## Problems

1. A well mixed lake of 107 m" of volume is loaded with 300 kg of N-NH4+.

- How much oxygen is consumed to oxidize completely this load?

- How much time is needed if the water temperature is 15°C?

- Suppose that the lake water is initially oxygen saturated, which oxygen concentration will be reached at the end of the oxidation process?

2. A shallow lake with a surface of 10h nr. an average depth of 2 m, an affluent inflow of 3 m/s and a initial value of the phosphorus concentration of 0.1 mg/1, is loaded with 100 kg/y of phosphorus.

- What will be the concentration at the steady state condition?

- Which is the order of magnitude of the phosphorus settled in the lake?

3. BOD, is 25 mg/1 at 25°C. Find the BOD, at 20°C.

4. The reaeration ratio of a river is 0.8 (1/day) at 15°C. Find the rate at 20°C.

5. A municipal waste water treatment discharges secondary effluent to a surface stream. The waste water has a flow of 100 1/s, a BOD, concentration of 30 mg/1 at 20°C, an O, concentration of 2 mg/1 and a temperature of 25°C. The stream has a summer minimum flow of 1 mVs, BOD, of 3 mg/1 a temperature of 22°C and an oxygen saturation concentration. Complete mixing is almost instantaneous. The velocity of river water is 0.2 m/s, and the depth of 0.8 m.

- Find the critical oxygen concentration and the distance from the treatment plant where the situation is most critical.

- Suppose a winter condition and evaluate the effect in this condition.

6. Consider a completely mixed shallow lake with an inflow of 401/s, an average depth of 3 m and an area of 150,000 nr. The average wind speed on the area is approximately 5 m/s. The inflow water is characterized by an oxygen concentration of 8 mg/1 and no BOD. The lake is impacted by a waste water discharge that produces 120 kg/day of BOD. The bottom of the lake is sandy and the Secchi depth is 2.25 m. The fraction of daylight is 0.5 while ¡j.nra for dominant species of phytoplankton is 2 1 /day. Due to the nutrient limitation ¿u. can be estimated to 1 1/day. by using the model portrayed in Section 3C.3. The chlorophyll-a concentration is found to be 20/u.g/l on average for the period considered. The O./chl-a ratio a, is estimated to be 0.2. A value of A, = 0.21/day can be used. Assuming a temperature of T - 20°C determine the BOD, and the oxygen concentration in the lake.