Math problem set Grade 11 Math

Pentley Well Field: Drawdown, Specific Capacity, and Yield

A grade 11 problem set on a fictional well field: compute drawdown and specific capacity, solve for a safe pumping rate, and check the field against district demand.

Grade: Grade 11
Subject: Math
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 5 and 7 track feet, gpm, and gpm-per-foot through the drawdown, specific-capacity, and MGD-to-gpm conversions, using units to guide each step, as this standard requires.

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: Problem 4 sets up and solves a one-variable equation for the maximum pumping rate given an allowable drawdown limit, the equation creation and solving this standard names.

All materials for HSA-CED.A.1 →

Download Word file

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 compute well drawdown and specific capacity from water-level readings.
Students will solve for the maximum pumping rate that keeps water above the pump bowls.
Students will compare combined well yield against a district demand in gpm.

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, yield

Teacher overview

When a well pump runs, the water level in the well drops from its resting height to a lower pumping level, and the size of that drop tells operators how hard they can push the well. Specific capacity, the pumping rate divided by the drawdown, turns that drop into a single number for comparing wells and setting safe limits. This set has grade 11 students work with two wells in the Pentley well field, a fictional field serving the Redhill district. A common student error is to confuse the static and pumping water levels, or to forget that drawdown is the difference between them rather than the pumping level itself.

Pentley Well Field: Drawdown, Specific Capacity, and Yield — Grade 11 Math

Name: ____________________________ Date: ______________

Problems

The Pentley well field is a fictional field. Use these readings:

Well 1: static water level 40 ft below ground; pumping water level 95 ft below ground at 220 gpm.
Well 2: static water level 45 ft below ground; pumping water level 85 ft below ground at 300 gpm.
Well 1's pump bowls sit 120 ft below ground; the pumping level must stay at least 10 ft above them.
The Redhill district needs 0.8 MGD from the field. Conversion: 1 MGD = 694 gpm.

Find Well 1's drawdown (drawdown = pumping water level minus static water level).
Specific capacity is the pumping rate divided by the drawdown, in gpm per foot. Find Well 1's specific capacity at 220 gpm.
Assume Well 1's specific capacity stays about 4.0 gpm per foot. Estimate its drawdown at a pumping rate of 300 gpm (drawdown = rate divided by specific capacity).
Well 1's pumping level must stay at least 10 ft above the bowls at 120 ft, so no lower than 110 ft below ground. With a 40 ft static level and 4.0 gpm per foot, find the maximum pumping rate before the water reaches 110 ft.
Find Well 2's drawdown and specific capacity from its readings.
Which well is more productive per foot of drawdown, and what does a higher specific capacity suggest about the aquifer at that well?
Convert the district demand of 0.8 MGD to gallons per minute.
Run Well 1 at its maximum from problem 4 and Well 2 at 300 gpm. Does the field meet the demand from problem 7, and by what margin?

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: 55 ft.
Drawdown = 95 ft pumping level minus 40 ft static level = 55 feet.
Answer: 4.0 gpm per ft.
Specific capacity = 220 gpm divided by 55 ft = 4.0 gallons per minute per foot.
Answer: 75 ft.
Drawdown = 300 gpm divided by 4.0 gpm per foot = 75 feet.
Answer: 280 gpm.
The maximum drawdown is 110 ft minus 40 ft static = 70 ft. Maximum rate = 70 ft x 4.0 gpm per foot = 280 gpm.
Answer: 40 ft drawdown, 7.5 gpm per ft.
Well 2 drawdown = 85 minus 45 = 40 ft. Specific capacity = 300 gpm divided by 40 ft = 7.5 gpm per foot.
Answer: Well 2 is more productive.
Well 2's specific capacity (7.5 gpm per foot) is higher than Well 1's (4.0), meaning less drawdown per gallon pumped. A higher specific capacity suggests a more permeable aquifer or a better-developed well at that site.
Answer: 555.2 gpm.
0.8 MGD x 694 gpm per MGD = 555.2 gallons per minute.
Answer: yes, by 24.8 gpm.
Well 1 at 280 gpm plus Well 2 at 300 gpm gives 580 gpm. That exceeds the 555.2 gpm demand by 24.8 gpm.

Differentiation

Support

Provide a labeled cross-section of a well showing ground surface, static water level, pumping water level, drawdown, and pump bowls, so students can see which measurement each problem asks for. Give the specific capacity of 4.0 gpm per foot as a reminder on problems 3 and 4.

Extension

Ask students to find what specific capacity Well 1 would need for a single well to meet the full district demand from problem 7 while keeping its pumping level above 110 ft, then explain why real wells lose specific capacity as the pumping rate climbs.

ELL supports

Pre-teach "static," "drawdown," and "yield" using the cross-section sketch with arrows for the resting and pumping water levels. Provide a sentence frame for problem 6: "Well ___ is more productive because its specific capacity is ___."