Problem $2(20$ points$)$

$1\mathrm{.}2.$ A $3\mathrm{.}78{10}^7\frac{L}{?}$ day wastewater treatment plant's influent and effluent concentrations of heavy

metals are as follows:

Concentration of the Metal

The plant produces a dewatered sludge cake at a solids concentration of $22\%($by weight$).$ Plant

records show that $45,000kg$ of sludge $($wet$)$ is disposed of on a pasture per day. Sludge disposal

on land is restricted only to sludges that have metal concentrations less than the following.

Maximum allowable

Metal Concentration

$($mg metal$/$kg dry sludge$)$

Cd $15$

Cr $1,000$

Hg $10$

Pb $1,000$

Does the sludge meet quality standards?

$($a$)$ Assume that the flowrate of solids into the plant is negligible compared to the influent flow

rate. Check to see whether this is a valid assumption $(13).$

$($b$)$ Assume that the density of the sludge is about that of water, so that $1$ kg of sludge

represents a volume of $1$ L $.$ Check to see whether this is a valid assumption $(7).$