Math problem set Grade 10 Math

Calder Ridge Reservoir and Dam: Volume, Head, and Flow Problems

A grade 10 problem set converting a fictional reservoir's acre-feet to gallons, finding pressure at a dam's turbines, and tracking powerhouse flow through unit chains.

Grade: Grade 10
Subject: Math
Material: Math problem set
Time: 45 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, 2, 4, 5, and 6 chain acre-feet to gallons and cubic feet, and cubic feet per second to gallons per minute and million gallons per day, keeping units consistent throughout.

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 7 has students create and solve a one-variable equation for the number of days a fixed daily draw takes to empty the reservoir, the equation-from-a-relationship skill this standard names.

All materials for HSA-CED.A.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 convert reservoir storage among acre-feet, gallons, and cubic feet.
Students will find water pressure at a dam's turbines from the height of water above them.
Students will convert powerhouse flow among cubic feet per second, gallons per minute, and million gallons per day.

Vocabulary

Reservoir: A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
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.
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: head, powerhouse

Teacher overview

The town of Calder Ridge, a fictional town used for this problem set, sits below a reservoir held back by an earthen dam with a small powerhouse at its base. The problems build one scenario in sequence: students find the reservoir's volume in several units, the water pressure at the turbines, and the flow the powerhouse draws, then use those results to estimate how long a drought could drain the reservoir. A common misconception in this work is using the pressure constant 0.433 psi per foot and its inverse 2.31 feet per psi interchangeably; another is comparing acre-feet directly to gallons without converting first.

Calder Ridge Reservoir and Dam: Volume, Head, and Flow Problems — Grade 10 Math

Name: ____________________________ Date: ______________

Problems

The town of Calder Ridge's reservoir holds 12,000 acre-feet of water when full. The dam is 180 feet tall, and when the reservoir is full the water surface stands 165 feet above the powerhouse turbines at the base. Use these facts for all problems:

1 acre-foot = 325,851 gallons.
1 acre-foot = 43,560 cubic feet.
Pressure (psi) = height of water above the point (feet) × 0.433.
1 cubic foot per second (cfs) = 448.8 gallons per minute (gpm).
1 million gallons per day (MGD) = 1.547 cubic feet per second.

Convert the reservoir's full volume of 12,000 acre-feet to gallons.
Convert the reservoir's full volume of 12,000 acre-feet to cubic feet.
Find the water pressure, in psi, at the turbine inlet 165 feet below the full water surface. Round to the nearest tenth.
The powerhouse draws water at 240 cubic feet per second. Convert that flow to gallons per minute.
Convert the 240 cubic feet per second flow to million gallons per day. Round to the nearest tenth.
At 240 cubic feet per second running continuously, how many acre-feet of water pass through the powerhouse in one full day? Round to the nearest tenth.
A drought stops all inflow to the reservoir while the powerhouse keeps drawing the daily amount from item 6. Write and solve an equation for the number of days the full 12,000 acre-foot reservoir would last. Round to the nearest whole day.
The dam is 180 feet tall, but the pressure in item 3 used a height of 165 feet. Explain why the height of water above the turbines, not the dam's full height, is the number that sets the pressure.
As the drought draws the reservoir down, the water surface drops lower each week. Explain what happens to the turbine-inlet pressure as the level falls, and why the powerhouse produces less power as a result.

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: 3,910,212,000 gal.
12,000 acre-feet × 325,851 gallons per acre-foot = 3,910,212,000 gallons.
Answer: 522,720,000 cu ft.
12,000 acre-feet × 43,560 cubic feet per acre-foot = 522,720,000 cubic feet.
Answer: 71.4 psi.
Pressure = height × 0.433 = 165 × 0.433 = 71.445, which rounds to 71.4 psi.
Answer: 107,712 gpm.
240 cubic feet per second × 448.8 gallons per minute per cfs = 107,712 gallons per minute.
Answer: 155.1 MGD.
240 cubic feet per second ÷ 1.547 cubic feet per second per MGD = 155.14, which rounds to 155.1 million gallons per day.
Answer: 476.0 acre-ft.
240 cubic feet per second × 86,400 seconds per day = 20,736,000 cubic feet per day. 20,736,000 ÷ 43,560 = 476.03, which rounds to 476.0 acre-feet.
Answer: 25 days.
Let d be the number of days. 476 acre-feet per day × d = 12,000 acre-feet, so d = 12,000 ÷ 476 = 25.2, which rounds to about 25 days.
Answer: Pressure depends on the water above the point.
Water pressure at any point comes only from the height of water standing above that point, not from the height of the structure. The turbines sit 165 feet below the water surface, so 165 feet is the head that produces the pressure, even though the dam itself is 180 feet tall.
Answer: Pressure and power both fall.
As the reservoir empties, the water surface drops, so the height of water above the turbines shrinks. Because pressure equals that height times 0.433, the turbine-inlet pressure falls, and a turbine driven by lower pressure and head produces less power.

Differentiation

Support

Provide the full list of conversion factors on a printed reference card and work through problem 1 together so students see one acre-foot conversion before continuing. For problem 6, give students the intermediate step that one day equals 86,400 seconds so they can focus on the unit chain.

Extension

Ask students to find how many days the reservoir would last if the powerhouse cut its draw in half to 120 cubic feet per second during the drought, and to explain why halving the flow exactly doubles the number of days once inflow is zero and only the fixed storage is left.

ELL supports

Provide a labeled side-view diagram of the dam showing the water surface, the 165-foot height above the turbines, and the powerhouse at the base. Pre-teach "reservoir," "head," and "powerhouse" with the diagram, and provide a flowchart of the unit chain from cubic feet per second to gallons per minute to million gallons per day for problems 4 and 5.