Worksheet Grade 12 Math

Ridgemoor Well Field: Drawdown, Specific Capacity, and Storage

A grade 12 worksheet on a fictional well field: drawdown, specific capacity, and density reasoning for water stored per square foot and per acre of aquifer.

Grade: Grade 12
Subject: Math
Material: Worksheet
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HSG-MG.A.2 Common Core Math

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

How this material aligns: Items 5, 6, and 7 apply density based on volume and area, computing gallons of water held per cubic foot, per square foot, and per acre of a porous aquifer, the modeling use of density this standard describes.

All materials for HSG-MG.A.2 →

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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 well drawdown and specific capacity from field readings.
Students will use porosity as a density to find water stored per unit of aquifer.
Students will scale a per-area storage figure up to the volume held beneath one acre.

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.
Porosity: Porosity measures how much empty space a rock or soil has between its grains, which tells you how much water it can hold. A sponge has high porosity, while a piece of glass has almost none.
Aquifer: An aquifer is an underground layer of rock, sand, or gravel that holds water in the tiny spaces between its grains. Wells reach down into aquifers to bring water up to the surface.
Acre-foot: The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: static water level, specific capacity

Teacher overview

The fictional Ridgemoor well field draws from a sand aquifer, and its operators track how far the water level drops when a well pumps and how much water the ground actually holds. This worksheet builds from a single well's drawdown up to the volume of water stored beneath an acre of the aquifer, treating porosity as a density: the share of each cubic foot of sand that is water. A common error at this grade is multiplying the full aquifer volume by 7.48 gallons per cubic foot while forgetting that only the pore space, not the solid sand, holds water.

Ridgemoor Well Field: Drawdown, Specific Capacity, and Storage — Grade 12 Math

Name: ____________________________ Date: ______________

Student Worksheet

All values below describe the fictional Ridgemoor well field. One well has a static water level (not pumping) of 60 ft below ground. While it pumps at 350 gpm, the water level falls to a pumping level of 118 ft below ground. The well is 200 ft deep with a 12-inch (1.0 ft) diameter casing. The sand aquifer is 30 ft thick with a porosity of 25 percent. Use: cylinder volume (cu ft) = 0.785 × diameter² × length; 1 cu ft = 7.48 gallons; 1 acre = 43,560 sq ft; 1 acre-foot = 325,851 gallons.

Find the well's drawdown, where drawdown = pumping level − static level.
Find the well's specific capacity in gpm per foot of drawdown, where specific capacity = pumping rate ÷ drawdown. Round to the nearest tenth.
Find the volume of one foot of the casing in cubic feet, then convert it to gallons per foot of casing. This is the casing's water density along its length.
While pumping, water still stands in the casing from the pumping level down to the well bottom. Find that standing column's length and its volume in gallons.
Treat porosity as a density: how many gallons of water does one cubic foot of this aquifer sand hold?
Find the gallons of water stored under each square foot of land above the aquifer, using the 30-foot thickness and 25 percent porosity.
Scale item 6 up to one full acre. Find the gallons of water stored beneath one acre of the aquifer, and confirm it using the acre-foot method.
The well pumps 350 gpm for 18 hours a day. Find the daily volume pumped, then find what percent of the one-acre stored water (item 7) that daily draw represents. Round the percent to the nearest tenth.
Over ten years, the well's specific capacity falls from about 6.0 to about 4.0 gpm per foot at the same pumping rate. Explain in one or two sentences what that decline tells the operator about the well or the aquifer.

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: 58 ft.
Drawdown = 118 ft − 60 ft = 58 ft. The pumping level is the deeper of the two, so the water dropped 58 feet under pumping.
Answer: 6.0 gpm/ft.
Specific capacity = 350 gpm ÷ 58 ft = 6.03 gpm per foot, which rounds to 6.0 gpm/ft. Each foot of drawdown buys about six gallons per minute of yield.
Answer: 5.87 gal/ft.
One foot of casing = 0.785 × 1.0² × 1 = 0.785 cu ft. In gallons: 0.785 cu ft × 7.48 gal/cu ft = 5.87 gallons per foot of casing.
Answer: 481 gal.
Standing column = well depth − pumping level = 200 − 118 = 82 ft. Volume = 82 ft × 5.87 gal/ft = 481.3 gallons, or about 481 gallons held in the casing.
Answer: 1.87 gal.
Each cubic foot of sand is 25 percent water: 0.25 cu ft of water × 7.48 gal/cu ft = 1.87 gallons of water per cubic foot of aquifer.
Answer: 56.1 gal.
Under one square foot, the water column is 30 ft × 0.25 = 7.5 cu ft of water. In gallons: 7.5 × 7.48 = 56.1 gallons per square foot of land.
Answer: 2,443,883 gal.
Acre-foot method: 30 ft × 0.25 porosity = 7.5 acre-feet of water per acre. 7.5 acre-feet × 325,851 gal/acre-foot = 2,443,883 gallons. The per-square-foot check gives 56.1 gal × 43,560 sq ft ≈ 2,444,000 gallons, matching within rounding.
Answer: 15.5 percent.
Daily draw = 350 gpm × 60 min × 18 hr = 378,000 gallons. As a share of the acre's stored water: 378,000 ÷ 2,443,883 = 0.1547, or about 15.5 percent. Drawing 15.5 percent of an acre's stored water each day only works if recharge and the surrounding aquifer keep refilling that acre.
Answer: the well or aquifer is losing yield.
A specific capacity falling from 6.0 to 4.0 gpm per foot means each foot of drawdown now yields less water, so the same pumping rate forces the level deeper. That usually points to a clogging or corroding well screen, or to a declining aquifer, and calls for well rehabilitation or reduced pumping.

Differentiation

Support

Provide a labeled well cross-section showing static level, pumping level, well bottom, and the aquifer band, and pre-compute the drawdown in item 1 so students can focus on the density steps. Supply the conversions on a reference card.

Extension

Ask students to find how many acres of this aquifer would need to be within the well's reach to hold enough stored water to supply a steady 350 gallons per minute for a full year, assuming no recharge. Have them state clearly which assumption in that estimate is least realistic and why.

ELL supports

Pre-teach "static," "drawdown," "porosity," and "specific capacity" with a diagram and a home-language gloss where possible. Provide a filled-in example of the density idea (one cubic foot of sand holding part water, part solid) before item 5, and give sentence frames for the written answer in item 9.