Example Problem $2$

A mixture of river water and effluent from a municipal wastewater treatment plant is completely mixed near the point of discharge. The dissolved oxygen concentration in the river at the mixing point is $5\mathrm{.}6m\frac{g}{L},$ and the ultimate BOD of the mixed water is $24m\frac{g}{L}.$ The temperature of the river is $21C.$ The deoxygenation constant for the river is $k_d=0\mathrm{.}06/$day$.$

a$.$ Estimate the reoxygenation coefficient assuming the river speed is $0\mathrm{.}25\frac{m}{s}$ and the average depth is $3$ m $.$

b$.$ Find the critical time downstream at which the minimum DO occurs.

c$.$ Find the minimum DO downstream.