Question

A well-mixed lake with a surface area of 3.0 (Km^2] and an average depth of 5 m is fed by a stream and rainfall. (Groundwater and runoff are insignificant inputs).

The stream's flow rate is 0.2 (m^3/s], and the concentration of phosphorous in the stream is 1 [mg/l]. Average rainfall is 0.7 [m/yr], and the rain has a phosphorous concentration of 0.01 [mg/l]. Phosphorous removal by evaporation and by biological processes is negligible. Phosphorous precipitates from the lake's water according to first-order kinetics,with a rate constant of 0.005/d. The outlet stream has a flow rate of 0.19 [m^3/s), which keeps the volume of water in the lake essentially constant.

Fig: 1