Worksheet Grade 9 Science

Ridgecomb Booster Station: Pipe Flow and Pressure Math

A grade 9 science worksheet where students use operator formulas to find pipe flow, convert units, and calculate pump pressure for a fictional town's booster station.

Grade: Grade 9
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: Items 2 through 8 chain a velocity, a flow conversion, and a pressure calculation across cubic feet per second, gallons per minute, and psi, requiring the consistent unit tracking this standard specifies.

All materials for HSN-Q.A.1 →

HSG-MG.A.1 Common Core Math

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

How this material aligns: Items 1 and 10 have students model the round pipe as a circular cross section to find its area and reason about how area changes with diameter, the geometric-modeling task this standard describes.

All materials for HSG-MG.A.1 →

HS-ETS1-3 NGSS

Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.

How this material aligns: Items 6 and 8 evaluate the booster station's delivered pressure against the 40 to 80 psi service target and the 20 psi minimum required at every connection, and item 9 explains the elevation trade-off behind that requirement.

All materials for HS-ETS1-3 →

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 calculate pipe flow using the continuity relationship Q equals area times velocity.
Students will convert flow among cubic feet per second, gallons per minute, and million gallons per day.
Students will calculate the pressure needed to lift water a given height using 0.433 psi per foot.

Vocabulary

Pressure zone: A pressure zone is a section of a water system that a utility manages separately because it sits at a different elevation than the rest of the town. Utilities create pressure zones so that water pressure stays safe and steady for everyone, whether they live at the bottom of a hill or near the top.
Flow rate: Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: booster pump, head

Teacher overview

Some neighborhoods sit too high for a water tower to serve them by gravity alone, so a booster pump station raises the pressure to reach them. Operators size these stations with the same formulas that appear on licensing exams: flow equals area times velocity, unit conversions between flow units, and the rule that each foot of water height adds 0.433 psi. This worksheet walks students through those calculations for the fictional town of Ridgecomb.

A common student error is to use a pipe's diameter directly in place of its cross-sectional area. Flow depends on the area the water moves through, so students must find the area first, then multiply by velocity.

Ridgecomb Booster Station: Pipe Flow and Pressure Math — Grade 9 Science

Name: ____________________________ Date: ______________

Student Worksheet

The town of Ridgecomb (a fictional town) uses a booster pump station to lift water from a low tank up to the Kestrel Ridge pressure zone. Use these facts throughout: pipe area (sq ft) = 0.785 × diameter², flow Q = area × velocity, 1 cfs = 448.8 gpm, 1 MGD = 694 gpm, pressure (psi) = height (ft) × 0.433, and 1 psi = 2.31 ft of height. Homes should receive between 40 and 80 psi, and most states require at least 20 psi at every connection.

The discharge pipe is 12 inches in diameter, which is 1 foot. Using area = 0.785 × diameter², find the pipe's cross-sectional area in square feet.
Water moves through the pipe at 4 feet per second. Using Q = area × velocity, find the flow in cubic feet per second (cfs).
Convert the flow from item 2 to gallons per minute, using 1 cfs = 448.8 gpm. Round to the nearest whole gpm.
Express the flow from item 3 in million gallons per day (MGD), using 1 MGD = 694 gpm. Round to the nearest hundredth.
The Kestrel Ridge zone sits 150 feet above the low tank's water surface. Using pressure = height × 0.433, find the pressure the pump must add just to lift water to that height, before any pressure is left for homes. Round to the nearest whole psi.
Homes in the zone should get between 40 and 80 psi. After the lift, a gauge at the base of the zone reads 65 psi. Is that within the target range?
A pressure gauge near the top of the zone reads 22 psi. Convert this reading to feet of water height above the gauge, using 1 psi = 2.31 ft. Round to the nearest foot.
Most states require at least 20 psi at every connection. Does the 22 psi reading in item 7 meet that minimum, and by how much?
Explain why lifting water to a higher pressure zone takes more pump pressure than serving a low neighborhood, using the height-to-pressure relationship.
A second pipe has a 6-inch diameter, which is half of the 12-inch pipe. Without recalculating from scratch, state whether its cross-sectional area is half, one-quarter, or double the area of the 12-inch pipe, and explain why.

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: 0.785 sq ft. Area = 0.785 × 1² = 0.785 × 1 = 0.785 square feet.
Answer: 3.14 cfs. Q = area × velocity = 0.785 × 4 = 3.14 cubic feet per second.
Answer: 1,409 gpm. 3.14 cfs × 448.8 gpm per cfs = 1,409.23, which rounds to 1,409 gallons per minute.
Answer: 2.03 MGD. 1,409 gpm ÷ 694 gpm per MGD = 2.0303, which rounds to 2.03 million gallons per day.
Answer: 65 psi. Pressure = 150 ft × 0.433 psi per foot = 64.95, which rounds to 65 psi.
Answer: Yes. 65 psi falls between 40 and 80 psi, so it is within the target range.
Answer: 51 ft. 22 psi × 2.31 ft per psi = 50.82, which rounds to 51 feet of height above the gauge.
Answer: Yes, by 2 psi. The reading of 22 psi is 2 psi above the 20 psi minimum.
Answer: Because pressure rises with height, and each foot of extra height adds 0.433 psi. A higher zone sits more feet above the tank, so the pump has to add more pressure to reach it than it would for a lower neighborhood.
Answer: One-quarter. Area depends on the diameter squared, so halving the diameter multiplies the area by one-half squared, which is one-fourth.

Differentiation

Support

Give students a labeled diagram of the pipe cross section and the pressure zone, and provide the area from item 1 already calculated so they can focus on the flow and pressure steps.

Extension

Have students suppose the 12-inch pipe must deliver exactly 2,000 gpm, and find what velocity, in feet per second, that would take, working backward through the conversions from gallons per minute to cubic feet per second to velocity.

ELL supports

Pre-teach "flow rate," "velocity," "pressure zone," and "booster pump" with a labeled diagram of water rising from a low tank to a high neighborhood. Provide the formulas as arrow rules on a printed strip.