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Worksheet Grade 10 Science

Stonehaven Wellfield and Ledger Creek: Testing Two Explanations

A grade 10 science worksheet where students weigh monitoring-well and stream gauge records to decide whether a fictional town's wellfield or a drought drained a creek.

Objectives

  1. Students will map the cone of depression around a wellfield from monitoring-well records and extend the pattern outward.
  2. Students will compare a stream reach's gain and loss above and below a wellfield to determine which way water moves between channel and aquifer.
  3. Students will separate a drought signal from a pumping signal using a control stream in an unpumped valley.

Vocabulary

Cone of depression
A cone of depression is the dip in the water table that forms in a circle around a well while it is pumping, like a shallow bowl scooped out of the underground water surface. The harder a well pumps, the wider and deeper this dip becomes.
Drawdown
Drawdown is how far the water level in a well drops when a pump pulls water out. The harder and longer you pump, the bigger the drawdown gets.

Also: gaining reach, losing reach, specific capacity, control site

Teacher overview

Stonehaven is a fictional town whose Ashgate wellfield pumps from a sand-and-gravel aquifer, with its wells set 300 feet from Ledger Creek. During one dry August the creek ran lower than the town had ever recorded, and two explanations were offered for it. The first was that the wellfield had begun taking water the creek would otherwise have received. The second was that the summer's poor rainfall had lowered every stream in the county. Both explanations predict a smaller creek, so neither can be settled by looking at the creek by itself. This worksheet hands students the records that do separate them: drawdown at three monitoring wells set at increasing distances, gauge readings above and below the wellfield in two different years, and a second stream draining a comparable valley that has no wells in it. Students rule out a clogged well screen before turning to the stream gauges, then state what a two-week shutdown ought to show if their diagnosis holds.

Stonehaven Wellfield and Ledger Creek: Testing Two Explanations — Grade 10 Science
Name: ____________________________ Date: ______________

Student Worksheet

Stonehaven is a fictional town, and every reading below belongs to that scenario. Its Ashgate wellfield pumps 620 gallons per minute without stopping through the summer. Melbury Brook, four miles away, drains a valley of similar size and soil that has no wells in it, so the town gauges it as a control.

Two explanations are on the table:

  • The pumping explanation. The wellfield lowers the water table beside the channel far enough that groundwater which used to seep into Ledger Creek stays in the aquifer, and the creek may even begin draining downward.
  • The drought explanation. Rainfall was well below normal, so every stream in the county carries less water, Ledger Creek included.

Monitoring wells, depth to water below the ground surface:

Monitoring well Distance from the wellfield Before pumping began After 60 days of pumping
MW-1 300 feet 22.0 feet 27.6 feet
MW-2 900 feet 21.4 feet 24.2 feet
MW-3 2,700 feet 20.8 feet 22.2 feet

Stream gauge readings, both taken in the last week of August:

Gauge Last August, before the wellfield opened This August, wellfield pumping
Gauge A, Ledger Creek one mile above the wellfield 4.60 cfs 3.91 cfs
Gauge B, Ledger Creek half a mile below the wellfield 5.30 cfs 3.20 cfs
Melbury Brook, control valley with no wells 2.40 cfs 2.04 cfs

Use 1 cubic foot per second = 448.8 gallons per minute.

  1. MW-1 sits 300 feet from the wellfield. Its depth to water was 22.0 feet before pumping began and 27.6 feet after 60 days of pumping. Find the drawdown at MW-1.

  2. MW-2, 900 feet out, went from 21.4 feet to 24.2 feet over the same 60 days, and MW-3, 2,700 feet out, went from 20.8 feet to 22.2 feet. Find both drawdowns. Each of these wells stands three times as far from the wellfield as the one before it, so if the pattern continues, what drawdown would you expect at a well 8,100 feet out?

  3. Describe the shape of the water table from the wellfield outward that these three drawdowns imply, and explain why that shape matters for a creek only 300 feet from the wellfield.

  4. A clogged well screen would also cut what a well delivers, so rule that out first. Two years ago the production well delivered 640 gallons per minute at 32 feet of drawdown. This August it delivered 620 gallons per minute at 31 feet of drawdown. Specific capacity is the pumping rate divided by the drawdown. Find this August's specific capacity, then say whether the screen has clogged.

  5. Last August, before the wellfield opened, Gauge A above the wellfield read 4.60 cfs and Gauge B below it read 5.30 cfs. How much flow did the creek gain between the two gauges, and what does that tell you about which way water was moving between the aquifer and the channel?

  6. This August, with the wellfield running, Gauge A read 3.91 cfs and Gauge B read 3.20 cfs. How much flow did the creek lose between the two gauges?

  7. Melbury Brook, in the control valley with no wells, fell from 2.40 cfs last August to 2.04 cfs this August. What percent of its flow did it lose?

  8. Gauge A sits a mile above the wellfield, outside the steep inner part of the cone, so its reading tracks the weather rather than the pumping. It fell from 4.60 cfs last August to 3.91 cfs this August. What percent of its flow did it lose, and how does that compare with Melbury Brook?

  9. Suppose the drought were responsible for the whole change. Gauge B read 5.30 cfs last August. If it fell by the same 15 percent that Melbury Brook and Gauge A fell, what would Gauge B read this August? Round to the nearest hundredth.

  10. Gauge B actually read 3.20 cfs this August. How much lower is that than the drought-only figure you predicted in item 9?

  11. The wellfield pumps 620 gallons per minute, and 1 cubic foot per second equals 448.8 gallons per minute. Convert the pumping rate to cubic feet per second, then compare it with the shortfall you found in item 10.

  12. State which of the two explanations the evidence supports, and name the two measurements that would have come out differently had the other explanation been the right one.

