Water for Schools
Menu

Worksheet Grade 11 Science

Barrowgate Water Mains: Testing a Sediment Scour Threshold

A grade 11 worksheet testing a utility's proportional flushing model against turbidity results from eight main segments, then planning a controlled follow-up trial.

Objectives

  1. Students will decide whether a proportional model is consistent with turbidity results from eight flushing trials.
  2. Students will explain how the balance of forces on a settled particle produces a scour threshold rather than a steady increase.
  3. Students will identify a confounded variable and plan a second round of trials that controls it.

Vocabulary

Turbidity
Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.

Also: unidirectional flushing, scour threshold, resuspension, confounded variable, observational study

Teacher overview

Water leaving a treatment plant still carries a small amount of fine material, and inside a buried pipe that material settles wherever the water moves slowly. In the fictional town of Barrowgate the source is a well field with naturally high iron, so iron oxide particles that slip past the filters drift to the bottom of the pipe and build up over years. Customers notice nothing until demand rises and the water speeds up, at which point the deposits lift and taps run brown. Utilities manage the problem with unidirectional flushing, closing valves so that water can travel only one way and then opening a single hydrant, which scours one segment at a known velocity.

The question this worksheet puts to students is how much material a given velocity actually removes. One reasonable guess is that the relationship is proportional, so that doubling the velocity roughly doubles the sediment carried out and the ratio of discharge turbidity to velocity stays about the same from segment to segment. Sediment transport usually does not behave that way. A settled particle stays where it is until drag from the passing water exceeds its weight and its grip on the deposit beneath it, so very little moves below a threshold velocity and a great deal moves above it. Students weigh the proportional model against eight flushing results and decide which description the measurements support.

Two difficulties are worth anticipating. The first is that students often read the highest turbidity as evidence of the worst pipe, when a turbidity reading taken in the flush discharge records what came out of the segment rather than what remains in it, which makes a high reading the mark of a successful flush. The second is the design of the trials themselves, because the Barrowgate crew worked down the map in order and the segments that happened to receive the highest velocities were also the ones that had gone longest without flushing.

Barrowgate Water Mains: Testing a Sediment Scour Threshold — Grade 11 Science
Name: ____________________________ Date: ______________

Student Worksheet

Barrowgate is a fictional town of about 9,000 people served by 8-inch cast-iron pipe. Over one week its crew flushed eight segments, one at a time. For each segment the crew opened a single hydrant, held a steady discharge velocity for six minutes, and recorded the highest turbidity the field meter reached during the flush. Turbidity is reported in nephelometric turbidity units, or NTU, and a higher reading means more sediment left the pipe. The crew also noted how many years had passed since each segment was last flushed.

Segment Flushing velocity (feet per second) Highest discharge turbidity (NTU) Years since last flushed
A 1.0 4 2
B 1.5 5 2
C 2.0 6 3
D 2.5 28 3
E 3.0 45 5
F 3.5 58 5
G 4.0 66 8
H 4.5 71 8
  1. Segment A was flushed at 1.0 foot per second and its discharge reached 4 NTU, which sets a ratio of 4 NTU for every foot per second. Using that ratio, predict the turbidity for segment H, which was flushed at 4.5 feet per second.
  2. Segment H actually reached 71 NTU. Divide that measurement by the 18 NTU the proportional ratio predicts, and state how many times larger the measurement is.
  3. Segment C was flushed at 2.0 feet per second and reached 6 NTU. Calculate its ratio of turbidity to velocity, in NTU per foot per second.
  4. Segment E was flushed at 3.0 feet per second and reached 45 NTU. Calculate the same ratio for segment E, then state whether it agrees with segment C's ratio of 3 NTU per foot per second.
  5. Segments C and D had both gone 3 years since their last flush. Segment C ran at 2.0 feet per second and reached 6 NTU, while segment D ran at 2.5 feet per second and reached 28 NTU. Calculate the increase in turbidity between them.
  6. Readings rise only from 4 NTU to 6 NTU as velocity goes from 1.0 to 2.0 feet per second, then rise from 6 NTU to 28 NTU as velocity goes from 2.0 to 2.5 feet per second. Give the lowest tested velocity at which the discharge turbidity jumps sharply.
  7. Explain why a settled particle stays on the bottom of a pipe at 2.0 feet per second and lifts at 2.5 feet per second. Name the force that grows with velocity, and name the two things that hold the particle in place.
  8. The crew did not assign the velocities at random; it chose a velocity for each segment as it worked down the map. State whether these eight trials were an experiment or an observational study, and explain the difference that random assignment would have made.
  9. Segments A and B had gone 2 years since their last flush and ran at the two lowest velocities, while segments G and H had gone 8 years and ran at the two highest. Explain why that pattern weakens the readings from G and H as evidence about velocity, and explain why the comparison between segments C and D is stronger.
  10. Design a second round of trials that would separate the effect of velocity from the effect of years since flushing. State the variable that must be held constant, how many velocities you would test, and how you would assign them to segments.

