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Math problem set Grade 9 Math

Kettleridge Wastewater Plant: BOD Loading and the Pounds Formula

A grade 9 problem set using the pounds formula to track BOD loading and removal at Kettleridge's wastewater plant, then writing an equation for load from concentration.

Objectives

  1. Students will apply the pounds formula to find daily loading from concentration and flow.
  2. Students will calculate removal efficiency as a percent.
  3. Students will write and solve an equation relating load to concentration at a fixed flow.

Vocabulary

Influent
Influent is the incoming dirty water that arrives at a treatment plant, ready to be cleaned. Operators test it to see how much work the plant has to do.
Effluent
Effluent is the cleaned water that leaves a treatment plant at the end of the process. It is tested carefully before being released to a river, lake, or the ocean.

Also: pounds formula, BOD, removal efficiency

Teacher overview

The fictional Kettleridge Water Resource Recovery Facility cleans sewage before returning it to a river. Operators use the pounds formula, where loading in pounds per day equals concentration in mg/L times flow in MGD times 8.34, to track how much material moves through the plant each day. This set follows one day's flow from dirty water to treated water, then turns the pounds formula into an equation students solve for a missing concentration. A common misconception is putting flow in gallons per minute into the pounds formula instead of MGD, or dropping the 8.34 factor.

Kettleridge Wastewater Plant: BOD Loading and the Pounds Formula — Grade 9 Math
Name: ____________________________ Date: ______________

Problems

Kettleridge (a fictional facility) treats 5 MGD. Its incoming (influent) BOD is 220 mg/L. Use the pounds formula: pounds per day = mg/L x MGD x 8.34.

  1. Find the influent BOD load in pounds per day, using 220 mg/L, 5 MGD, and 8.34.
  2. Secondary treatment rules require effluent BOD at or below 30 mg/L. Find the effluent BOD load at 30 mg/L and 5 MGD.
  3. How many pounds of BOD does the plant remove each day? Subtract the effluent load from the influent load.
  4. Find the BOD removal efficiency as a percent, using (influent - effluent) / influent x 100 with the two concentrations.
  5. Write an equation for the effluent load P (pounds per day) in terms of the effluent concentration c (mg/L), with the flow held at 5 MGD.
  6. Use your equation from problem 5 to find the effluent concentration when the measured load is 834 pounds per day.
  7. Kettleridge adds chlorine for disinfection at 2.0 mg/L into the 5 MGD flow. Find the chlorine feed in pounds per day.
  8. The treated water still carries nitrogen at 8 mg/L, a nutrient plants need but one that feeds algae in excess. Find the nitrogen load returned to the river each day at 5 MGD.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 9,174 lb/day. 220 mg/L x 5 MGD x 8.34 = 9,174 pounds per day. (220 x 5 = 1,100; 1,100 x 8.34 = 9,174.)
  2. Answer: 1,251 lb/day. 30 mg/L x 5 MGD x 8.34 = 1,251 pounds per day. (30 x 5 = 150; 150 x 8.34 = 1,251.)
  3. Answer: 7,923 lb/day. 9,174 - 1,251 = 7,923 pounds per day of BOD removed.
  4. Answer: 86 percent. (220 - 30) / 220 x 100 = 190 / 220 x 100 = 86.36%, about 86%.
  5. Answer: P = 41.7c. Since 5 MGD x 8.34 = 41.7, the effluent load is P = c x 41.7 = 41.7c.
  6. Answer: 20 mg/L. 834 = 41.7c, so c = 834 / 41.7 = 20 mg/L.
  7. Answer: 83.4 lb/day. 2.0 mg/L x 5 MGD x 8.34 = 83.4 pounds per day of chlorine. (2.0 x 5 = 10; 10 x 8.34 = 83.4.)
  8. Answer: 333.6 lb/day. 8 mg/L x 5 MGD x 8.34 = 333.6 pounds per day of nitrogen. (8 x 5 = 40; 40 x 8.34 = 333.6.)

Differentiation

Support

Give students the pounds formula on a card with its three slots labeled (concentration, flow, and the 8.34 factor) and one filled example that is not in this set. Provide the product 5 times 8.34 equal to 41.7 already computed for problems 5 and 6, and allow a calculator.

Extension

Ask students to find the plant's BOD load if the flow rises to 6 million gallons per day while the influent concentration stays the same, then explain in one sentence why the load grows even though the concentration did not change.

ELL supports

Pre-teach "influent," "effluent," "load," and "removal" with arrows on a simple plant diagram showing dirty water going in and treated water coming out. Provide a sentence frame for problem 4: "The removal efficiency is ___ percent because ___."