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Worksheet Grade 12 Science

Wren Hollow: A Wet-Weather Month Against Secondary Treatment Limits

A grade 12 worksheet in which students audit a fictional plant's wet February against 7-day, 30-day and 85 percent removal limits, then trace storm loads downstream.

Objectives

  1. Students will calculate 7-day averages, 30-day averages, and 30-day percent removal from a month of plant monitoring data and test each against the secondary treatment standard.
  2. Students will explain how dilute wet-weather influent and shortened treatment time can cause a plant to fail a limit even when most of its results look good.
  3. Students will calculate BOD mass loads and a downstream mixed concentration and use them to evaluate the plant's effect on a receiving stream.

Vocabulary

Inflow and infiltration
Rainwater and groundwater that sneak into sewer pipes through cracks, bad joints, and improper connections. The extra water can overload sewers and treatment plants during storms.

Also: BOD, TSS, 7-day average, 30-day average, percent removal, mass load

Teacher overview

The Wren Hollow Water Resource Recovery Facility is a fictional plant that discharges to Larrow Creek. Federal secondary treatment standards hold its effluent BOD and TSS to a 30-day average of no more than 30 mg/L and a 7-day average of no more than 45 mg/L, and require it to remove at least 85 percent of each, with percent removal figured from the 30-day average influent and effluent concentrations. In this worksheet students act as the compliance analyst for February 2026, a month in which a rain-on-snow event in the third week sent groundwater and stormwater into the sewers. They compute every average the permit requires, find which limits the plant passed and failed, follow the storm-week load into the creek, and evaluate two proposed fixes.

Two misconceptions come up often. The first is that a passing monthly average means the plant had a good month; a single bad week can still violate the 7-day limit. The second is that low effluent concentrations guarantee a passing percent removal. When extra water dilutes the incoming sewage, the plant has less to remove in concentration terms, and percent removal can fall below 85 percent while every effluent result stays under its limit. February at Wren Hollow shows both cases. Students who read the regulation may find that it lets a permitting authority adjust the 85 percent requirement for a separately sewered plant with less concentrated influent, but only when the dilution is not caused by excessive inflow and infiltration (40 CFR 133.103), so that provision would not excuse this month. Calendar weeks run Sunday through Saturday, and February 2026 begins on a Sunday, so the month divides into four complete weeks of three samples each.

Wren Hollow: A Wet-Weather Month Against Secondary Treatment Limits — Grade 12 Science
Name: ____________________________ Date: ______________

Student Worksheet

You are the compliance analyst for the Wren Hollow Water Resource Recovery Facility, a fictional plant. Use the reference information and the two data tables below for every item.

Reference information

  • 30-day average limit: effluent BOD and TSS each 30 mg/L or less. Wren Hollow's permit computes the 30-day average as the mean of all samples taken in the calendar month.
  • 7-day average limit: effluent BOD and TSS each 45 mg/L or less, computed as the mean of the samples taken in each calendar week (Sunday through Saturday).
  • Percent removal limit: at least 85 percent for BOD and for TSS, computed from the 30-day average influent and the 30-day average effluent concentrations: percent removal = (average influent - average effluent) / average influent x 100.
  • Raw domestic sewage BOD typically runs about 100 to 300 mg/L.
  • Mass load (kg/day) = concentration (mg/L) x flow (m³/day) / 1,000.
  • Most fish need dissolved oxygen above 5 mg/L, and cold water holds more oxygen than warm water.
  • Round concentrations and percents to the nearest tenth and loads to the nearest tenth of a kilogram per day.

Table 1. Wren Hollow plant monitoring data, February 2026 (24-hour composite samples; concentrations in mg/L)

Date Week Plant flow (m³/day) Influent BOD Effluent BOD Influent TSS Effluent TSS
Mon Feb 2 1 7,400 210 12 228 18
Wed Feb 4 1 7,600 225 14 240 20
Fri Feb 6 1 7,500 216 13 234 22
Mon Feb 9 2 7,500 220 11 236 19
Wed Feb 11 2 7,700 208 13 222 21
Fri Feb 13 2 7,600 214 15 230 20
Mon Feb 16 3 18,500 96 50 88 40
Wed Feb 18 3 20,000 84 47 76 44
Fri Feb 20 3 17,800 102 44 94 42
Mon Feb 23 4 12,000 150 20 120 28
Wed Feb 25 4 11,000 162 16 132 26
Fri Feb 27 4 10,000 174 13 126 30

Table 2. Larrow Creek just upstream of the Wren Hollow outfall

Date Creek flow (m³/day) Creek BOD (mg/L)
Wed Feb 4 40,000 2.0
Wed Feb 18 150,000 4.0

  1. Calculate the 7-day average effluent BOD for each of the four weeks.

  2. Calculate the 30-day average effluent BOD for February.

  3. Using your answers to items 1 and 2, state whether Wren Hollow met the 30-day BOD limit and the 7-day BOD limit. For any limit it missed, give the week and the amount by which the average exceeded the limit.

