10}^4}{G}x(1mi\frac{n}{60}s)=$

min.

$($b$)$ Volume of $tank$ is

$V=Qt=50,000(\frac{m^3}{d})t=$

$m^3$

$($c$)$ The tank will contain three cross$-$flow paddies $50$ II lengtn will oe avided into three compartments. For equal

distribution of velocity gradients, the end area of each compartment should be square, i$.$e$.,$ depth equals $\frac{1}{3}$ length.

Assuming maximum depth of $5m,$ length is:

$3xd=$

$m$

Width is $dxLxw=$

$W=$

$m$

Power requirements:

$($a$)$ Assume G value tapered as follows: $($remember$,$ the average of all three must be what you assumed earlier$)$

First compartment, $G=$

$g^{-1}$

Second Compartment,

Third compartment,

G

G

$($b$)$ Power requirement for compartment $1,2$ and $3$

Where

$p=G^{2}V$

At $15C$

$m^3$

$=$

$P_1=$

$P{a}^{**}$ or $N**\frac{g}{m^2}$

$P_2=$

W

$=$

$kW$

$P_3=$

$W=$

$kW$

$kW$

Paddle configuration

$($a$)$ Assume each paddle has four boards $2\mathrm{.}5m$ long and $w$ wide. There are three paddle wheels per compartment.

$($b$)$ Calculate width of paddle $($w$)$ from power input and paddle velocity:

$P=\frac{C_D{A}_p{v}_p^3}{2}$

At $15C_{}=999\mathrm{.}103k\frac{g}{m^3}$

$($Table A$-1$ in Textbook$)$

Assume paddle velocity in the middle of design range $($gee above$)=$

$\frac{m}{5}$

$CD$ :

$($reference table above, $1\mathrm{.}8)$

$A_p=$ length of boards $x($w$)x$ number of boards

$3$ paddles at

in terms of $w$

boards per paddle $=$

boards

$P($in terms of $(w)$

$r=$ boards $2\mathrm{.}5m($length$)x(w)$

Set equal to average power found above:

$P($from average $G$ value$)=$

Solve for width of paddle:

$w=$

$m$