Math problem set Grade 6 Science

Grindleford Water Main: Pipe Flow and Pressure Problems

A grade 6 science problem set on a fictional town's water main, finding flow from pipe area times water speed and pressure from tower height.

Grade: Grade 6
Subject: Science
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Problems 2, 6, and 7 apply the constant rates 448.8 gpm per cfs and 0.433 psi per foot to convert between quantities, the unit-rate reasoning this standard requires.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 2, 4, 6, and 7 have students multiply and add multi-digit decimals, such as 2.4 times 448.8 and 90 times 0.433, exercising the standard-algorithm decimal fluency this standard expects.

All materials for 6.NS.B.3 →

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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 pipe flow in cubic feet per second using the rule flow equals area times speed.
Students will convert flow to gallons per minute and convert tower height to pressure using given unit rates.

Vocabulary

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: cross-section area, velocity, pressure

Teacher overview

Water moves through a pipe at a certain speed, and the amount that passes each second depends on both that speed and how wide the pipe is. This set uses the water main of Grindleford, a fictional town, to practice two ideas an operator uses every day: flow equals area times speed, and every foot of water height in the tower adds a fixed amount of pressure below it. Students work one step at a time, first finding flow, then converting units.

A common misconception is that flow depends on the pipe's width alone. Flow depends on both the cross-section area and the water's speed, so a slow, wide pipe and a fast, narrow pipe can move the same amount. A second error is mixing up the two conversions; students should notice that a pressure value in psi is always a smaller number than the height in feet that produced it.

Grindleford Water Main: Pipe Flow and Pressure Problems — Grade 6 Science

Name: ____________________________ Date: ______________

Problems

Use these facts about Grindleford (a fictional town) for every problem below.

The main pipe has a cross-section area of 0.8 square feet.
The water in it moves at a speed of 3 feet per second.
Flow rule: flow (cfs) = area (sq ft) times speed (ft per second).
1 cubic foot per second (cfs) = 448.8 gpm.
1 foot of water height = 0.433 psi.
The tower's water surface sits 90 feet above Oak Lane.

Find the flow through the main pipe in cubic feet per second (cfs). Use flow = area times speed.
Convert your flow from problem 1 into gallons per minute (gpm). Round to the nearest whole gpm.
A wider pipe on Birch Street has a cross-section area of 1.2 square feet and the same water speed of 3 feet per second. Find its flow in cfs.
The main pipe and the Birch Street pipe join at a tank. Add their two flows from problems 1 and 3 to find the total flow into the tank, in cfs.
A third pipe carries 5 cfs through a cross-section area of 1.0 square foot. Find the water speed in feet per second, using speed = flow divided by area.
Find the water pressure at Oak Lane, which sits 90 feet below the tower's water surface. Use pressure = height times 0.433. Round to the nearest whole psi.
Complete the ratio table for pressure at three homes below the tower. Round each pressure to the nearest tenth of a psi.

Height of water above the home (ft) Pressure at the home (psi)

20

40

60
A neighbor says a wider pipe always carries more water than a narrow one. Explain why that is not always true, using the flow rule from this set.

Height of water above the home (ft)	Pressure at the home (psi)
20
40
60

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: 2.4 cfs.
Flow = area times speed = 0.8 sq ft times 3 ft per second = 2.4 cfs.
Answer: 1,077 gpm.
2.4 cfs times 448.8 gpm per cfs = 1,077.12 gpm, which rounds to 1,077 gpm.
Answer: 3.6 cfs.
Flow = 1.2 sq ft times 3 ft per second = 3.6 cfs.
Answer: 6.0 cfs.
2.4 cfs plus 3.6 cfs = 6.0 cfs total into the tank.
Answer: 5 ft per second.
Speed = flow divided by area = 5 cfs divided by 1.0 sq ft = 5 feet per second.
Answer: 39 psi.
Pressure = 90 ft times 0.433 = 38.97 psi, which rounds to 39 psi.
Answer: 8.7, 17.3, 26.0 psi.
Each height times 0.433: 20 ft gives 8.66, rounded to 8.7 psi; 40 ft gives 17.32, rounded to 17.3 psi; 60 ft gives 25.98, rounded to 26.0 psi. Doubling the height doubles the pressure.
Answer: A wider pipe carries more water only when the speed stays the same. Flow depends on area times speed, so a narrow pipe with fast water can move as much as, or more than, a wide pipe with slow water.

Differentiation

Support

Give students the flow rule and the two conversions on a printed strip, written as arrow rules: "area times speed gives flow" and "feet times 0.433 gives psi." Let them start with problem 7, the ratio table, so the pattern that doubling height doubles pressure is visible before the single-answer problems. Accept unrounded calculator answers.

Extension

Ask students to work problem 2 backward. Suppose a pipe must deliver 2,244 gpm; what flow in cfs is that, and what water speed would a 1.0 square foot pipe need to reach it? Have them show each step and check that their speed is reasonable for a pipe.

ELL supports

Pre-teach flow, area, speed, and pressure with a labeled drawing of a pipe and a tower, marking area across the pipe and height up the tower. Allow students to record answers as a number and unit beside the drawing rather than in full sentences for problems 1 through 7.