Math problem set Grade 7 Math
Greystile's Three New Wells: A Grade 7 Drawdown Problem Set
A grade 7 problem set where students find drawdown and specific capacity for a fictional town's three wells, then size the pumping day around a demand figure.
Objectives
- Students will compute drawdown as the difference between two water levels.
- Students will compute specific capacity as gallons per minute for each foot of drawdown.
- Students will find how many hours three wells need to meet a stated daily demand.
Vocabulary
- 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: static water level, pumping water level, specific capacity, yield
Teacher overview
When a pump starts, the water in a well drops from its resting height to a lower working height, and the difference between those two heights is called the drawdown. Dividing a well's yield by its drawdown gives its specific capacity, the number of gallons per minute the well delivers for each foot the water falls, and a driller uses that number to compare wells that were finished in different rock. This set follows three new wells at the fictional town of Greystile and ends by sizing the town's pumping day. The predictable error is dividing the yield by the pumping water level: a student who computes 180 divided by 66 reports about 2.7, when the drawdown of 24 feet gives the correct 7.5.
Problems
Greystile is a fictional town that drilled three new wells. The table below lists each well's static water level, its pumping water level, and its yield. All depths are measured down from the ground surface.
| Well | Static water level (feet) | Pumping water level (feet) | Yield (gallons per minute) |
|---|---|---|---|
| A | 42 | 66 | 180 |
| B | 38 | 78 | 220 |
| C | 45 | 61 | 140 |
- What is Well A's drawdown, in feet?
- What is Well A's specific capacity, in gallons per minute for each foot of drawdown?
- Greystile tests Well A again at a slower pump speed. It yields 120 gallons per minute with a drawdown of 16 feet. What is Well A's specific capacity in this second test?
- What is Well B's specific capacity, in gallons per minute for each foot of drawdown?
- What is Well C's specific capacity, in gallons per minute for each foot of drawdown?
- Which well delivers the most water for each foot of drawdown?
- If all three wells run at the same time, what is their combined yield in gallons per minute?
- Greystile needs 648,000 gallons on a summer day. Running all three wells together, how many hours of pumping does that take?
- The town wants to meet the same 648,000-gallon demand in 16 hours instead. What combined yield would that take, in gallons per minute?
- How many more gallons per minute is your answer to problem 9 than the combined yield you found in problem 7?
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: 24 feet.
Drawdown is the pumping water level minus the static water level. For Well A, 66 minus 42 equals 24 feet. - Answer: 7.5 gallons per minute per foot.
Divide the yield by the drawdown: 180 divided by 24 equals 7.5 gallons per minute for each foot of drawdown. - Answer: 7.5 gallons per minute per foot.
Divide 120 by 16 to get 7.5. The second test gives the same constant as the first, so Well A's yield and drawdown are proportional over this range. - Answer: 5.5 gallons per minute per foot.
Well B's drawdown is 78 minus 38, or 40 feet. Then 220 divided by 40 equals 5.5. - Answer: 8.75 gallons per minute per foot.
Well C's drawdown is 61 minus 45, or 16 feet. Then 140 divided by 16 equals 8.75. - Answer: Well C.
Its specific capacity of 8.75 is larger than Well A's 7.5 and Well B's 5.5, even though Well C has the smallest yield of the three. - Answer: 540 gallons per minute.
Add the three yields: 180 plus 220 plus 140 equals 540 gallons per minute. - Answer: 20 hours.
First convert the combined yield to gallons per hour: 540 times 60 equals 32,400 gallons per hour. Then divide the demand by that rate: 648,000 divided by 32,400 equals 20 hours. - Answer: 675 gallons per minute.
Divide the demand by the hours: 648,000 divided by 16 equals 40,500 gallons per hour. Then divide by 60 minutes: 40,500 divided by 60 equals 675 gallons per minute. - Answer: 135 gallons per minute.
Subtract the two combined rates: 675 minus 540 equals 135 gallons per minute.
Differentiation
Support
Give these students a well-profile sketch with the ground surface, the static water level, and the pumping water level already labeled, so the subtraction in problems 1, 4, and 5 has a picture behind it. Assign problems 1 through 7 and allow a calculator.
Extension
Ask these students to decide which single well Greystile should rebuild first if a rebuild raises that well's specific capacity by two gallons per minute for each foot of drawdown. Have them state the new yield each choice would produce at that well's current drawdown, then justify the choice in two sentences.
ELL supports
Pre-teach "static," "pumping," "drawdown," and "yield" with a two-picture card showing a well at rest and the same well with the pump running, with both water lines marked. Provide the frame "The water falls from ___ feet to ___ feet, so the drawdown is ___ feet" for problems 1, 4, and 5.