Worksheet Grade 12 Science

Ferngate High-Service Pump: Tank Fill, Pressure, and Energy

A grade 12 science worksheet using operator math to find a fictional booster station's tank fill time, discharge pressure, and daily energy cost.

Grade: Grade 12
Subject: Science
Material: Worksheet
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: Students carry units through the flow, volume, pressure, and energy conversions in items 1 through 11, the multi-step dimensional analysis this standard requires of operator math.

All materials for HSN-Q.A.1 →

HSN-Q.A.3 Common Core Math

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

How this material aligns: Items 6, 7, and 11 ask students to report fill time, discharge pressure, and cost per million gallons at an accuracy matched to the given data, the reporting judgment this standard names.

All materials for HSN-Q.A.3 →

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 8 through 12 price the booster pump's daily energy and reduce it to $125 per million gallons delivered, then account for the elevated tank's gravity supply, the energy cost-benefit reasoning this standard weighs.

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 the daily volume a booster pump delivers and the time it needs to fill an elevated tank.
Students will convert tank height to discharge pressure using the standard 0.433 psi per foot rule.
Students will calculate the pump's daily energy use and the energy cost per million gallons delivered.

Vocabulary

Key words: discharge pressure, elevated storage, kilowatt-hour, pump run time, million gallons per day

Teacher overview

The fictional town of Ferngate runs a high-service booster station that pumps treated water up into an elevated storage tank, which then supplies homes by gravity. This worksheet has students size the pump's daily output, find how long it takes to fill the tank, convert the tank's height into discharge pressure, and price out the electricity the pump uses. A common error to watch for is treating the pump's full-speed flow rate as the whole day's production. The pump only runs part of each day, so the daily volume comes from the running hours, not from a full 24 hours.

Ferngate High-Service Pump: Tank Fill, Pressure, and Energy — Grade 12 Science

Name: ____________________________ Date: ______________

Student Worksheet

The Ferngate booster station (a fictional system used for this worksheet) has these design values:

The pump discharges 1,200 gpm while it runs.
The pump runs 10 hours per day to meet demand.
The motor draws 75 kW of electric power whenever it is running.
The elevated tank is a cylinder 60 feet in diameter with a full water depth of 24 feet.
When the tank is full, its water surface sits 130 feet above the pump.
Electricity costs $0.12 per kWh.

Use these formulas and conversions for every item:

1 MGD = 694 gpm
Cylinder volume (cu ft) = 0.785 x diameter squared x depth
1 cubic foot = 7.48 gallons
Discharge pressure (psi) = 0.433 x height of water above the pump (ft)

Convert the pump's discharge rate of 1,200 gpm to million gallons per day (MGD). Round to the nearest hundredth.
The pump runs 10 hours per day at 1,200 gpm. Calculate the total volume it delivers in one day, in gallons.
Express the daily volume from item 2 in million gallons per day (MGD).
Calculate the volume of the elevated tank in cubic feet, using the cylinder formula with a 60-foot diameter and a 24-foot depth.
Convert the tank volume from item 4 to gallons.
Starting from empty, how many minutes does the pump need to fill the tank completely at 1,200 gpm? Round to the nearest whole minute.
When the tank is full, its water surface is 130 feet above the pump. Calculate the discharge pressure at the pump, in psi. Round to the nearest whole psi.
Calculate the pump's daily energy use, in kilowatt-hours, from its 75 kW draw and 10 hours of running.
Calculate the pump's energy use over a 30-day month, in kilowatt-hours.
Calculate the monthly energy cost at $0.12 per kWh.
Calculate the energy cost per million gallons of water delivered. Use one day: the daily energy cost divided by the daily volume in million gallons.
Explain why the daily volume in item 2 is far less than the pump would deliver if it ran continuously for all 24 hours.

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: 1.73 MGD.
1,200 gpm / 694 gpm per MGD = 1.729, which rounds to 1.73 MGD.
Answer: 720,000 gallons.
1,200 gpm x 60 minutes per hour x 10 hours = 720,000 gallons in one day.
Answer: 0.72 MGD.
720,000 gallons is 0.72 million gallons delivered in one day, so 0.72 MGD.
Answer: 67,824 cu ft.
Volume = 0.785 x 60 x 60 x 24 = 0.785 x 3,600 x 24 = 67,824 cubic feet.
Answer: 507,324 gallons.
67,824 cu ft x 7.48 gallons per cu ft = 507,323.52, which rounds to 507,324 gallons.
Answer: 423 minutes.
507,324 gallons / 1,200 gpm = 422.8, which rounds to 423 minutes, or about 7.0 hours.
Answer: 56 psi.
0.433 psi per foot x 130 feet = 56.29, which rounds to 56 psi.
Answer: 750 kWh.
75 kW x 10 hours = 750 kilowatt-hours per day.
Answer: 22,500 kWh.
750 kWh per day x 30 days = 22,500 kilowatt-hours in the month.
Answer: $2,700.
22,500 kWh x $0.12 per kWh = $2,700 for the month.
Answer: $125 per million gallons.
Daily energy cost = 750 kWh x $0.12 = $90. Daily volume = 0.72 million gallons. $90 / 0.72 = $125 per million gallons.
Answer: The pump only runs 10 of the 24 hours in a day.
Because the pump is off for 14 hours, it moves water for less than half the day. Running all 24 hours at 1,200 gpm would deliver 1,728,000 gallons (1.73 MGD), more than twice the 720,000 gallons it actually delivers in 10 hours.

Differentiation

Support

Provide the four formulas and conversions on a printed reference card, and work items 1 and 2 together as a class before students continue. Accept unrounded calculator answers alongside the rounded values, and note beside item 4 that the 0.785 formula uses the full diameter, not the radius.

Extension

Ask students to find the electricity cost of delivering water for a full year at the same daily schedule, then estimate how much the town would save each year by shifting the pump's run time to overnight hours billed at a lower rate they choose and state.

ELL supports

Pre-teach "discharge pressure," "kilowatt-hour," and "run time" with a labeled diagram of a pump lifting water into a tall tank. Allow students to answer item 12 with a labeled sketch and numbers rather than full sentences.

Extensions

Have students find out whether their local utility uses elevated tanks or ground-level tanks with pumps that run on demand, and write one question for the public works department asking how the system keeps pressure steady overnight when most pumps are off.