Worksheet Grade 8 Science

Quillfoot's Hydrant Flow Test: Velocity in the Water Main

A grade 8 science worksheet using Q = A x V on a fictional district's hydrant test to find velocity, travel time, and whether pressure stays above the required minimum.

Grade: Grade 8
Subject: Science
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Printed worksheet, Calculators

Standards

MS-ETS1-1 NGSS

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

How this material aligns: Item 8 asks students to state the fire-flow criterion and the minimum-pressure constraint the district must meet, which is the precise problem definition this standard requires.

All materials for MS-ETS1-1 →

8.EE.C.7 Common Core Math

Solve linear equations in one variable, including equations with variables on both sides, and recognizing equations with one solution, infinitely many solutions, or no solutions.

How this material aligns: Items 1, 2, and 9 solve the one-variable equation Q = A x V, with rational coefficients, for an unknown velocity or an unknown cross-sectional area.

All materials for 8.EE.C.7 →

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 solve Q = A x V for velocity and for cross-sectional area using given flow values.
Students will calculate how long water takes to travel a stated length of main at a known velocity.
Students will judge a hydrant test result against a stated minimum pressure requirement.

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: velocity, cross-sectional area, hydrant flow test, residual pressure, water age

Teacher overview

When a fire crew opens a hydrant, the utility learns how much water the buried main can actually deliver and how much pressure is left while that water moves, which operators call the residual pressure. The relationship behind the test is Q = A x V, where Q is the flow, A is the pipe's cross-sectional area, and V is how fast the water travels. Students often assume a wider pipe makes water move faster; at the same flow, a wider pipe does the opposite, because the same volume spreads across more area each second. This worksheet walks through one test on a fictional district's main and ends with the pressure requirement the district has to meet.

Quillfoot's Hydrant Flow Test: Velocity in the Water Main — Grade 8 Science

Name: ____________________________ Date: ______________

Student Worksheet

The fictional Quillfoot Water District tested the hydrant at the corner of Halberd Street. Use Q = A x V for every flow question, and use this table of pipe sizes.

Pipe diameter	Cross-sectional area (square feet)
6 inch	0.196
8 inch	0.349
12 inch	0.785

The test measured a flow of 3.49 cubic feet per second in Quillfoot's 8-inch main, which has a cross-sectional area of 0.349 square feet. Find the velocity of the water in feet per second.
Suppose the same 3.49 cubic feet per second moved through a 12-inch main with a cross-sectional area of 0.785 square feet. Find that velocity in feet per second, rounded to the nearest tenth.
Compare your answers to items 1 and 2. Explain why the larger pipe carries the same flow at a lower velocity.
One cubic foot per second equals 448.8 gallons per minute. Convert the tested flow of 3.49 cubic feet per second to gallons per minute, rounded to the nearest whole gallon.
The hydrant sits 2,400 feet from the storage tank along the 8-inch main. At the velocity you found in item 1, how many seconds does water take to travel from the tank to the hydrant?
Before the test, the pressure at the hydrant read 62 pounds per square inch. During the test it dropped to 34 pounds per square inch. How many psi did the pressure drop?
Most states require distribution pressure to stay at or above 20 psi. How far above that minimum was Quillfoot's reading during the test?
Write one criterion and one constraint the Quillfoot district must meet when it tests this hydrant.
On another street, a crew measured a velocity of 6.0 feet per second while the main carried 1.176 cubic feet per second. Find the cross-sectional area, then name which pipe size in the table matches it.
A dead-end main carries very little flow, so the water moves slowly and can sit for days. Explain why slow-moving water in a dead-end main is a water quality problem, not just a pressure problem.

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: 10.0 feet per second.
Rearranging Q = A x V gives V = Q divided by A, so V = 3.49 divided by 0.349 = 10.0 feet per second.
Answer: 4.4 feet per second.
V = 3.49 divided by 0.785 = 4.446, which rounds to 4.4 feet per second.
Answer: The same volume spreads over a larger area each second.
Because Q stays fixed at 3.49 cubic feet per second, a larger A forces a smaller V. The 12-inch pipe has more than twice the area of the 8-inch pipe, so the water crosses any point more slowly.
Answer: 1,566 gpm.
3.49 x 448.8 = 1,566.312 gallons per minute, which rounds to 1,566 gallons per minute.
Answer: 240 seconds.
Time = distance divided by velocity, so 2,400 feet divided by 10.0 feet per second = 240 seconds, which is 4 minutes.
Answer: 28 psi.
62 minus 34 equals a drop of 28 pounds per square inch while the hydrant was flowing.
Answer: 14 psi.
34 minus 20 equals 14, so the reading stayed 14 pounds per square inch above the minimum.
Answer: A criterion is delivering the flow firefighting needs; a constraint is holding pressure at or above the minimum.
Accept any pair in which the criterion states a goal the design must achieve, such as supplying at least the tested 1,566 gallons per minute at this hydrant, and the constraint states a limit the district cannot cross, such as never dropping below 20 psi anywhere in the zone.
Answer: 0.196 square feet.
A = Q divided by V = 1.176 divided by 6.0 = 0.196 square feet, which matches the 6-inch pipe in the table.
Answer: Slow water sits long enough to lose its disinfectant and warm up.
Water that creeps along a dead-end main can take days to reach the last house. During that time the chlorine residual fades and the water warms, so bacteria have a better chance to grow even though the pressure at the tap looks normal. Operators call that long time in the pipe the water age.

Differentiation

Support

Work item 1 as a class with the division set up in words, "flow divided by area equals velocity," before students try item 2. Give students a filled-in version of the pipe table with the areas circled so they do not have to search for the right row.

Extension

Ask students to find the velocity in the fictional Quillfoot 6-inch main at the same tested flow, then explain, using all three velocities, what would happen to the travel time from the tank if the district replaced its 8-inch main with a 12-inch main.

ELL supports

Pre-teach "flow," "velocity," and "area" with a demonstration using a wide tray and a narrow channel of the same water. Provide the labeled triangle for Q, A, and V so students can see which quantity to divide. Allow students to answer items 3 and 10 with a labeled sketch plus one sentence.

Extensions

Have students find how many minutes water would take to travel one mile through the fictional Quillfoot 8-inch main at the velocity from item 1, then discuss what that travel time means for how quickly a taste complaint from one neighborhood can be traced back to the plant.