  13. The town council proposes shutting the wellfield down for two weeks in the middle of the dry season while the stream gauges and the monitoring wells keep recording. State what the pumping explanation predicts for Gauge B and for MW-1 over those two weeks, what the drought explanation predicts, and which result would show the diagnosis to be wrong.

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: 5.6 feet.
    Drawdown is the drop in water level a well causes, so subtract the earlier reading from the later one: 27.6 feet minus 22.0 feet gives 5.6 feet at MW-1, the closest of the three wells to the wellfield.

  2. Answer: 0.7 feet.
    At MW-2, subtracting 21.4 from 24.2 gives 2.8 feet. At MW-3, subtracting 20.8 from 22.2 gives 1.4 feet. Drawdown falls by about half with each tripling of distance, from 5.6 to 2.8 to 1.4 feet, so a well at 8,100 feet would be expected to show roughly 0.7 feet.

  3. Answer: A cone of depression.
    The water table is pulled down hardest at the wellfield and climbs back toward its original elevation with distance, giving a broad cone-shaped hollow centered on the pumps. Because the creek runs only 300 feet away, it lies inside the steep inner part of that cone, where the water table has dropped at least the 5.6 feet measured at MW-1. Once the water table beside the channel drops below the streambed, groundwater can no longer seep into the creek, and creek water can begin draining downward instead.

  4. Answer: 20.0 gallons per minute per foot.
    Dividing 620 by 31 gives 20.0 gallons per minute for each foot of drawdown this August. Dividing 640 by 32 gives the same 20.0 for two years ago. The well still delivers exactly as much water per foot of drawdown as it did before, so a clogged screen does not explain the change and the cause lies outside the well.

  5. Answer: 0.70 cfs gained.
    Subtracting 4.60 from 5.30 gives 0.70 cubic feet per second more water leaving the reach than entering it. Water was seeping out of the aquifer and into the channel along that stretch, which is what a groundwater-fed creek looks like in late summer.

  6. Answer: 0.71 cfs lost.
    Subtracting 3.20 from 3.91 gives 0.71 cubic feet per second. Less water now leaves the reach than enters it, so the direction of seepage has reversed and the channel is losing water to the aquifer.

  7. Answer: 15.0 percent.
    Subtracting 2.04 from 2.40 gives a loss of 0.36 cubic feet per second, and dividing 0.36 by 2.40 gives 0.150, or 15.0 percent. Because no wells pump in this valley, that figure measures the drought on its own.

  8. Answer: 15.0 percent.
    Subtracting 3.91 from 4.60 gives 0.69, and dividing 0.69 by 4.60 gives 0.150, or 15.0 percent. The reach above the wellfield lost the same share Melbury Brook lost, which is what a drought acting alone would produce.

  9. Answer: 4.51 cfs.
    Multiplying 5.30 by 0.85 gives 4.505, which rounds to 4.51 cubic feet per second. That is the reading Gauge B would show if the drought were the whole story.

  10. Answer: 1.31 cfs.
    Subtracting 3.20 from 4.51 gives 1.31 cubic feet per second missing from the reach below the wellfield, over and above what the drought accounts for.

  11. Answer: 1.38 cfs.
    Dividing 620 by 448.8 gives 1.381, or about 1.38 cubic feet per second. The shortfall of 1.31 from item 10 is roughly 95 percent of that, so nearly all the water the wellfield pumps is water the creek no longer carries.

  12. Answer: The wellfield is taking water from the creek.
    Two measurements separate the explanations. First, the reach beside the wellfield switched from gaining 0.70 cubic feet per second to losing 0.71, and a dry summer of this size, which took only 15.0 percent off the unpumped control brook, would shrink a gaining reach rather than turn it into a losing one. Second, the control brook and the upstream gauge both fell 15.0 percent, which fixes the drought's effect at about 15 percent, while Gauge B fell far more than that. Had the drought explanation been right, Gauge B would have read near 4.51 cubic feet per second and the reach would still have been gaining.

  13. Answer: Gauge B rises and MW-1 recovers.
    Under the pumping explanation, stopping the pumps lets the water table around MW-1 climb back toward its original 22.0 feet and returns the reach to gaining water, so Gauge B should rise back above Gauge A within days. Under the drought explanation, MW-1 would still recover once the pumps stop, yet the creek would not respond, since the rainfall deficit is untouched by the pumps, so Gauge B would stay below Gauge A and both gauges would go on falling together. If MW-1 recovered toward 22.0 feet while Gauge B stayed below Gauge A through two weeks with no pumping, the diagnosis would be wrong and the drought explanation would stand.

Differentiation

Support

Give students the three drawdowns in the fictional Stonehaven records already computed, 5.6, 2.8, and 1.4 feet, so they can begin at the pattern in item 2 rather than at the subtraction. Work item 5 through as a class on a cross-section drawing, adding arrows that show water moving from the aquifer into the channel. A two-column organizer headed "what the drought explains" and "what the drought does not explain" helps students hold the two accounts apart as the evidence accumulates.

Extension

Have students find what Gauge B would have read this August if the fictional Ashgate wellfield had run at half its rate, 310 gallons per minute, assuming the depletion stays proportional to the pumping rate. Ask them to use that result to judge a proposal to alternate the wellfield on and off week by week, and to say what the monitoring wells would have to show for the proposal to be working.

ELL supports

Pre-teach "gaining reach" and "losing reach" with one cross-section of a channel and water table drawn twice, the seepage arrows reversed between the two drawings. Provide the two explanations from this fictional scenario as short labeled cards students can set beside each piece of evidence as they work, and allow items 3, 12, and 13 to be answered with a labeled sketch plus a phrase rather than full sentences.