  4. Calculate the four 7-day average effluent TSS values and the 30-day average effluent TSS. State whether every TSS concentration limit was met.

  5. Calculate the 30-day average influent BOD, then the February BOD percent removal. Does the plant meet the 85 percent requirement for BOD?

  6. Calculate the 30-day average influent TSS, then the February TSS percent removal. Does the plant meet the 85 percent requirement for TSS? If not, by how many percentage points does it fall short?

  7. Keep the 30-day average effluent TSS from item 4 fixed. What 30-day average influent TSS would have given exactly 85 percent removal? Set up and solve the equation.

  8. Calculate the BOD percent removal for week 1 alone and for week 3 alone, using each week's average influent and effluent. The permit does not apply the 85 percent test weekly, yet operators track these values. Give two separate physical reasons, one about the influent and one about the treatment process, that explain why week 3 fell so far below week 1.

  9. Calculate the influent BOD load in kg/day on February 4 and on February 18. Compare the two loads and explain what the comparison tells you about where the extra water in week 3 came from.

  10. Calculate the effluent BOD load the plant sent to Larrow Creek on February 4 and on February 18. How many times larger was the February 18 load?

  11. Assume the effluent mixes completely with the creek just below the outfall. Use Table 2 and your item 10 loads to calculate the mixed BOD concentration in the creek on February 4 and on February 18.

  12. BOD is oxygen that microbes will consume over the following days as they break down organic matter. Using your item 11 results and the reference information, explain how the February 18 discharge could affect fish and other oxygen-dependent organisms downstream. Name one condition that makes the effect smaller in February and one that would make the same discharge more harmful in late summer.

  13. The utility's engineer proposes a flow equalization basin that would store peak wet-weather flow and feed it to the plant gradually. Suppose that with the basin in place, effluent TSS on each of the three week 3 sample days had been 20 mg/L, while every other value in Table 1 stayed the same. Recalculate the 30-day average effluent TSS and the February TSS percent removal, and state whether the plant would have passed.

  14. A second proposal is a sewer inflow and infiltration program: lining cracked sewer pipes and disconnecting roof drains and sump pumps that empty into the sanitary sewer. Write a short recommendation (5 to 7 sentences) to the utility board comparing the equalization basin and the inflow and infiltration program. For each option, say which of February's two compliance failures it addresses and cite at least two numbers from your work. Name one cost or trade-off for each option, and explain which option does more to protect Larrow Creek over the long term.

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: Week 1: 13.0 mg/L; week 2: 13.0 mg/L; week 3: 47.0 mg/L; week 4: 16.3 mg/L.
    Week 1: (12 + 14 + 13) / 3 = 39 / 3 = 13.0. Week 2: (11 + 13 + 15) / 3 = 39 / 3 = 13.0. Week 3: (50 + 47 + 44) / 3 = 141 / 3 = 47.0. Week 4: (20 + 16 + 13) / 3 = 49 / 3 = 16.33, which rounds to 16.3.

  2. Answer: 22.3 mg/L.
    Sum of all twelve effluent BOD results = 39 + 39 + 141 + 49 = 268 mg/L. 268 / 12 = 22.33, which rounds to 22.3 mg/L. Students who average the four weekly averages get the same value here because every week has three samples.

  3. Answer: The 30-day BOD limit was met; the 7-day BOD limit was exceeded in week 3 by 2.0 mg/L.
    22.3 mg/L is below the 30 mg/L 30-day limit. Weeks 1, 2 and 4 (13.0, 13.0 and 16.3 mg/L) are below the 45 mg/L 7-day limit, while week 3 at 47.0 mg/L is over it: 47.0 - 45 = 2.0 mg/L. A passing monthly average does not cancel the weekly violation, which would be reported on its own.

  4. Answer: Weekly averages 20.0, 20.0, 42.0 and 28.0 mg/L; 30-day average 27.5 mg/L; all TSS concentration limits were met.
    Week 1: (18 + 20 + 22) / 3 = 60 / 3 = 20.0. Week 2: (19 + 21 + 20) / 3 = 60 / 3 = 20.0. Week 3: (40 + 44 + 42) / 3 = 126 / 3 = 42.0. Week 4: (28 + 26 + 30) / 3 = 84 / 3 = 28.0. Monthly: (60 + 60 + 126 + 84) / 12 = 330 / 12 = 27.5. Every weekly average is at or below 45 mg/L, and 27.5 mg/L is below 30 mg/L, though only by 2.5 mg/L.

