$2-26.$ A sewage lagoon that has a surface area of $10$ ha and a depth of $1m$ is receiving $8,640\frac{m^3}{d}$ of sewage containing $100m\frac{g}{L}$ of biodegradable contaminant. At steady state, the effluent from the lagoon must not exceed $20m\frac{g}{L}$ of biodegradable contaminant. Assuming the lagoon is well mixed and that there are no losses or gains of water in the lagoon other than the sewage input, what biodegradation reaction rate coefficient $(d^{-1})$ must be achieved for a first$-$order reaction?

Answer: $k=0\mathrm{.}3478$ or $0\mathrm{.}35d^{-1}$

$2-27.$ Repeat Problem $2-26$ with two lagoons in series $($see Figure P$-2-27).$ Each lagoon has a surface area of $5ha$ and a depth of $1m.$

$C_{in}=100m\frac{g}{L}$

$Q_{in}=8,640\frac{m^3}{d}$

Lagoon $1$

Lagoon $2$

$C_{\text{o}\text{u}\text{t}}=20m\frac{g}{L}$

Area $=5ha$

Area $=5ha$

$Q_{\text{o}\text{u}\text{t}}=8,640\frac{m^3}{d}$