Worksheet Grade 11 Math

Draycott Municipal Well: Drawdown and Specific-Capacity Worksheet

A grade 11 worksheet on a new municipal well: students find drawdown, specific capacity, an average rate of change, and a pump discharge pressure in feet of head.

Grade: Grade 11
Subject: Math
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: Calculator

Standards

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Items 1 through 4 and item 6 carry gallons per minute, feet, and psi through drawdown, specific-capacity, and head calculations, using consistent units to guide each solution as this standard requires.

All materials for HSN-Q.A.1 →

HSF-IF.B.6 Common Core Math

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

How this material aligns: Item 5 treats drawdown as a function of pumping time and has students calculate its average rate of change, in feet per hour, over the specified four-hour test interval, the interval calculation this standard names.

All materials for HSF-IF.B.6 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate a well's drawdown and specific capacity from pumping-test data.
Students will find an average rate of change and convert a pump pressure to feet of head.

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, specific capacity, feet of head

Teacher overview

The fictional town of Draycott has drilled a new municipal well and run a pumping test to see how the well behaves under load. This worksheet has students work with that test data to find the well's drawdown and specific capacity, describe how fast the water level dropped, and check the pump pressure the well delivers. These are the same numbers an engineer reviews before approving a new well for service.

Draycott Municipal Well: Drawdown and Specific-Capacity Worksheet — Grade 11 Math

Name: ____________________________ Date: ______________

Student Worksheet

Use these results from the fictional Draycott well for all items.

Static water level (no pumping): 60 feet below the ground surface.
While pumping at 350 gpm, the water level dropped to 95 feet below the ground surface.
During a 4-hour pumping test, the drawdown grew from 0 feet to 35 feet.
The pump must deliver 45 psi at the surface. Use 1 psi = 2.31 feet of head.
Distribution systems usually run between 40 and 80 psi.

Find the drawdown while pumping, using drawdown = pumping water level minus static water level.
Find the well's specific capacity, using specific capacity = pumping rate divided by drawdown. Give your answer in gpm per foot.
Suppose the town later pumps this well at 500 gpm and the specific capacity stays about 10 gpm per foot. Estimate the new drawdown.
At that 500 gpm rate, what would the new pumping water level be, in feet below the ground surface?
The drawdown grew from 0 feet to 35 feet during the 4-hour test. Find the average rate of change of drawdown, in feet per hour.
The pump must deliver 45 psi at the surface. Using 1 psi = 2.31 feet, how many feet of head does that 45 psi represent? Round to the nearest foot.
Explain why pumping the same well at a higher rate generally causes a larger drawdown.
Distribution systems usually run between 40 and 80 psi. Is the pump's 45 psi inside that normal range?

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: 35 feet. Drawdown is the pumping level minus the static level, 95 feet minus 60 feet, which is 35 feet.
Answer: 10 gpm/ft. Specific capacity is the pumping rate divided by the drawdown, 350 gpm divided by 35 feet, which is 10 gallons per minute per foot.
Answer: 50 feet. At 500 gpm with a specific capacity of about 10 gpm per foot, the drawdown is 500 divided by 10, which is 50 feet.
Answer: 110 feet. The new pumping level is the static level plus the new drawdown, 60 feet plus 50 feet, which is 110 feet below the surface.
Answer: 8.75 feet per hour. The average rate of change is the change in drawdown divided by the time, 35 feet divided by 4 hours, which is 8.75 feet per hour.
Answer: 104 feet. Multiplying 45 psi by 2.31 feet per psi gives 103.95, which rounds to 104 feet of head.
Answer: A higher pumping rate needs water to flow toward the well faster, which requires a steeper slope in the water table around the well, so the water level in the well settles lower and the drawdown is larger.
Answer: yes. The pump delivers 45 psi, which falls between 40 and 80 psi, so it is inside the normal distribution range.

Differentiation

Support

Provide the drawdown and specific-capacity formulas with labeled blanks, and give item 1's answer as a worked model so students can carry the same steps into items 2 through 4. Allow a calculator throughout.

Extension

Ask students to find the pumping rate, in gallons per minute, that would produce a 25-foot drawdown in the fictional Draycott well if the specific capacity stays at 10 gpm per foot, and to explain how they reversed the calculation.

ELL supports

Provide a labeled side-view diagram of a well showing the static level, the pumping level, and the drawdown between them. Allow students to answer item 7 with a sentence frame: "A higher rate causes more drawdown because ___."