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: 18 NTU.
    Segment A of the fictional Barrowgate flushing log gives 4 NTU divided by 1.0 foot per second, or 4 NTU for each foot per second. Applying that ratio to segment H gives 4 x 4.5 = 18 NTU.
  2. Answer: about 3.9 times.
    71 divided by 18 is 3.94, so the measurement is roughly 3.9 times the predicted value. A model that misses by this much at the top of the tested range is not describing the process well.
  3. Answer: 3 NTU per foot per second.
    6 NTU divided by 2.0 feet per second gives 3 NTU per foot per second.
  4. Answer: 15 NTU per foot per second.
    45 NTU divided by 3.0 feet per second gives 15 NTU per foot per second, which is five times segment C's ratio. Under a proportional model the two ratios would agree, so the model does not hold across the range the crew tested.
  5. Answer: 22 NTU.
    28 NTU minus 6 NTU is 22 NTU. Velocity rose only 0.5 feet per second between these two segments, while the larger rise of 1.0 foot per second from segment A to segment C changed the reading by just 2 NTU.
  6. Answer: 2.5 feet per second.
    Readings stay between 4 and 6 NTU at 1.0, 1.5, and 2.0 feet per second, then reach 28 NTU at 2.5 feet per second. The lowest tested velocity that produces a sharp rise is therefore 2.5 feet per second, which places the threshold above 2.0 and at or below 2.5 feet per second.
  7. Answer: Drag from the moving water grows until it overcomes the particle's weight and its grip on the deposit.
    Faster water pulls harder on the surface of a deposit, and that pull is the force that grows with velocity. Holding the particle in place are its own weight, which presses it down, and the cohesion between it and the packed material around it. Below the threshold the pull is too small to break either hold, so the deposit stays put and the discharge runs nearly clear. Once the pull exceeds both, whole patches of deposit release at once, which is why the readings jump rather than climb steadily.
  8. Answer: An observational study.
    The crew recorded the velocity it happened to use on each segment rather than assigning velocities, so the trials describe what occurred without imposing a treatment. Random assignment would have broken the link between the velocity a segment received and any other property that segment carried, such as its age or its flushing history, which would allow the differences in turbidity to be credited to velocity.
  9. Answer: Velocity and years since flushing rise together across the table, so the C and D pair, which shares a flushing age and straddles the jump, isolates velocity best.
    In segments G and H the highest velocities arrived at the segments with the longest accumulation, so a reader cannot tell whether 66 and 71 NTU reflect the faster water or the eight years of settled material. Segments C and D had gone the same 3 years since flushing, so the amount available to lift was similar and velocity is the variable that differs, which makes their 22 NTU gap the cleanest evidence in the table for a threshold.
  10. Answer: Hold years since flushing constant and assign the velocities at random.
    A workable plan selects segments that were all last flushed in the same year, chooses four or five velocities spanning roughly 1.5 to 3.5 feet per second so that the suspected threshold near 2.5 sits inside the range, and assigns those velocities to segments by drawing lots rather than by position on the map. Repeating each velocity on more than one segment would also let students see how much two segments treated alike still differ.

Differentiation

Support

Give students the ratio column for the fictional Barrowgate table already worked out, so that items 3 and 4 become a comparison of 3 against 15 NTU per foot per second rather than two divisions. For items 7 through 10, supply a two-column organizer headed "what the reading shows" and "what else could explain it," and let students fill the second column with phrases before writing.

Extension

Have students plot discharge turbidity against flushing velocity for the eight Barrowgate segments, draw the straight line through the origin that segment A's ratio predicts, and mark how far each point sits from that line. Ask them to describe in one sentence what the pattern of those gaps shows about where the proportional model breaks down, and to state what the readings below 2.5 feet per second imply about how much material a slow flush actually removes.

ELL supports

Pre-teach "flushing," "turbidity," "sediment," "threshold," and "confounded" using a labeled cutaway drawing of a Barrowgate pipe that shows a deposit along the bottom and an arrow for the moving water. Provide a sentence frame for items 8 through 10: "The reading for segment ___ could also be explained by ___, so the crew should ___." Short phrases are acceptable in place of full paragraphs on those items.