Math problem set Grade 9 Science

Pump Station Horsepower at Haldane: A Grade 9 Energy Problem Set

A grade 9 problem set where students find water horsepower, brake horsepower, motor power, and the daily energy cost of a fictional high-service pump station.

Grade: Grade 9
Subject: Science
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: Items 1 through 6 carry gallons per minute, feet of head, horsepower, kilowatts, and dollars through one chained calculation, requiring the consistent unit tracking across steps this standard specifies.

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: Item 8 rearranges the brake-horsepower relationship to solve for the horsepower a more efficient pump would draw, the one-variable equation solving this standard describes.

All materials for HSA-CED.A.1 →

HS-ESS3-2 NGSS

Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.

How this material aligns: Items 6, 7, and 8 set the station's daily energy cost and its wire-to-water efficiency against what a more efficient pump would draw, the cost-benefit weighing of an energy resource this standard requires.

All materials for HS-ESS3-2 →

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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 water horsepower from a pump's flow and total head.
Students will use pump and motor efficiency to find brake horsepower and motor input power.
Students will convert horsepower to kilowatts and calculate a daily energy cost.

Vocabulary

Key words: water horsepower, brake horsepower, total head, efficiency, kilowatt-hour

Teacher overview

A high-service pump station lifts treated water up to a reservoir or into the distribution system, and the electricity to run it is often one of a utility's largest operating costs. Operators track the water horsepower a pump adds to the water, the brake horsepower the pump shaft actually needs, and the electrical power the motor draws, because efficiency losses grow the bill at every step. This set follows the fictional Haldane pump station through that chain to a daily energy cost. A common misconception is that a pump's electrical draw equals its water horsepower; because no pump or motor is perfectly efficient, the electrical power drawn is always larger than the water horsepower delivered.

Pump Station Horsepower at Haldane: A Grade 9 Energy Problem Set — Grade 9 Science

Name: ____________________________ Date: ______________

Problems

The Haldane pump station (a fictional station) lifts treated water to a storage reservoir. Use these numbers for every problem:

The pump moves 1,400 gpm against a total head of 180 feet.
The pump efficiency is 0.75, and the motor efficiency is 0.90.
The station runs 20 hours per day, and electricity costs $0.12 per kWh.
Water horsepower = (flow in gpm x total head in feet) divided by 3,960. Also, 1 horsepower = 0.746 kilowatts.

Calculate the water horsepower the pump adds to the water. Round to the nearest tenth.
Calculate the brake horsepower the pump needs, using brake horsepower = water horsepower divided by pump efficiency. Round to the nearest tenth.
Calculate the motor input power in horsepower, using motor input = brake horsepower divided by motor efficiency. Round to the nearest tenth.
Convert the motor input power from item 3 into kilowatts. Round to the nearest tenth.
Calculate the energy the station uses in one day, in kilowatt-hours, using the 20 hours of daily run time.
Calculate the station's daily energy cost at $0.12 per kWh. Round to the nearest cent.
Calculate the station's wire-to-water efficiency, the pump efficiency times the motor efficiency, and state it as a percent. In one sentence, explain what that number means.
Suppose Haldane replaced the pump with one that has a pump efficiency of 0.85, with the motor efficiency still 0.90. Calculate the new brake horsepower for the same water horsepower from item 1, and explain in one sentence why a more efficient pump lowers the energy bill.

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: 63.6 hp.
Water horsepower = (1,400 gpm x 180 ft) divided by 3,960 = 252,000 divided by 3,960 = 63.6 water horsepower.
Answer: 84.8 hp.
Brake horsepower = 63.6 divided by 0.75 = 84.8 brake horsepower.
Answer: 94.2 hp.
Motor input = 84.8 divided by 0.90 = 94.2 horsepower.
Answer: 70.3 kW.
94.2 hp x 0.746 kW per hp = 70.3 kilowatts.
Answer: 1,406 kWh.
70.3 kW x 20 hours = 1,406 kilowatt-hours in one day.
Answer: $168.72.
1,406 kWh x $0.12 per kWh = $168.72 per day.
Answer: 67.5 percent.
Wire-to-water efficiency = 0.75 x 0.90 = 0.675, or 67.5 percent. It means only about 68 percent of the electrical energy drawn ends up as useful water horsepower; the rest is lost as heat and friction in the pump and motor.
Answer: 74.8 hp.
New brake horsepower = 63.6 divided by 0.85 = 74.8 brake horsepower. Because the more efficient pump needs less brake horsepower for the same water horsepower, the motor draws less electricity, which lowers the daily energy bill.

Differentiation

Support

Provide the four formulas as a labeled ladder, with a blank beside each rung, so students can see that each answer feeds the next step. Work items 1 and 2 together, then let students continue the ladder on their own.

Extension

Ask students to find how many dollars per day the more efficient pump from item 8 would save, by carrying its brake horsepower through the motor, kilowatt, and cost steps and comparing the result with item 6.

ELL supports

Pre-teach "horsepower," "efficiency," and "kilowatt-hour" with a simple diagram: energy goes in at the motor, some is lost, and the rest lifts the water. Provide a sentence frame for item 7: "Wire-to-water efficiency means that out of all the electricity used, ___."