  5. Answer: 30-day average influent BOD 171.8 mg/L; BOD percent removal 87.0 percent, which meets the 85 percent requirement.
    Influent BOD sums by week: 210 + 225 + 216 = 651; 220 + 208 + 214 = 642; 96 + 84 + 102 = 282; 150 + 162 + 174 = 486. Total 651 + 642 + 282 + 486 = 2,061. 2,061 / 12 = 171.75, which rounds to 171.8 mg/L. Percent removal = (171.8 - 22.3) / 171.8 x 100 = 149.5 / 171.8 x 100 = 87.0 percent. Using the unrounded averages, (171.75 - 22.33) / 171.75 x 100 also gives 87.0 percent.

  6. Answer: 30-day average influent TSS 168.8 mg/L; TSS percent removal 83.7 percent, which fails the 85 percent requirement by 1.3 percentage points.
    Influent TSS sums by week: 228 + 240 + 234 = 702; 236 + 222 + 230 = 688; 88 + 76 + 94 = 258; 120 + 132 + 126 = 378. Total 702 + 688 + 258 + 378 = 2,026. 2,026 / 12 = 168.83, which rounds to 168.8 mg/L. Percent removal = (168.8 - 27.5) / 168.8 x 100 = 141.3 / 168.8 x 100 = 83.7 percent. 85.0 - 83.7 = 1.3 percentage points short. The plant fails a TSS requirement in a month when every TSS concentration result passed.

  7. Answer: 183.3 mg/L.
    Set (I - 27.5) / I = 0.85. Then I - 27.5 = 0.85I, so 0.15I = 27.5 and I = 27.5 / 0.15 = 183.33, which rounds to 183.3 mg/L. The actual average of 168.8 mg/L was 14.5 mg/L lower than this, mostly because of the dilute week 3 samples (76 to 94 mg/L).

  8. Answer: Week 1: 94.0 percent; week 3: 50.0 percent.
    Week 1 average influent BOD = 651 / 3 = 217.0 mg/L, so (217.0 - 13.0) / 217.0 x 100 = 204 / 217 x 100 = 94.0 percent. Week 3 average influent BOD = 282 / 3 = 94.0 mg/L, so (94.0 - 47.0) / 94.0 x 100 = 47 / 94 x 100 = 50.0 percent. Influent reason: groundwater and stormwater entering the sewers diluted the sewage, so the influent concentration fell to 84 to 102 mg/L, at or below the bottom of the typical 100 to 300 mg/L range, and the same effluent concentration would represent a smaller percent removed. Process reason: flow rose to about 2.4 to 2.7 times the week 1 average of 7,500 m³/day, so water spent much less time in the aeration basin for microbes to consume organic matter and moved through the clarifiers faster, carrying out solids that contain BOD. Full credit requires one reason of each kind.

  9. Answer: February 4: 1,710.0 kg/day; February 18: 1,680.0 kg/day.
    February 4: 225 x 7,600 / 1,000 = 1,710.0 kg/day. February 18: 84 x 20,000 / 1,000 = 1,680.0 kg/day. The two loads differ by less than 2 percent, so the town produced about the same mass of organic waste on both days. Almost all of the extra flow on February 18 was clean or nearly clean water, such as groundwater leaking into cracked pipes and snowmelt or rain entering through roof drains, sump pumps and manholes, which raised the volume and diluted the sewage without adding much BOD.

  10. Answer: February 4: 106.4 kg/day; February 18: 940.0 kg/day; about 8.8 times larger.
    February 4: 14 x 7,600 / 1,000 = 106.4 kg/day. February 18: 47 x 20,000 / 1,000 = 940.0 kg/day. 940.0 / 106.4 = 8.83, about 8.8 times. The influent load barely changed (item 9), yet the load reaching the creek rose almost ninefold, because the plant removed a much smaller share of it.

