$[40]4.$ A batch settling test has been performed on an industrial wastewater having an initial suspended solids of $597m\frac{g}{L}$ to develop criteria for the design of a primary clarifier. The test column was $5in.$ in diameter and $8ft$ high, and sampling ports were located $2,4,6,$ and $8ft$ from the water surface in the column. The suspended solids remaining after the various sampling times are given below:

$\backslash$table$[[$Depth$,$ ft$,$Time $($min$)],[10,20,30,45,60],[394,352,243,182,148],[4,460,406,337,295,216],[6,512,429,376,318,306],[8,1018,1142,1208,1315,1405]]$

The wastewater flow is $2\mathrm{.}5$ MGD$.$

Determine:

a$.$ The design overflow rate and detention time if $65\%$ percent of the suspended solids are to be removed. Use scale$-$up factors: $0\mathrm{.}65$ for overflow rate and $1\mathrm{.}75$ for detention time.

b$.$ The diameter if a circular clarifier is used.

c$.$ The design diameter if equipment is available in $5-$ft increments of tank diameter.

d$.$ The depth of the tank.