Math problem set Grade 9 Science

Pinehaven Well: Drawdown, Specific Capacity, and Safe Yield

A grade 9 problem set where students use a fictional town well's water levels to find drawdown and specific capacity, then set up equations for safe pumping yield.

Grade: Grade 9
Subject: Science
Material: Math problem set
Time: 40 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: Problems 1 through 8 carry gallons per minute, feet of drawdown, and gallons per day through specific-capacity and yield calculations, converting a per-minute pump rate to a daily total with consistent units.

All materials for HSN-Q.A.1 →

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Problems 3 and 6 create and solve one-variable equations, drawdown equals yield divided by specific capacity, to find an unknown drawdown and the maximum yield that keeps the water level safe.

All materials for HSA-CED.A.1 →

HS-ESS3-1 NGSS

Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity.

How this material aligns: Items 6 through 10 use drawdown and specific-capacity evidence to explain how much the aquifer can yield, whether that limit covers the town's daily demand, and how the cone of depression and well interference constrain pumping decisions.

All materials for HS-ESS3-1 →

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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 its static and pumping water levels.
Students will set up equations to predict drawdown at a new pump rate and find the maximum safe yield.

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.
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.

Also: static water level, pumping water level, specific capacity, well yield

Teacher overview

When a pump pulls water from a well, the water level inside the well drops. The distance it drops is the drawdown, and the well's specific capacity, its yield divided by that drawdown, tells operators how hard they can safely pump. This set follows a new municipal well drawing from the Pinehaven aquifer, a fictional groundwater source, from a first pumping test through a safe-yield decision. A common misconception is to confuse drawdown, which is a difference between two water levels, with the pumping water level itself, which is a depth measured from the ground; the problems keep the two separate on purpose.

Pinehaven Well: Drawdown, Specific Capacity, and Safe Yield — Grade 9 Science

Name: ____________________________ Date: ______________

Problems

Use these facts about the Pinehaven well in the town of Pinehaven, a fictional community, for every problem. Depths are measured downward from the ground surface, and the pump intake sits at 120 feet.

Static water level (pump off): 60 ft below the ground surface.
Pumping water level during the first test: 90 ft below the ground surface.
Well yield during that first test: 300 gpm.
Drawdown = pumping water level - static water level.
Specific capacity = well yield / drawdown.

Find the drawdown during the first pumping test, in feet.
Find the well's specific capacity, in gallons per minute per foot of drawdown.
The town wants to pump the well harder, at 450 gpm. Assuming the specific capacity stays the same, set up and solve an equation for the new drawdown in feet.
Using your answer to problem 3, find the new pumping water level, in feet below the ground surface, at the 450 gpm rate.
The pump intake sits 120 ft below the ground surface. At the 450 gpm rate, how many feet of water still stand above the pump intake?
To protect the pump, the town wants the pumping water level to stay no deeper than 110 ft. Set up and solve an equation for the maximum yield, in gpm, that keeps the water level at or above that depth.
Convert that maximum safe yield to gallons per day, assuming the well runs continuously for 24 hours.
The town's daily demand is 600,000 gallons per day. Can the well meet that demand at the safe yield, and by how many gallons is it over or under?
Explain why pumping the well faster increases the drawdown, using the idea of a cone of depression forming in the aquifer around the well.
Suppose the town drills a second identical well close to the first, and both pump at once. Explain why each well's drawdown is likely to be larger than it would be if that well pumped alone.

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: 30 ft. Drawdown = 90 ft - 60 ft = 30 ft.
Answer: 10 gpm/ft. Specific capacity = 300 gpm / 30 ft = 10 gallons per minute per foot of drawdown.
Answer: 45 ft. Set drawdown = yield / specific capacity, so drawdown = 450 gpm / 10 gpm/ft = 45 ft.
Answer: 105 ft. Pumping water level = static level + drawdown = 60 ft + 45 ft = 105 ft below the surface.
Answer: 15 ft. 120 ft - 105 ft = 15 ft of water still stands above the pump intake.
Answer: 500 gpm. The deepest allowed pumping level is 110 ft, so the maximum drawdown is 110 ft - 60 ft = 50 ft. Then yield = specific capacity x drawdown = 10 gpm/ft x 50 ft = 500 gpm.
Answer: 720,000 gpd. 500 gpm x 60 minutes/hour x 24 hours = 720,000 gallons per day.
Answer: Yes, by 120,000 gallons. 720,000 gpd - 600,000 gpd = 120,000 gallons per day of surplus.
Answer: Pumping lowers the water level right at the well, and the water table slopes down toward the well from all sides, forming a cone of depression. Pumping faster pulls water in more quickly than the aquifer can supply it near the well, so the level at the well drops further and the cone deepens, which means a larger drawdown.
Answer: The two wells share the same aquifer, so their cones of depression overlap. Each well is now drawing from water that the other well is also lowering, so the water level at each well drops more than it would from that well's pumping alone. This overlap is called well interference.

Differentiation

Support

Provide a labeled vertical diagram showing the ground surface, static water level, pumping water level, and pump intake, so students can see that drawdown is the gap between the two water levels. Give the specific-capacity value already computed for use in problems 3 and 6.

Extension

Ask students to explain how the pumping water level would change if the specific capacity actually dropped at high pumping rates, a real effect in many wells, and to discuss why assuming a constant specific capacity can make a well look safer than it is.

ELL supports

Pre-teach "static" (not moving, pump off) and "drawdown" (how far the water drops) with a two-panel picture of a well with the pump off and on. Allow students to answer problems 9 and 10 with a labeled sketch plus a short sentence.

Extensions

Have students contact their local water department or read a public well log to find the static level, pumping level, and yield of a real municipal well, then calculate its specific capacity and compare it with the Pinehaven well in this set.