  11. Answer: February 4: 3.9 mg/L; February 18: 9.1 mg/L.
    Mixed concentration = (creek load + effluent load) / (creek flow + plant flow). February 4: (40,000 x 2.0 + 7,600 x 14) / (40,000 + 7,600) = (80,000 + 106,400) / 47,600 = 186,400 / 47,600 = 3.92, which rounds to 3.9 mg/L. February 18: (150,000 x 4.0 + 20,000 x 47) / (150,000 + 20,000) = (600,000 + 940,000) / 170,000 = 1,540,000 / 170,000 = 9.06, which rounds to 9.1 mg/L. Students who work in kg/day get the same result: on February 18 the creek carries 150,000 x 4.0 / 1,000 = 600.0 kg/day, and (600.0 + 940.0) x 1,000 / 170,000 = 9.06 mg/L.

  12. Answer: The February 18 discharge more than doubles the oxygen demand in the creek, which could pull dissolved oxygen down downstream; cold water and high creek flow limit the harm in February, while warm, low-flow summer conditions would make it worse.
    As microbes consume the 9.1 mg/L of BOD over the following days, they use dissolved oxygen that fish and invertebrates need, compared with 3.9 mg/L of demand on February 4. If dissolved oxygen falls below 5 mg/L, many fish species are stressed or move away, and sensitive invertebrates can be lost from that reach. Conditions that reduce the effect in February: cold water holds more oxygen to begin with, microbes break down organic matter more slowly in cold water, and the high storm flow moves and mixes the water quickly, which spreads the demand over a longer reach. Conditions that would make it worse in late summer: warm water holds less oxygen, microbes work faster so the oxygen drop is sharper and closer to the outfall, and low creek flow provides less dilution. Accept any one well-reasoned condition for each season.

  13. Answer: 30-day average effluent TSS 22.0 mg/L; TSS percent removal 87.0 percent; the plant would have passed.
    New week 3 effluent TSS sum = 20 + 20 + 20 = 60. Monthly sum = 60 + 60 + 60 + 84 = 264, and 264 / 12 = 22.0 mg/L. The influent is unchanged at 168.8 mg/L, so percent removal = (168.8 - 22.0) / 168.8 x 100 = 146.8 / 168.8 x 100 = 87.0 percent, above 85 percent. Lower effluent TSS from steadier treatment is enough to offset the diluted influent in this month.

  14. Answer: A strong recommendation explains that the basin mainly fixes the treatment-time problem behind the week 3 failures, while the inflow and infiltration program attacks their shared cause, the extra water, and is the better long-term protection for Larrow Creek; a basin can be justified as a near-term step.
    Score on four points. (a) Equalization basin: it addresses the week 3 BOD 7-day violation (47.0 against 45 mg/L) by keeping flow through the plant steady, and item 13 shows it would also lift TSS removal from 83.7 to 87.0 percent; trade-off: construction cost, land, and the need to clean and aerate stored sewage, and it does not stop the dilute influent (week 3 influent BOD 84 to 102 mg/L) from reaching the plant. (b) Inflow and infiltration program: it reduces the extra water itself, which addresses both the dilution behind the 83.7 percent TSS removal and the peak flows (up to 20,000 m³/day against about 7,500 m³/day) that cut treatment time; trade-off: the work is spread across many pipes and private properties, it takes years, and results are hard to guarantee. (c) Long-term creek protection: the item 9 and 10 loads show the town's waste load stayed near 1,700 kg/day while the load to the creek rose to 940.0 kg/day, so keeping storm water out of the sewers prevents the high-flow condition that let that load through. (d) Clear, plain prose of 5 to 7 sentences. Accept a recommendation for the basin if it is supported with the data and acknowledges that dilution remains.

Differentiation

Support

Give students a blank summary grid with rows for weeks 1 to 4 and the month, and columns for influent BOD, effluent BOD, influent TSS and effluent TSS averages, so items 1 to 6 become filling in and checking one table. Work week 1 BOD together as a class before students continue, and provide the rearranged form I = E / (1 - 0.85) for item 7.

Extension

Have students calculate the BOD percent removal for each of the twelve sample days, average those twelve percentages, and compare the result with the 87.0 percent from item 5. They should explain why the two methods give different answers (the daily percentages average about 81.8 percent) and why a rule based on average concentrations gives more weight to the dry-weather days, whose influent was more concentrated and whose removal was higher. Students can also estimate the monthly mass of BOD discharged to Larrow Creek, stating the assumption they use for days that were not sampled.

ELL supports

Pre-teach "influent," "effluent," "average," "limit," "load," and "inflow and infiltration" with a labeled sketch of a sewer pipe with cracks and a roof drain feeding a plant, and the plant feeding a creek. Provide sentence frames for items 3, 9 and 14, such as "The plant met the ___ limit because ___" and "Option ___ addresses ___ because the data show ___." Allow item 12 to be answered as a labeled diagram with short captions.