A lake with 2.5 x 108 m² water is fed by an upstream river having a flowrate of 20 m/s with phosphorus concentration of 0.002mg/L. Another source of phosphorus coming into the lake is effluent from a wastewater treatment plant at a rate of 5 g/s (negligibly small flow rate). Phosphorus is removed from water via two pathways I. Phosphorus is taken up by algae at a rate of 0.1 mg/m3-day II. Phosphorus forms insoluble precipitates with Ca2+, Mg2+ and Fe3+ and the precipitates settle out of water at a rate (vs) of 10 m/yr. The surface area of the lake is 5 x 107 m2. The mass removal rate due to settling is therefore equal to: Mass removal due to precipitation = Vs x surface area x conc of P in the lake Answer these questions: a) Write a mass balance equation for phosphorus in the lake. Derive the equation for phosphorus concentration at steady-state.
b) What is the steady state concentration of phosphorus in lake?