Math problem set Grade 10 Math
Oxbow Bend Nitrogen Loading and Water Reuse Problems
A grade 10 problem set applying the pounds formula to nitrogen at a fictional plant, treating the nutrient as both a river pollutant and a fertilizer resource.
Objectives
- Students will calculate nitrogen loading in pounds per day using the pounds formula.
- Students will compute removal efficiency and interpret reclaimed water's nitrogen as both pollutant and fertilizer.
Vocabulary
Key words: pounds formula, loading, removal efficiency, reclaimed water
Teacher overview
The fictional Oxbow Bend Water Reclamation Facility treats wastewater and then sends the cleaned water to irrigate a nearby hay field instead of discharging it to a creek. Nitrogen is the thread through this set: in the creek it would feed algae and lower oxygen, but on the field the same nitrogen acts as fertilizer. Students use the pounds formula to track nitrogen loads and removal. A common misconception here is putting flow into the pounds formula in the wrong units; the formula needs flow in MGD, not gpm or gallons per day, or every load comes out wrong by a large factor.
Problems
The Oxbow Bend Water Reclamation Facility (a fictional plant used for this set) treats 3.0 MGD. The influent total nitrogen is 35 mg/L, and after treatment the effluent total nitrogen is 8 mg/L. Use the pounds formula: loading (lbs/day) = concentration (mg/L) × flow (MGD) × 8.34. Fish generally need dissolved oxygen above 5 mg/L.
Find the nitrogen load entering the plant each day, using the influent concentration of 35 mg/L.
Find the nitrogen load leaving in the effluent each day, using the effluent concentration of 8 mg/L.
How many pounds of nitrogen does the plant remove each day? Subtract the effluent load from the influent load.
Find the nitrogen removal efficiency as a percent, using (influent − effluent) / influent × 100 with the concentrations. Round to the nearest tenth.
The plant sends its full 3.0 MGD of reclaimed water to a hay field instead of the creek. How many pounds of nitrogen does that reclaimed water carry onto the field each day? This equals the effluent load from problem 2.
Over a 30-day month, how many pounds of nitrogen does the reclaimed water deliver to the field?
The hay field is 600 acres. Find the nitrogen delivered per acre over the month. Round to the nearest whole pound.
In a creek, the same effluent nitrogen would feed algae. Explain in two or three sentences how excess nitrogen can drive the creek's dissolved oxygen below the 5 mg/L that fish need.
Suppose the plant upgrades and cuts the effluent nitrogen to 4 mg/L. Find the new effluent nitrogen load in pounds per day at 3.0 MGD.
Find the new removal efficiency at the 4 mg/L effluent concentration, and compare it to your answer from problem 4.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 875.7 lb/day. 35 mg/L × 3.0 MGD × 8.34 = 875.7 pounds per day.
Answer: 200.2 lb/day. 8 mg/L × 3.0 MGD × 8.34 = 200.16, about 200.2 pounds per day.
Answer: 675.5 lb/day. 875.7 − 200.2 = 675.5 pounds of nitrogen removed each day.
Answer: 77.1 percent. (35 − 8) / 35 × 100 = 27 / 35 × 100 = 77.14, which rounds to 77.1%.
Answer: 200.2 lb/day. The reclaimed water carries the effluent load onto the field, which is the 200.2 pounds per day found in problem 2. On the field this nitrogen acts as fertilizer rather than as a pollutant.
Answer: 6,006 lb. 200.2 pounds per day × 30 days = 6,006 pounds in the month.
Answer: 10 lb per acre. 6,006 pounds / 600 acres = 10.01, about 10 pounds of nitrogen per acre for the month.
Answer: Nitrogen is a nutrient that feeds algae. Extra nitrogen lets algae grow fast, and when that algae dies, bacteria break it down and use up oxygen in the water. That drop can pull dissolved oxygen below the 5 mg/L fish need, which is why the same nitrogen that fertilizes a field is a pollutant in a creek.
Answer: 100.1 lb/day. 4 mg/L × 3.0 MGD × 8.34 = 100.08, about 100.1 pounds per day.
Answer: 88.6 percent. (35 − 4) / 35 × 100 = 31 / 35 × 100 = 88.57, which rounds to 88.6%. This is higher than the 77.1% from problem 4, so the upgrade removes a larger share of the incoming nitrogen.
Differentiation
Support
Provide the pounds formula written out with the influent numbers already placed (35 × 3.0 × 8.34) so students see the structure before working the effluent case. Give a printed reminder that flow in the pounds formula must be in MGD, since that is the step students most often miss.
Extension
Ask students to find the effluent concentration, in mg/L, that would push the plant's nitrogen removal efficiency to exactly 90 percent, working backward from the removal-efficiency formula. Then have them discuss one tradeoff of removing more nitrogen, such as added energy or chemical use.
ELL supports
Pre-teach "loading," "effluent," and "reclaimed water" with a labeled flow diagram showing water entering the plant, leaving as effluent, and going to the field. Provide a sentence frame for problem 8: "Extra nitrogen lowers oxygen because ___."
Extensions
Have students compare the field application rate from problem 7 against a typical fertilizer bag's nitrogen recommendation for hay, which a local extension office can supply. A short paragraph can weigh whether the reclaimed water alone meets the crop's nitrogen need or whether the grower would still add fertilizer, connecting the nutrient's two roles.